diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/environment/Dockerfile b/tasks/construct-ae-p32-spherical-design-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/environment/instance.json b/tasks/construct-ae-p32-spherical-design-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d94df81357a6b1efcb639c2bf4362d52d05b841a
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"t": 15, "N": 120, "family": "ae_p32_spherical_designs", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/instruction.md b/tasks/construct-ae-p32-spherical-design-l4-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c2adf61c375b11fda0027532ed5c9103734045b2
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/instruction.md
@@ -0,0 +1,18 @@
+Spherical designs on the 2-sphere.
+
+A finite set X of points on the unit sphere S^2 in R^3 is a spherical t-design if for every polynomial P(x, y, z)
+of degree at most t, the average of P over the points of X equals the average of P over the whole sphere
+(with respect to the uniform surface measure).  Equivalently, the average over X of every spherical harmonic of
+degree 1, 2, ..., t is zero.
+
+Construct a spherical 15-design with exactly N = 120 distinct points.
+
+Numerical acceptance test: the points are normalised to unit length (each submitted vector must have length
+between 0.5 and 2), no two points may be closer than about 1.4e-4 (cosine of the angle between them at most
+1 - 1e-8), and for every real spherical harmonic Y of degree 1 <= l <= 15, normalised so that the average of
+Y^2 over the sphere is 1, the average of Y over your N points must be at most 1e-10 in absolute value.
+Submit coordinates in full double precision.
+
+Answer format: {"points": [[x_1, y_1, z_1], ..., [x_120, y_120, z_120]]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/solution/solve.sh b/tasks/construct-ae-p32-spherical-design-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..18c931542c41761a547b713e328567a7235f880b
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"points": [[-0.6797362419565781, -0.33277023955514695, 0.6536226809384437], [0.9801860827417008, 0.15541248185198572, -0.12280962374376724], [-0.3823571350063186, 0.8762371708640566, -0.2932770732701655], [0.3500260050652461, 0.4693794053767845, -0.810656998727699], [-0.9252524215421856, 0.31148183475383806, -0.2165341152075223], [-0.8028751795388819, 0.5942166570117791, -0.047937569923326415], [0.9411767716104404, -0.11357414266783164, -0.3182564982812067], [0.5455876838366907, 0.6106872341378278, -0.57392959612378], [-0.6412872169310772, 0.13608281469447756, 0.7551371881622717], [-0.2372974023137689, 0.809467473527512, 0.5370776034765591], [-0.3947825917146027, 0.23995242593194074, 0.8868875568912205], [0.9113699693951687, 0.055300862047331555, 0.4078560941575733], [-0.5397252540054079, 0.36684176490126075, -0.7577095549832575], [0.8016749830843496, -0.1644483972035289, 0.5746946547114373], [0.9247922568423781, -0.3526296817317806, -0.1428691332868096], [0.6298851578000957, 0.7707875110554769, -0.09555783999260146], [0.5753134850032517, -0.812185246924901, -0.0967962739517948], [0.5084525205046247, 0.1572835460061077, -0.84660375651673], [-0.609491345316079, 0.03426651273046633, -0.792051832956713], [-0.29264806552077166, 0.3191283639683885, -0.9013956939423495], [0.8872813344789636, 0.4610629154725389, -0.012362097766637315], [0.3606369080646163, 0.6205957767889955, 0.6962771735259291], [-0.00023848372415500132, -0.5904346259692939, -0.8070854326414356], [0.20979503312414355, 0.9170896508743264, 0.3390171328054762], [0.5263128854633881, -0.6146007032128523, 0.5875889057882815], [-0.2532144149054432, 0.7720523247516029, -0.5829388200572506], [-0.47669612414939083, -0.36334007146921266, -0.8004653632017416], [0.07982820524837961, -0.9646719607545845, 0.25106864754629943], [-0.17213409201077784, -0.6932396751390268, 0.6998489888402795], [-0.9206723260159624, -0.30179443639955467, -0.24755319886164412], [-0.1100621437913961, 0.23310490807175346, 0.9662030978717163], [-0.7237504904149406, -0.2431994149893688, -0.6457857788562411], [0.16917907011643418, 0.3482149666622287, 0.9220221142830369], [-0.6375964411512174, 0.7230487656098056, -0.26584066803527], [-0.3249827612067025, 0.9450225159380641, 0.03631321093705114], [-0.09238461887404388, -0.8027957015019319, -0.5890536001464711], [-0.08513114350537372, 0.05745800633776875, -0.9947116496317696], [0.7308387504036453, 0.48201462653379945, 0.4832562681599897], [0.07542695096381344, 0.8706689309249304, -0.4860518365260451], [0.7496717991090104, -0.5847703664914679, -0.3098964538262642], [-0.4939774403572348, 0.7657996350999625, 0.41174896150309703], [-0.9945653660678366, 0.05388530583914211, -0.08908482717596868], [-0.45222510388103154, -0.8768969013966191, -0.16292415333767507], [-0.555616798196136, 0.5157977196645684, 0.6521063455841429], [-0.8250561456611922, -0.040354678507057644, 0.5636078924476569], [-0.07371848361924495, -0.9969841828065062, -0.024251276389541623], [0.313904108513361, 0.9368371568818964, -0.154273627506055], [-0.2931030552474718, 0.553871996585522, 0.7793050817253568], [-0.05830229280822639, -0.3817517013274294, 0.9224242414349901], [0.24133322848954428, 0.10398578762566588, -0.964855029939049], [0.40905343284884715, 0.8166763966875912, -0.40708101425630994], [-0.744302178262258, -0.594119396653777, 0.3050187042687872], [-0.5078253457390879, -0.7228716164583563, -0.46858301755810444], [-0.7770683738167835, 0.3448147106281137, 0.5265620170010269], [-0.8711077716599404, -0.31760656920362323, 0.3745628349854764], [0.13968437948565993, -0.951755945487426, -0.2732194984935044], [-0.35968253798612154, -0.05225213307288253, -0.9316105336765982], [-0.7323178194584046, -0.6508186783983738, -0.20036381697173197], [0.7749722629403157, -0.45121878076455924, 0.44251508850943233], [0.1542400205626462, -0.5950273254559362, 0.7887664407272852], [0.6797362419565781, 0.33277023955514656, -0.6536226809384438], [-0.9801860827417008, -0.15541248185198597, 0.12280962374376757], [0.38235713500631807, -0.8762371708640567, 0.2932770732701656], [-0.3500260050652461, -0.46937940537678435, 0.810656998727699], [0.9252524215421853, -0.3114818347538383, 0.21653411520752286], [0.8028751795388817, -0.5942166570117793, 0.04793756992332698], [-0.9411767716104403, 0.11357414266783138, 0.3182564982812073], [-0.5455876838366903, -0.6106872341378281, 0.57392959612378], [0.641287216931077, -0.1360828146944773, -0.7551371881622718], [0.2372974023137693, -0.8094674735275118, -0.537077603476559], [0.3947825917146024, -0.23995242593194113, -0.8868875568912206], [-0.9113699693951689, -0.055300862047331534, -0.4078560941575728], [0.5397252540054077, -0.3668417649012604, 0.7577095549832578], [-0.8016749830843497, 0.16444839720352944, -0.5746946547114369], [-0.9247922568423782, 0.35262968173178016, 0.14286913328681017], [-0.6298851578000954, -0.7707875110554772, 0.09555783999260137], [-0.5753134850032513, 0.8121852469249013, 0.09679627395179492], [-0.5084525205046252, -0.15728354600610775, 0.8466037565167298], [0.6094913453160783, -0.03426651273046651, 0.7920518329567136], [0.2926480655207713, -0.3191283639683883, 0.9013956939423498], [-0.8872813344789636, -0.4610629154725391, 0.012362097766637214], [-0.36063690806461574, -0.6205957767889954, -0.6962771735259295], [0.00023848372415520504, 0.5904346259692946, 0.8070854326414351], [-0.20979503312414297, -0.9170896508743263, -0.3390171328054767], [-0.5263128854633887, 0.6146007032128521, -0.5875889057882812], [0.2532144149054428, -0.7720523247516031, 0.5829388200572505], [0.47669612414939, 0.363340071469213, 0.8004653632017419], [-0.07982820524837969, 0.9646719607545844, -0.25106864754629976], [0.17213409201077778, 0.693239675139027, -0.6998489888402794], [0.9206723260159625, 0.30179443639955417, 0.247553198861644], [0.11006214379139577, -0.23310490807175321, -0.9662030978717164], [0.7237504904149397, 0.24319941498936892, 0.6457857788562419], [-0.16917907011643493, -0.3482149666622282, -0.9220221142830369], [0.6375964411512169, -0.7230487656098057, 0.2658406680352708], [0.3249827612067026, -0.945022515938064, -0.03631321093705124], [0.09238461887404477, 0.8027957015019324, 0.5890536001464702], [0.08513114350537372, -0.05745800633776881, 0.9947116496317696], [-0.7308387504036452, -0.48201462653380006, -0.48325626815998934], [-0.07542695096381373, -0.8706689309249305, 0.48605183652604506], [-0.7496717991090102, 0.584770366491468, 0.3098964538262647], [0.4939774403572353, -0.7657996350999622, -0.4117489615030969], [0.9945653660678365, -0.05388530583914246, 0.08908482717596902], [0.45222510388103226, 0.8768969013966189, 0.16292415333767477], [0.5556167981961362, -0.515797719664568, -0.652106345584143], [0.8250561456611925, 0.040354678507057255, -0.5636078924476566], [0.0737184836192453, 0.9969841828065062, 0.024251276389541523], [-0.3139041085133609, -0.9368371568818965, 0.15427362750605467], [0.29310305524747216, -0.5538719965855227, -0.7793050817253562], [0.05830229280822626, 0.3817517013274294, -0.9224242414349901], [-0.2413332284895443, -0.10398578762566636, 0.964855029939049], [-0.4090534328488471, -0.8166763966875913, 0.40708101425630966], [0.7443021782622581, 0.5941193966537769, -0.3050187042687873], [0.5078253457390888, 0.7228716164583561, 0.468583017558104], [0.777068373816784, -0.3448147106281133, -0.5265620170010267], [0.8711077716599406, 0.31760656920362307, -0.37456283498547627], [-0.13968437948565937, 0.9517559454874259, 0.27321949849350474], [0.35968253798612104, 0.05225213307288293, 0.9316105336765983], [0.732317819458405, 0.6508186783983732, 0.20036381697173208], [-0.774972262940316, 0.45121878076455946, -0.44251508850943183], [-0.15424002056264627, 0.5950273254559363, -0.7887664407272851]]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/task.toml b/tasks/construct-ae-p32-spherical-design-l4-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..2e05c1cf5d7d2912911774f3a7d447a2ed46501f
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p32-spherical-design-l4-s0"
+version = "0.2.0"
+description = "construct/ae_p32_spherical_designs"
+authors = []
+keywords = ["rlmath", "construct", "ae_p32_spherical_designs"]
+
+[metadata]
+subset = "construct"
+family = "ae_p32_spherical_designs"
+problem_key = "spherical_t_design_s2"
+domain = "discrete_geometry"
+tier = "research"
+level = "4"
+source = "AlphaEvolve-Repository-of-Problems/32-spherical-designs"
+source_license = "CC-BY-4.0"
+tags = ["float_tolerance", "numerical_design"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/tests/check.py b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..5973c15b3df2d6228d713d9b186ced8e47dcbb48
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/check.py
@@ -0,0 +1,53 @@
+"""Spherical t-design with N points on S^2 (numerical, tolerance 1e-10 on every harmonic average).
+
+Upstream (AlphaEvolve `spherical_t_designs.ipynb`) scored sum_k dim_k/C_k(1) * sum_{i,j} C_k(<x_i,x_j>), whose
+pair sums cancel to ~1e-10 in float64 and can even go negative; its printed acceptance test
+`calculate_design_score(...) < 1e-8` compares the NEGATED error and is therefore always true (bug).  Here we
+evaluate the point averages of an orthonormal real spherical-harmonic basis directly (no cancellation).
+"""
+import numpy as np
+
+from run import Invalid, float_matrix
+
+TOL = 1e-10
+
+
+def harmonics(X, t):
+    """Rows: real spherical harmonics Y_lm (1 <= l <= t) normalised so that their mean square on S^2 is 1."""
+    ct = np.clip(X[:, 2], -1.0, 1.0)
+    st = np.sqrt(np.maximum(0.0, 1.0 - ct * ct))
+    ph = np.arctan2(X[:, 1], X[:, 0])
+    P = {(0, 0): np.ones_like(ct)}
+    for m in range(1, t + 1):
+        P[(m, m)] = (np.sqrt(3.0) if m == 1 else np.sqrt((2 * m + 1) / (2 * m))) * st * P[(m - 1, m - 1)]
+    for m in range(0, t):
+        P[(m + 1, m)] = np.sqrt(2 * m + 3) * ct * P[(m, m)]
+    for m in range(0, t + 1):
+        for l in range(m + 2, t + 1):
+            a = np.sqrt((4 * l * l - 1) / (l * l - m * m))
+            b = np.sqrt(((l - 1) ** 2 - m * m) / (4 * (l - 1) ** 2 - 1))
+            P[(l, m)] = a * (ct * P[(l - 1, m)] - b * P[(l - 2, m)])
+    rows = []
+    for l in range(1, t + 1):
+        rows.append(P[(l, 0)])
+        for m in range(1, l + 1):
+            rows.append(P[(l, m)] * np.cos(m * ph))
+            rows.append(P[(l, m)] * np.sin(m * ph))
+    return np.array(rows)
+
+
+def check(inst, ans):
+    t, n = inst["t"], inst["N"]
+    X = np.array(float_matrix(ans.get("points"), n, 3, "points"))
+    nr = np.linalg.norm(X, axis=1)
+    if nr.min() < 0.5 or nr.max() > 2.0:
+        raise Invalid("points must be (approximately) unit vectors")
+    X = X / nr[:, None]
+    G = X @ X.T
+    np.fill_diagonal(G, -1.0)
+    if G.max() > 1.0 - 1e-8:
+        raise Invalid("two points coincide (or nearly: distance < 1.4e-4)")
+    dev = np.abs(harmonics(X, t).mean(axis=1)).max()
+    if not dev <= TOL:
+        raise Invalid(f"not a {t}-design: some harmonic of degree <= {t} has point average {dev:.3e} > {TOL}")
+    return None, {"max_harmonic_average": float(dev)}
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/tests/instance.json b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d94df81357a6b1efcb639c2bf4362d52d05b841a
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"t": 15, "N": 120, "family": "ae_p32_spherical_designs", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/tests/run.py b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p32-spherical-design-l4-s0/tests/test.sh b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p32-spherical-design-l4-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dbd884c9e5a17d88847f0c06dd7eb420bf5ca4e7
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"N": 180, "t": 54, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/instruction.md b/tasks/construct-ae-p38-factorial-factors-l3-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..aaeaf241f8f59e4a12ee2bab7d8a4c8f6cd03f39
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/instruction.md
@@ -0,0 +1,13 @@
+Factoring N! into N large factors (Erdos-Guy-Selfridge).
+
+Let N = 180. Write N! as a product of exactly N positive integers,
+
+    N! = a_1 * a_2 * ... * a_N,
+
+such that every factor satisfies a_i >= 54. (The order of the factors does not matter; repeated values are
+allowed.) The check is exact: the product of your numbers must equal N! and every number must be an integer
+>= 54.
+
+Answer format: {"factors": [a_1, a_2, ..., a_N]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ed931869d426a6d487c1a69254934ab9ced3e583
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 57, 57, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 58, 59, 59, 59, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 61, 61, 62, 62, 62, 62, 62, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 67, 67, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 69, 69, 69, 69, 69, 69, 71, 71, 73, 73, 74, 74, 74, 74, 79, 79, 82, 82, 82, 82, 83, 83, 86, 86, 86, 86, 89, 89, 92, 94, 94, 94, 97, 101, 103, 106, 106, 106, 107, 109, 113, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/task.toml b/tasks/construct-ae-p38-factorial-factors-l3-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..e69d206e3b278e9ad7e0ed90b78df01bae3487e6
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p38-factorial-factors-l3-s0"
+version = "0.2.0"
+description = "construct/ae_p38_factorial_factors"
+authors = []
+keywords = ["rlmath", "construct", "ae_p38_factorial_factors"]
+
+[metadata]
+subset = "construct"
+family = "ae_p38_factorial_factors"
+problem_key = "factorial_into_n_large_factors_A034258"
+domain = "number_theory"
+tier = "research"
+level = "3"
+source = "AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "exact_integer", "ilp_friendly", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/check.py
@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dbd884c9e5a17d88847f0c06dd7eb420bf5ca4e7
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"N": 180, "t": 54, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc1bdc9e9a06390290e95fa25d8a6ed18b951a5d
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"N": 357, "t": 108, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/instruction.md b/tasks/construct-ae-p38-factorial-factors-l3-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..90fdd969279cd223fafcd9e529513c793dbb343c
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/instruction.md
@@ -0,0 +1,13 @@
+Factoring N! into N large factors (Erdos-Guy-Selfridge).
+
+Let N = 357. Write N! as a product of exactly N positive integers,
+
+    N! = a_1 * a_2 * ... * a_N,
+
+such that every factor satisfies a_i >= 108. (The order of the factors does not matter; repeated values are
+allowed.) The check is exact: the product of your numbers must equal N! and every number must be an integer
+>= 108.
+
+Answer format: {"factors": [a_1, a_2, ..., a_N]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c138023163ddf57a6a47f39e6e026b56ad8e8d27
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [972, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 109, 109, 109, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 110, 111, 111, 111, 111, 111, 111, 111, 111, 111, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 113, 113, 113, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 115, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 116, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117, 118, 118, 118, 118, 118, 118, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 119, 120, 120, 120, 120, 120, 120, 122, 122, 122, 122, 122, 123, 123, 123, 123, 123, 123, 123, 123, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 127, 127, 129, 129, 129, 129, 129, 129, 129, 129, 131, 131, 134, 134, 134, 134, 134, 137, 137, 139, 139, 141, 141, 141, 141, 141, 141, 141, 142, 142, 142, 142, 142, 146, 146, 146, 146, 149, 149, 151, 151, 157, 157, 158, 158, 158, 158, 159, 159, 159, 159, 159, 159, 163, 163, 166, 166, 166, 166, 167, 167, 173, 173, 178, 178, 178, 178, 179, 181, 191, 193, 194, 194, 194, 197, 199, 200, 202, 202, 202, 206, 206, 206, 211, 214, 214, 214, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/task.toml b/tasks/construct-ae-p38-factorial-factors-l3-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5b971314e2e04fd7fd25267e9efe2b496010e1b3
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p38-factorial-factors-l3-s7"
+version = "0.2.0"
+description = "construct/ae_p38_factorial_factors"
+authors = []
+keywords = ["rlmath", "construct", "ae_p38_factorial_factors"]
+
+[metadata]
+subset = "construct"
+family = "ae_p38_factorial_factors"
+problem_key = "factorial_into_n_large_factors_A034258"
+domain = "number_theory"
+tier = "research"
+level = "3"
+source = "AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "exact_integer", "ilp_friendly", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/check.py
@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc1bdc9e9a06390290e95fa25d8a6ed18b951a5d
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"N": 357, "t": 108, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/environment/Dockerfile b/tasks/construct-ae-p38-factorial-factors-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/environment/instance.json b/tasks/construct-ae-p38-factorial-factors-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..069e7e0cb2e9f80f8a9c33acc6927c9cb0147fb2
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"N": 395, "t": 120, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/instruction.md b/tasks/construct-ae-p38-factorial-factors-l3-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..9f87490ac6216cfee91017e85c8c0943087a26a7
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/instruction.md
@@ -0,0 +1,13 @@
+Factoring N! into N large factors (Erdos-Guy-Selfridge).
+
+Let N = 395. Write N! as a product of exactly N positive integers,
+
+    N! = a_1 * a_2 * ... * a_N,
+
+such that every factor satisfies a_i >= 120. (The order of the factors does not matter; repeated values are
+allowed.) The check is exact: the product of your numbers must equal N! and every number must be an integer
+>= 120.
+
+Answer format: {"factors": [a_1, a_2, ..., a_N]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/solution/solve.sh b/tasks/construct-ae-p38-factorial-factors-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6bcd3cab0b7d4b80a81a84ad6cecef0b253a5f72
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"factors": [120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 122, 122, 122, 122, 122, 122, 123, 123, 123, 123, 123, 123, 123, 123, 123, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 125, 125, 125, 125, 125, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 126, 127, 127, 127, 129, 129, 129, 129, 129, 129, 129, 129, 129, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 131, 131, 131, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 133, 134, 134, 134, 134, 134, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 136, 137, 137, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 138, 139, 139, 141, 141, 141, 141, 141, 141, 141, 141, 142, 142, 142, 142, 142, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145, 146, 146, 146, 146, 146, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 149, 149, 151, 151, 157, 157, 158, 158, 158, 158, 158, 159, 159, 159, 159, 159, 159, 159, 163, 163, 166, 166, 166, 166, 167, 167, 169, 169, 169, 169, 171, 173, 173, 177, 177, 177, 177, 177, 177, 178, 178, 178, 178, 179, 179, 181, 181, 191, 191, 193, 193, 194, 194, 194, 194, 197, 197, 199, 202, 202, 202, 206, 206, 206, 211, 214, 214, 214, 218, 218, 218, 223, 226, 226, 226, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/task.toml b/tasks/construct-ae-p38-factorial-factors-l3-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..bfdbd0c8fd624e4147c4073fd85ce79bad40b26e
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p38-factorial-factors-l3-s9"
+version = "0.2.0"
+description = "construct/ae_p38_factorial_factors"
+authors = []
+keywords = ["rlmath", "construct", "ae_p38_factorial_factors"]
+
+[metadata]
+subset = "construct"
+family = "ae_p38_factorial_factors"
+problem_key = "factorial_into_n_large_factors_A034258"
+domain = "number_theory"
+tier = "research"
+level = "3"
+source = "AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "exact_integer", "ilp_friendly", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/check.py b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..93ec67a19039afa8b4ce6e39811691b802132562
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/check.py
@@ -0,0 +1,12 @@
+"""Factor N! into N factors, each >= t (AlphaEvolve problem 38 / OEIS A034258). Exact big-integer check."""
+import math
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    f = int_list(ans.get("factors"), n, t, None, "factors")
+    if math.prod(f) != math.factorial(n):
+        raise Invalid(f"the product of the factors is not {n}!")
+    return None, {"min_factor": min(f)}
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/instance.json b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..069e7e0cb2e9f80f8a9c33acc6927c9cb0147fb2
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"N": 395, "t": 120, "family": "ae_p38_factorial_factors", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/run.py b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/test.sh b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p38-factorial-factors-l3-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s2/instruction.md b/tasks/construct-ae-p52-erdos-squarefree-l3-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..8819d1672c63a1ceb17e2d26e4373ab3530ce6a4
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s2/instruction.md
@@ -0,0 +1,8 @@
+Erdos squarefree problem.
+
+Let N = 1344. Find a set A of distinct integers in {1, 2, ..., N} with 54 <= |A| <= 128 such that for ALL a, b in A
+(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
+
+Answer format: {"A": [a_1, a_2, ..., a_m]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s2/task.toml b/tasks/construct-ae-p52-erdos-squarefree-l3-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..cc985ddb954c54a07f13ad24ca201d7bb73e11bc
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p52-erdos-squarefree-l3-s2"
+version = "0.2.0"
+description = "construct/ae_p52_erdos_squarefree"
+authors = []
+keywords = ["rlmath", "construct", "ae_p52_erdos_squarefree"]
+
+[metadata]
+subset = "construct"
+family = "ae_p52_erdos_squarefree"
+problem_key = "erdos_ab_plus_1_never_squarefree"
+domain = "number_theory"
+tier = "research"
+level = "3"
+source = "AlphaEvolve-Repository-of-Problems/52-erdos-squarefree"
+source_license = "CC-BY-4.0"
+tags = ["exact_integer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/environment/Dockerfile b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/environment/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e35a23e095c01a138d48653720efa9abe1483148
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/environment/instance.json
@@ -0,0 +1 @@
+{"N": 790, "t": 32, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/instruction.md b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b50cb70db421645e33b06ed058deed380d898e7d
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/instruction.md
@@ -0,0 +1,8 @@
+Erdos squarefree problem.
+
+Let N = 790. Find a set A of distinct integers in {1, 2, ..., N} with 32 <= |A| <= 84 such that for ALL a, b in A
+(including a = b) the number a*b + 1 is NOT squarefree, i.e. a*b + 1 is divisible by p^2 for some prime p.
+
+Answer format: {"A": [a_1, a_2, ..., a_m]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/solution/solve.sh b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..60c024e4eb907081bf4603d6cab9641097e729c3
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": [7, 32, 57, 82, 107, 132, 157, 182, 207, 232, 257, 282, 307, 332, 357, 382, 407, 432, 457, 482, 507, 532, 557, 582, 607, 632, 657, 682, 707, 732, 757, 782]}
+RLMATH_EOF
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/task.toml b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5b0783d712188de0a92cb955d7c4ea226406ff7e
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p52-erdos-squarefree-l3-s5"
+version = "0.2.0"
+description = "construct/ae_p52_erdos_squarefree"
+authors = []
+keywords = ["rlmath", "construct", "ae_p52_erdos_squarefree"]
+
+[metadata]
+subset = "construct"
+family = "ae_p52_erdos_squarefree"
+problem_key = "erdos_ab_plus_1_never_squarefree"
+domain = "number_theory"
+tier = "research"
+level = "3"
+source = "AlphaEvolve-Repository-of-Problems/52-erdos-squarefree"
+source_license = "CC-BY-4.0"
+tags = ["exact_integer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/check.py b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..87e15b242f211059193ba122baecdee9add99130
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/check.py
@@ -0,0 +1,38 @@
+"""Erdos squarefree problem (AlphaEvolve problem 52): A in [1, N], |A| >= t, ab+1 NOT squarefree for all a, b in A
+(a = b included). The repo's problem page says "square-free"; the notebook and the Erdos problem ask for
+"never squarefree", which is what we check. Exact: for every pair we find a prime p with p^2 | ab+1."""
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _primes(n):
+    s = np.ones(n + 1, dtype=bool)
+    s[:2] = False
+    for i in range(2, int(n ** .5) + 1):
+        if s[i]:
+            s[i * i::i] = False
+    return np.nonzero(s)[0]
+
+
+def check(inst, ans):
+    n, t = inst["N"], inst["t"]
+    a = ans.get("A")
+    if not isinstance(a, list) or not (t <= len(a) <= 2 * t + 20):
+        raise Invalid(f"A must be a list of {t}..{2 * t + 20} integers")
+    int_list(a, None, 1, n, "A")
+    if len(set(a)) != len(a):
+        raise Invalid("A must consist of distinct integers")
+    x = np.array(sorted(a), dtype=np.int64)
+    iu, ju = np.triu_indices(len(x))
+    va, vb = x[iu], x[ju]
+    left = np.ones(len(iu), dtype=bool)  # pairs without a square divisor found yet
+    for p in _primes(int((n * n + 1) ** .5) + 1):
+        q = int(p) * int(p)
+        idx = np.nonzero(left)[0]
+        hit = ((va[idx] % q) * (vb[idx] % q) + 1) % q == 0
+        left[idx[hit]] = False
+        if not left.any():
+            return None, {"size": len(a)}
+    k = int(np.nonzero(left)[0][0])
+    raise Invalid(f"{int(va[k])}*{int(vb[k])}+1 = {int(va[k]) * int(vb[k]) + 1} is squarefree")
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/instance.json b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e35a23e095c01a138d48653720efa9abe1483148
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/instance.json
@@ -0,0 +1 @@
+{"N": 790, "t": 32, "family": "ae_p52_erdos_squarefree", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/run.py b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/test.sh b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-ae-p52-erdos-squarefree-l3-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-ae-p54-touching-cylinders-l2-s0/instruction.md b/tasks/construct-ae-p54-touching-cylinders-l2-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..49b50952eba6cc77cbbe823ba4591a38095ffeb0
--- /dev/null
+++ b/tasks/construct-ae-p54-touching-cylinders-l2-s0/instruction.md
@@ -0,0 +1,14 @@
+Nine pairwise touching cylinders of arbitrary radii.
+
+Find 9 infinite circular cylinders in R^3 with radii r_i in [0.1, 10] such that every two of them touch
+externally, i.e. for every pair the distance between the axes equals r_i + r_j (checked with absolute tolerance
+1e-09).
+
+Describe cylinder i by a point (x, y, z) on its axis, an axis direction (dx, dy, dz) (any non-zero length; it is
+normalized) and its radius r. Distances between skew axes are |(p_j - p_i) . (v_i x v_j)| / |v_i x v_j|
+(parallel axes: distance between the lines). Every point must satisfy |x|, |y|, |z| <= 1000, and for every pair
+the midpoint of the common perpendicular of the two axes must lie in [-100, 100]^3.
+
+Answer format: {"cylinders": [[x, y, z, dx, dy, dz, r], ... 9 rows]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p54-touching-cylinders-l2-s0/task.toml b/tasks/construct-ae-p54-touching-cylinders-l2-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..dff6823b7222f832c55e0d703b89480e1dc6c775
--- /dev/null
+++ b/tasks/construct-ae-p54-touching-cylinders-l2-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p54-touching-cylinders-l2-s0"
+version = "0.2.0"
+description = "construct/ae_p54_touching_cylinders"
+authors = []
+keywords = ["rlmath", "construct", "ae_p54_touching_cylinders"]
+
+[metadata]
+subset = "construct"
+family = "ae_p54_touching_cylinders"
+problem_key = "mutually_touching_infinite_cylinders"
+domain = "discrete_geometry"
+tier = "research"
+level = "2"
+source = "AlphaEvolve-Repository-of-Problems/54-pairwise-touching-cylinders"
+source_license = "CC-BY-4.0"
+tags = ["float_tolerance", "nonlinear_system"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-ae-p58-happy-ending-l4-s0/instruction.md b/tasks/construct-ae-p58-happy-ending-l4-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..21e61976510d0e557eadc07c2c3690713ca826bb
--- /dev/null
+++ b/tasks/construct-ae-p58-happy-ending-l4-s0/instruction.md
@@ -0,0 +1,12 @@
+Erdos-Szekeres happy ending problem (lower-bound construction).
+
+Place n = 64 distinct points with integer coordinates (|x|, |y| <= 10^18) in the plane such that
+1. no three of the points are collinear, and
+2. no 8 of the points are in convex position (i.e. the points contain no convex 8-gon: no 8-point
+   subset whose points are all vertices of its convex hull).
+
+Everything is checked with exact integer arithmetic.
+
+Answer format: {"points": [[x_1, y_1], [x_2, y_2], ..., [x_64, y_64]]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-ae-p58-happy-ending-l4-s0/task.toml b/tasks/construct-ae-p58-happy-ending-l4-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..c51e0c95ad0015e6e97526d214f25c7de187ea40
--- /dev/null
+++ b/tasks/construct-ae-p58-happy-ending-l4-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-ae-p58-happy-ending-l4-s0"
+version = "0.2.0"
+description = "construct/ae_p58_happy_ending"
+authors = []
+keywords = ["rlmath", "construct", "ae_p58_happy_ending"]
+
+[metadata]
+subset = "construct"
+family = "ae_p58_happy_ending"
+problem_key = "erdos_szekeres_no_convex_k_gon_2pow_k_minus_2"
+domain = "discrete_geometry"
+tier = "research"
+level = "4"
+source = "AlphaEvolve-Repository-of-Problems/58-erdos-szekeres-happy-ending"
+source_license = "CC-BY-4.0"
+tags = ["exact_integer", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-all-interval-l3-s0/environment/Dockerfile b/tasks/construct-mc-all-interval-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-all-interval-l3-s0/environment/instance.json b/tasks/construct-mc-all-interval-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c945459801c354acf98b51792b30dea25223fab4
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 14, "fixed": [["x", 6, 3], ["x", 12, 6], ["d", 3, 10], ["d", 11, 2]], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l3-s0/instruction.md b/tasks/construct-mc-all-interval-l3-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..63f217eaea144aadd36766f5e1623bfb28ad9fa4
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/instruction.md
@@ -0,0 +1,10 @@
+An all-interval series of size 14 is a permutation x[0..13] of 0..13 such that the absolute differences d[i] = |x[i+1] - x[i]| (i = 0..12) form a permutation of 1..13.
+
+Find an all-interval series of size 14.
+
+Some values are fixed in advance and your answer must agree with them:
+x[6] = 3, x[12] = 6, d[3] = 10, d[11] = 2
+
+Answer format: {"x": [x_0, x_1, ..., x_13]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-all-interval-l3-s0/solution/solve.sh b/tasks/construct-mc-all-interval-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..885169fdbe5ada4afee8be54e3689bbc1f1d3c86
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 13, 1, 12, 2, 11, 3, 10, 4, 9, 5, 8, 6, 7]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-all-interval-l3-s0/task.toml b/tasks/construct-mc-all-interval-l3-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..e1fbbf4fed5666cdf0cb432bc303ccb3396147de
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-all-interval-l3-s0"
+version = "0.2.0"
+description = "construct/mc_all_interval"
+authors = []
+keywords = ["rlmath", "construct", "mc_all_interval"]
+
+[metadata]
+subset = "construct"
+family = "mc_all_interval"
+problem_key = "all_interval_series"
+domain = "combinatorics"
+tier = "competition"
+level = "3"
+source = "MathConstraint/all_interval"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-all-interval-l3-s0/tests/check.py b/tasks/construct-mc-all-interval-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2e39eec264b6422a47e35921b8cdbe1fa1748307
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/tests/check.py
@@ -0,0 +1,17 @@
+"""All-interval series of size n (MathConstraint all_interval, CC-BY-4.0). Accepts any valid series."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    d = [abs(x[i + 1] - x[i]) for i in range(n - 1)]
+    if sorted(d) != list(range(1, n)):
+        raise Invalid("consecutive differences are not a permutation of 1..n-1")
+    seqs = {"x": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-all-interval-l3-s0/tests/instance.json b/tasks/construct-mc-all-interval-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c945459801c354acf98b51792b30dea25223fab4
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 14, "fixed": [["x", 6, 3], ["x", 12, 6], ["d", 3, 10], ["d", 11, 2]], "family": "mc_all_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-all-interval-l3-s0/tests/run.py b/tasks/construct-mc-all-interval-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-all-interval-l3-s0/tests/test.sh b/tasks/construct-mc-all-interval-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-all-interval-l3-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-bibd-l4-s2/instruction.md b/tasks/construct-mc-bibd-l4-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..e40f98b297a007b1df33b5ef142f28e44af4e6bb
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-s2/instruction.md
@@ -0,0 +1,7 @@
+A balanced incomplete block design BIBD(16, 4, 3) is a collection of b = 60 blocks, each a set of 4 distinct points from {0, 1, ..., 15}, such that every pair of distinct points is contained in exactly 3 of the blocks (consequently every point lies in exactly r = 15 blocks). The same block may appear more than once.
+
+Construct a BIBD(16, 4, 3).
+
+Answer format: {"blocks": [[p, p, ...], ...]}: a list of exactly 60 blocks, each a list of 4 distinct integers in 0..15
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-bibd-l4-s2/task.toml b/tasks/construct-mc-bibd-l4-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..3e06a050140f488c0ca4bf8b4b537d82c520b119
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-bibd-l4-s2"
+version = "0.2.0"
+description = "construct/mc_bibd"
+authors = []
+keywords = ["rlmath", "construct", "mc_bibd"]
+
+[metadata]
+subset = "construct"
+family = "mc_bibd"
+problem_key = "bibd"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "MathConstraint/bibd"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-bibd-l4-s5/instruction.md b/tasks/construct-mc-bibd-l4-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..58f8d8257521b22b6df80c1eba2c118f728cf818
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-s5/instruction.md
@@ -0,0 +1,7 @@
+A balanced incomplete block design BIBD(19, 9, 4) is a collection of b = 19 blocks, each a set of 9 distinct points from {0, 1, ..., 18}, such that every pair of distinct points is contained in exactly 4 of the blocks (consequently every point lies in exactly r = 9 blocks). The same block may appear more than once.
+
+Construct a BIBD(19, 9, 4).
+
+Answer format: {"blocks": [[p, p, ...], ...]}: a list of exactly 19 blocks, each a list of 9 distinct integers in 0..18
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-bibd-l4-s5/task.toml b/tasks/construct-mc-bibd-l4-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..fd9c52424a6fdea0268fbcaf0702f2f35f0fd542
--- /dev/null
+++ b/tasks/construct-mc-bibd-l4-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-bibd-l4-s5"
+version = "0.2.0"
+description = "construct/mc_bibd"
+authors = []
+keywords = ["rlmath", "construct", "mc_bibd"]
+
+[metadata]
+subset = "construct"
+family = "mc_bibd"
+problem_key = "bibd"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "MathConstraint/bibd"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-costas-array-l1-s0/environment/Dockerfile b/tasks/construct-mc-costas-array-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-costas-array-l1-s0/environment/instance.json b/tasks/construct-mc-costas-array-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d11a024f5a56d48a4ac3f3c469035c294decc374
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 8, "fixed": [], "family": "mc_costas_array", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-costas-array-l1-s0/instruction.md b/tasks/construct-mc-costas-array-l1-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b97047fe438ea0e3de18bfc6f3cfe351c10f2f91
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/instruction.md
@@ -0,0 +1,7 @@
+A Costas array of order 8 is a 8x8 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..7] of 0..7, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over all column pairs i < j are pairwise distinct.
+
+Find a Costas array of order 8.
+
+Answer format: {"x": [x_0, x_1, ..., x_7]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-costas-array-l1-s0/solution/solve.sh b/tasks/construct-mc-costas-array-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5c71af1344697aebeae90ab133bb3d111a6e085d
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [4, 7, 3, 2, 0, 5, 6, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-costas-array-l1-s0/task.toml b/tasks/construct-mc-costas-array-l1-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..611cd1da3ffe32efebce7e89139c76e70f3d6ac1
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-costas-array-l1-s0"
+version = "0.2.0"
+description = "construct/mc_costas_array"
+authors = []
+keywords = ["rlmath", "construct", "mc_costas_array"]
+
+[metadata]
+subset = "construct"
+family = "mc_costas_array"
+problem_key = "costas_array"
+domain = "combinatorics"
+tier = "competition"
+level = "1"
+source = "MathConstraint/costas_array"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-costas-array-l1-s0/tests/check.py b/tasks/construct-mc-costas-array-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c86323a5b639b23787ecd4d5f358b986bbd91b6c
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/tests/check.py
@@ -0,0 +1,22 @@
+"""Costas array of order n (MathConstraint costas_array, CC-BY-4.0). Accepts any valid array.
+Adapted from pilot/grader.py check_costas; adds the optional fixed entries (upstream partial assignment)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    for name, i, v in inst.get("fixed", []):
+        if x[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    vecs = set()
+    for i, j in itertools.combinations(range(n), 2):
+        d = (j - i, x[j] - x[i])
+        if d in vecs:
+            raise Invalid(f"repeated displacement vector {d}")
+        vecs.add(d)
+    return None, {}
diff --git a/tasks/construct-mc-costas-array-l1-s0/tests/instance.json b/tasks/construct-mc-costas-array-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d11a024f5a56d48a4ac3f3c469035c294decc374
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 8, "fixed": [], "family": "mc_costas_array", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-costas-array-l1-s0/tests/run.py b/tasks/construct-mc-costas-array-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-costas-array-l1-s0/tests/test.sh b/tasks/construct-mc-costas-array-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l1-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-costas-array-l5-s1/environment/Dockerfile b/tasks/construct-mc-costas-array-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-costas-array-l5-s1/environment/instance.json b/tasks/construct-mc-costas-array-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b199e9ac93d5ab27c9283557e8a3005378797c7c
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 22, "fixed": [], "family": "mc_costas_array", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-costas-array-l5-s1/instruction.md b/tasks/construct-mc-costas-array-l5-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..6e18925fd1dc8135abd4517272a1013aeee7ea2b
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/instruction.md
@@ -0,0 +1,7 @@
+A Costas array of order 22 is a 22x22 grid with exactly one mark in every row and every column such that the displacement vectors between pairs of marks are all distinct. Encode it as a permutation x[0..21] of 0..21, where x[c] is the row of the mark in column c; the condition is that the vectors (j - i, x[j] - x[i]) over all column pairs i < j are pairwise distinct.
+
+Find a Costas array of order 22.
+
+Answer format: {"x": [x_0, x_1, ..., x_21]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-costas-array-l5-s1/solution/solve.sh b/tasks/construct-mc-costas-array-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..8a502d9ddba175f9ca5d77d50ff12a00fc23e4bd
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0, 14, 17, 16, 1, 6, 12, 10, 3, 13, 2, 21, 7, 4, 5, 20, 15, 9, 11, 18, 8, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-costas-array-l5-s1/task.toml b/tasks/construct-mc-costas-array-l5-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..42a89c0a7386e284a94e340f0d0800ebbbfa6a2a
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-costas-array-l5-s1"
+version = "0.2.0"
+description = "construct/mc_costas_array"
+authors = []
+keywords = ["rlmath", "construct", "mc_costas_array"]
+
+[metadata]
+subset = "construct"
+family = "mc_costas_array"
+problem_key = "costas_array"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/costas_array"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-costas-array-l5-s1/tests/check.py b/tasks/construct-mc-costas-array-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c86323a5b639b23787ecd4d5f358b986bbd91b6c
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/tests/check.py
@@ -0,0 +1,22 @@
+"""Costas array of order n (MathConstraint costas_array, CC-BY-4.0). Accepts any valid array.
+Adapted from pilot/grader.py check_costas; adds the optional fixed entries (upstream partial assignment)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, 0, n - 1, "x")
+    if sorted(x) != list(range(n)):
+        raise Invalid("x is not a permutation of 0..n-1")
+    for name, i, v in inst.get("fixed", []):
+        if x[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    vecs = set()
+    for i, j in itertools.combinations(range(n), 2):
+        d = (j - i, x[j] - x[i])
+        if d in vecs:
+            raise Invalid(f"repeated displacement vector {d}")
+        vecs.add(d)
+    return None, {}
diff --git a/tasks/construct-mc-costas-array-l5-s1/tests/instance.json b/tasks/construct-mc-costas-array-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b199e9ac93d5ab27c9283557e8a3005378797c7c
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 22, "fixed": [], "family": "mc_costas_array", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-costas-array-l5-s1/tests/run.py b/tasks/construct-mc-costas-array-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-costas-array-l5-s1/tests/test.sh b/tasks/construct-mc-costas-array-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-costas-array-l5-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-debruijn-l4-s3/environment/Dockerfile b/tasks/construct-mc-debruijn-l4-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-debruijn-l4-s3/environment/instance.json b/tasks/construct-mc-debruijn-l4-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b4633a50ce94fb2fb02bc37793891ba30ae9d10c
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/environment/instance.json
@@ -0,0 +1 @@
+{"b": 6, "n": 3, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l4-s3/instruction.md b/tasks/construct-mc-debruijn-l4-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..52fb3207d26b9ea152707cebaf7a763555168863
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/instruction.md
@@ -0,0 +1,7 @@
+A De Bruijn sequence B(6, 3) is a cyclic sequence x[0..215] of length 6^3 = 216 over the alphabet {0, ..., 5} in which every word of length 3 over that alphabet appears exactly once as a window x[i], x[i+1], ..., x[i+2] (indices taken modulo 216).
+
+Find a De Bruijn sequence B(6, 3).
+
+Answer format: {"seq": [x_0, x_1, ..., x_215]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-debruijn-l4-s3/solution/solve.sh b/tasks/construct-mc-debruijn-l4-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9469e5bed018af12e0c1dc62c4cffc0d8e9dfda5
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"seq": [0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 1, 1, 0, 1, 2, 0, 1, 3, 0, 1, 4, 0, 1, 5, 0, 2, 1, 0, 2, 2, 0, 2, 3, 0, 2, 4, 0, 2, 5, 0, 3, 1, 0, 3, 2, 0, 3, 3, 0, 3, 4, 0, 3, 5, 0, 4, 1, 0, 4, 2, 0, 4, 3, 0, 4, 4, 0, 4, 5, 0, 5, 1, 0, 5, 2, 0, 5, 3, 0, 5, 4, 0, 5, 5, 1, 1, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 5, 1, 2, 2, 1, 2, 3, 1, 2, 4, 1, 2, 5, 1, 3, 2, 1, 3, 3, 1, 3, 4, 1, 3, 5, 1, 4, 2, 1, 4, 3, 1, 4, 4, 1, 4, 5, 1, 5, 2, 1, 5, 3, 1, 5, 4, 1, 5, 5, 2, 2, 2, 3, 2, 2, 4, 2, 2, 5, 2, 3, 3, 2, 3, 4, 2, 3, 5, 2, 4, 3, 2, 4, 4, 2, 4, 5, 2, 5, 3, 2, 5, 4, 2, 5, 5, 3, 3, 3, 4, 3, 3, 5, 3, 4, 4, 3, 4, 5, 3, 5, 4, 3, 5, 5, 4, 4, 4, 5, 4, 5, 5, 5]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-debruijn-l4-s3/task.toml b/tasks/construct-mc-debruijn-l4-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..316cab466d872975249621a37da4d5dcde5b7b28
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-debruijn-l4-s3"
+version = "0.2.0"
+description = "construct/mc_debruijn"
+authors = []
+keywords = ["rlmath", "construct", "mc_debruijn"]
+
+[metadata]
+subset = "construct"
+family = "mc_debruijn"
+problem_key = "de_bruijn_sequence"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "MathConstraint/debruijn"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-debruijn-l4-s3/tests/check.py b/tasks/construct-mc-debruijn-l4-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c9d6f0177d2b3bde8306d74939ee9704c1501a23
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/tests/check.py
@@ -0,0 +1,15 @@
+"""De Bruijn sequence B(b, n) (MathConstraint debruijn, CC-BY-4.0). Accepts any valid cyclic sequence."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    b, n = inst["b"], inst["n"]
+    m = b ** n
+    x = int_list(ans.get("seq"), m, 0, b - 1, "seq")
+    seen = set()
+    for i in range(m):
+        w = tuple(x[(i + k) % m] for k in range(n))
+        if w in seen:
+            raise Invalid(f"window {w} occurs twice")
+        seen.add(w)
+    return None, {}
diff --git a/tasks/construct-mc-debruijn-l4-s3/tests/instance.json b/tasks/construct-mc-debruijn-l4-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b4633a50ce94fb2fb02bc37793891ba30ae9d10c
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/tests/instance.json
@@ -0,0 +1 @@
+{"b": 6, "n": 3, "family": "mc_debruijn", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-debruijn-l4-s3/tests/run.py b/tasks/construct-mc-debruijn-l4-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-debruijn-l4-s3/tests/test.sh b/tasks/construct-mc-debruijn-l4-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-debruijn-l4-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-golomb-l6-s2/instruction.md b/tasks/construct-mc-golomb-l6-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b657be7eb5e69a1b1097219e16b85dbf0f99ceda
--- /dev/null
+++ b/tasks/construct-mc-golomb-l6-s2/instruction.md
@@ -0,0 +1,7 @@
+A Golomb ruler with 18 marks is a list of integers 0 = a_0 < a_1 < ... < a_17 such that all 153 differences a_j - a_i (i < j) are distinct; its length is a_17.
+
+Find a Golomb ruler with 18 marks and length at most 216.
+
+Answer format: {"marks": [a_0, a_1, ..., a_17]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-golomb-l6-s2/task.toml b/tasks/construct-mc-golomb-l6-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..97a17921e200a14e8d06c8f4e57bb9ec64c884de
--- /dev/null
+++ b/tasks/construct-mc-golomb-l6-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-golomb-l6-s2"
+version = "0.2.0"
+description = "construct/mc_golomb"
+authors = []
+keywords = ["rlmath", "construct", "mc_golomb"]
+
+[metadata]
+subset = "construct"
+family = "mc_golomb"
+problem_key = "golomb_ruler"
+domain = "combinatorics"
+tier = "competition"
+level = "6"
+source = "MathConstraint/golomb"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/environment/Dockerfile b/tasks/construct-mc-graceful-graph-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/environment/instance.json b/tasks/construct-mc-graceful-graph-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6fbb17d260f30348b95697517a326b572a6d52f1
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"k": 3, "p": 7, "num_vertices": 21, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], [10, 13], [11, 14], [12, 15], [13, 16], [14, 17], [15, 18], [16, 19], [17, 20]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/instruction.md b/tasks/construct-mc-graceful-graph-l4-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..749f1ec16670af15aba8725199bceae5fa6126df
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/instruction.md
@@ -0,0 +1,10 @@
+Let G be the graph with 21 vertices 0..20 made of 7 disjoint copies of the complete graph K_3 (copy g has vertices g*3, ..., g*3+2), where for each g < 6 and each i < 3 vertex g*3+i is also joined to vertex (g+1)*3+i. G has 39 edges, in this order (index: edge):
+0:(0,1), 1:(0,2), 2:(1,2), 3:(3,4), 4:(3,5), 5:(4,5), 6:(6,7), 7:(6,8), 8:(7,8), 9:(9,10), 10:(9,11), 11:(10,11), 12:(12,13), 13:(12,14), 14:(13,14), 15:(15,16), 16:(15,17), 17:(16,17), 18:(18,19), 19:(18,20), 20:(19,20), 21:(0,3), 22:(1,4), 23:(2,5), 24:(3,6), 25:(4,7), 26:(5,8), 27:(6,9), 28:(7,10), 29:(8,11), 30:(9,12), 31:(10,13), 32:(11,14), 33:(12,15), 34:(13,16), 35:(14,17), 36:(15,18), 37:(16,19), 38:(17,20)
+
+A graceful labelling assigns every vertex a distinct label from {0, 1, ..., 39} such that the 39 edge labels d[t] = |label(u) - label(v)| (for edge t = (u, v)) are all distinct (hence exactly 1..39).
+
+Find a graceful labelling of G.
+
+Answer format: {"labels": [l_0, l_1, ..., l_20]} (label of vertex i)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/solution/solve.sh b/tasks/construct-mc-graceful-graph-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bf8c72f48ca35efa21625f93b72ed0e15c309c65
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"labels": [1, 2, 4, 37, 6, 27, 0, 39, 5, 38, 9, 29, 3, 17, 35, 19, 32, 7, 8, 15, 34]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/task.toml b/tasks/construct-mc-graceful-graph-l4-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..86e6de7c66976b2604eda3fdd46fe995a036b697
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-graceful-graph-l4-s0"
+version = "0.2.0"
+description = "construct/mc_graceful_graph"
+authors = []
+keywords = ["rlmath", "construct", "mc_graceful_graph"]
+
+[metadata]
+subset = "construct"
+family = "mc_graceful_graph"
+problem_key = "graceful_labeling"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "MathConstraint/graceful_graph"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/tests/check.py b/tasks/construct-mc-graceful-graph-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..f4d33af1d63c0495c3b32d34db6ae10f0fb45923
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/tests/check.py
@@ -0,0 +1,19 @@
+"""Graceful labelling of K_k x P_p (MathConstraint graceful_graph, CC-BY-4.0): distinct vertex labels in
+0..m (m = number of edges) whose edge differences |l(u) - l(v)| are all distinct."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    nv, edges = inst["num_vertices"], inst["edges"]
+    m = len(edges)
+    x = int_list(ans.get("labels"), nv, 0, m, "labels")
+    if len(set(x)) != nv:
+        raise Invalid("vertex labels must be distinct")
+    d = [abs(x[u] - x[v]) for u, v in edges]
+    if len(set(d)) != m:
+        raise Invalid("edge labels are not distinct")
+    seqs = {"labels": x, "d": d}
+    for name, i, v in inst.get("fixed", []):
+        if seqs[name][i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    return None, {}
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/tests/instance.json b/tasks/construct-mc-graceful-graph-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..6fbb17d260f30348b95697517a326b572a6d52f1
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"k": 3, "p": 7, "num_vertices": 21, "edges": [[0, 1], [0, 2], [1, 2], [3, 4], [3, 5], [4, 5], [6, 7], [6, 8], [7, 8], [9, 10], [9, 11], [10, 11], [12, 13], [12, 14], [13, 14], [15, 16], [15, 17], [16, 17], [18, 19], [18, 20], [19, 20], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], [10, 13], [11, 14], [12, 15], [13, 16], [14, 17], [15, 18], [16, 19], [17, 20]], "fixed": [], "family": "mc_graceful_graph", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/tests/run.py b/tasks/construct-mc-graceful-graph-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-graceful-graph-l4-s0/tests/test.sh b/tasks/construct-mc-graceful-graph-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-graceful-graph-l4-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-hadamard-l4-s0/environment/Dockerfile b/tasks/construct-mc-hadamard-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-hadamard-l4-s0/environment/instance.json b/tasks/construct-mc-hadamard-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..32470738c6f4cfb931dd55b0b7db8645fa000721
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 29, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l4-s0/instruction.md b/tasks/construct-mc-hadamard-l4-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..710e74375fa594e40d70f05c1424f51c9d4759f0
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/instruction.md
@@ -0,0 +1,7 @@
+Find two sequences x[0..28] and y[0..28] with entries in {-1, +1} (a Legendre pair of length 29) such that
+  (a) sum(x) = 1 and sum(y) = 1, and
+  (b) for every k = 1..14: sum_{i=0}^{28} x[i]*x[(i+k) mod 29] + sum_{i=0}^{28} y[i]*y[(i+k) mod 29] = -2.
+
+Answer format: {"x": [x_0, ..., x_28], "y": [y_0, ..., y_28]} with entries -1 or 1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-hadamard-l4-s0/solution/solve.sh b/tasks/construct-mc-hadamard-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bfebdda60d4d491584a4ddb8a46d9ca8d219efca
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1], "y": [1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-hadamard-l4-s0/task.toml b/tasks/construct-mc-hadamard-l4-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..e03de761f4d09f2dd7d0cc84a2c72ab68a290993
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-hadamard-l4-s0"
+version = "0.2.0"
+description = "construct/mc_hadamard"
+authors = []
+keywords = ["rlmath", "construct", "mc_hadamard"]
+
+[metadata]
+subset = "construct"
+family = "mc_hadamard"
+problem_key = "legendre_pair"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "MathConstraint/hadamard"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-hadamard-l4-s0/tests/check.py b/tasks/construct-mc-hadamard-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc4b93160fd7473dd14935db9d712e52abdd00c2
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/tests/check.py
@@ -0,0 +1,18 @@
+"""Legendre pair of odd length n (MathConstraint hadamard, CC-BY-4.0): x, y in {-1,+1}^n with
+sum(x) = sum(y) = 1 and PAF_x(k) + PAF_y(k) = -2 for k = 1..(n-1)/2 (periodic autocorrelation)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = int_list(ans.get("x"), n, -1, 1, "x")
+    y = int_list(ans.get("y"), n, -1, 1, "y")
+    if 0 in x or 0 in y:
+        raise Invalid("entries must be -1 or +1")
+    if sum(x) != 1 or sum(y) != 1:
+        raise Invalid("sum(x) and sum(y) must both equal 1")
+    for k in range(1, (n - 1) // 2 + 1):
+        p = sum(x[i] * x[(i + k) % n] for i in range(n)) + sum(y[i] * y[(i + k) % n] for i in range(n))
+        if p != -2:
+            raise Invalid(f"PAF_x({k}) + PAF_y({k}) = {p}, need -2")
+    return None, {}
diff --git a/tasks/construct-mc-hadamard-l4-s0/tests/instance.json b/tasks/construct-mc-hadamard-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..32470738c6f4cfb931dd55b0b7db8645fa000721
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 29, "family": "mc_hadamard", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-hadamard-l4-s0/tests/run.py b/tasks/construct-mc-hadamard-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-hadamard-l4-s0/tests/test.sh b/tasks/construct-mc-hadamard-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-hadamard-l4-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-langford-l4-s1/instruction.md b/tasks/construct-mc-langford-l4-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c775937cc1184fd8021102636546aa7b167acd1c
--- /dev/null
+++ b/tasks/construct-mc-langford-l4-s1/instruction.md
@@ -0,0 +1,7 @@
+A Langford sequence L(2,28) is a sequence seq[0..55] of length 56 that contains exactly two copies of each integer 1..28, such that the two copies of every value v are exactly v+1 positions apart (their indices differ by v+1). Example: L(2,3) = [2, 3, 1, 2, 1, 3].
+
+Find a Langford sequence L(2,28).
+
+Answer format: {"seq": [s_0, s_1, ..., s_55]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-langford-l4-s1/task.toml b/tasks/construct-mc-langford-l4-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..af893a6be160d79c36d26d37a026e4a89f237605
--- /dev/null
+++ b/tasks/construct-mc-langford-l4-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-langford-l4-s1"
+version = "0.2.0"
+description = "construct/mc_langford"
+authors = []
+keywords = ["rlmath", "construct", "mc_langford"]
+
+[metadata]
+subset = "construct"
+family = "mc_langford"
+problem_key = "langford_pairing"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "MathConstraint/langford"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-low-autocorrelation-l2-s2/instruction.md b/tasks/construct-mc-low-autocorrelation-l2-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..adfef05ec3088fc983ef41480efa3b8c36b5f535
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l2-s2/instruction.md
@@ -0,0 +1,11 @@
+For a sequence seq[0..12] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{13-k-1} seq[i]*seq[i+k] for k = 1..12 and the energy E = sum_k C_k^2.
+
+Find a sequence of length 13 with E <= 28.
+
+Some values are fixed in advance and your answer must agree with them:
+seq[8] = 1, seq[10] = -1, c[4] = 2, c[5] = -1
+(c[j] denotes C_{j+1}, the autocorrelation at shift j+1.)
+
+Answer format: {"seq": [s_0, s_1, ..., s_12]} with every s_i equal to -1 or 1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-low-autocorrelation-l2-s2/task.toml b/tasks/construct-mc-low-autocorrelation-l2-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..dcef9a0471238e604745e657111b76aa40564736
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l2-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-low-autocorrelation-l2-s2"
+version = "0.2.0"
+description = "construct/mc_low_autocorrelation"
+authors = []
+keywords = ["rlmath", "construct", "mc_low_autocorrelation"]
+
+[metadata]
+subset = "construct"
+family = "mc_low_autocorrelation"
+problem_key = "low_autocorrelation_binary_sequence"
+domain = "combinatorics"
+tier = "competition"
+level = "2"
+source = "MathConstraint/low_autocorrelation"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-low-autocorrelation-l6-s3/instruction.md b/tasks/construct-mc-low-autocorrelation-l6-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..26c973ddb8742bca8019276f109f09c64ac68822
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l6-s3/instruction.md
@@ -0,0 +1,7 @@
+For a sequence seq[0..55] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{56-k-1} seq[i]*seq[i+k] for k = 1..55 and the energy E = sum_k C_k^2.
+
+Find a sequence of length 56 with E <= 240.
+
+Answer format: {"seq": [s_0, s_1, ..., s_55]} with every s_i equal to -1 or 1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-low-autocorrelation-l6-s3/task.toml b/tasks/construct-mc-low-autocorrelation-l6-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..b8d4ff9f8abb0d0a3d845b011f3fe14f797eadab
--- /dev/null
+++ b/tasks/construct-mc-low-autocorrelation-l6-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-low-autocorrelation-l6-s3"
+version = "0.2.0"
+description = "construct/mc_low_autocorrelation"
+authors = []
+keywords = ["rlmath", "construct", "mc_low_autocorrelation"]
+
+[metadata]
+subset = "construct"
+family = "mc_low_autocorrelation"
+problem_key = "low_autocorrelation_binary_sequence"
+domain = "combinatorics"
+tier = "competition"
+level = "6"
+source = "MathConstraint/low_autocorrelation"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-magic-sequence-l5-s3/instruction.md b/tasks/construct-mc-magic-sequence-l5-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..7d15ea656b5eff690c721ea4320faec44101b710
--- /dev/null
+++ b/tasks/construct-mc-magic-sequence-l5-s3/instruction.md
@@ -0,0 +1,7 @@
+A magic sequence of length 50 is a sequence x[0], x[1], ..., x[49] of non-negative integers such that for every i in 0..49, x[i] equals the number of times the value i occurs in the sequence.
+
+Find a magic sequence of length 50.
+
+Answer format: {"x": [x_0, x_1, ..., x_49]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-magic-sequence-l5-s3/task.toml b/tasks/construct-mc-magic-sequence-l5-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..8f7d879f3374b4bb14db43e436a6a5883de31d6a
--- /dev/null
+++ b/tasks/construct-mc-magic-sequence-l5-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-magic-sequence-l5-s3"
+version = "0.2.0"
+description = "construct/mc_magic_sequence"
+authors = []
+keywords = ["rlmath", "construct", "mc_magic_sequence"]
+
+[metadata]
+subset = "construct"
+family = "mc_magic_sequence"
+problem_key = "magic_sequence"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/magic_sequence"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-magic-sequence-l5-s4/instruction.md b/tasks/construct-mc-magic-sequence-l5-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..8e2a946ba584f178abe8eb37a5c75dba05d97f46
--- /dev/null
+++ b/tasks/construct-mc-magic-sequence-l5-s4/instruction.md
@@ -0,0 +1,7 @@
+A magic sequence of length 200 is a sequence x[0], x[1], ..., x[199] of non-negative integers such that for every i in 0..199, x[i] equals the number of times the value i occurs in the sequence.
+
+Find a magic sequence of length 200.
+
+Answer format: {"x": [x_0, x_1, ..., x_199]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-magic-sequence-l5-s4/task.toml b/tasks/construct-mc-magic-sequence-l5-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..40822699b6712081399df8145f04f8e4ec0f9121
--- /dev/null
+++ b/tasks/construct-mc-magic-sequence-l5-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-magic-sequence-l5-s4"
+version = "0.2.0"
+description = "construct/mc_magic_sequence"
+authors = []
+keywords = ["rlmath", "construct", "mc_magic_sequence"]
+
+[metadata]
+subset = "construct"
+family = "mc_magic_sequence"
+problem_key = "magic_sequence"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/magic_sequence"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-clique-l2-s2/environment/Dockerfile b/tasks/construct-mc-max-clique-l2-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-clique-l2-s2/environment/instance.json b/tasks/construct-mc-max-clique-l2-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d89bac32e48a76ae6b7e7c63051a5eaea3157724
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 40, "k": 8, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 11], [0, 12], [0, 16], [0, 18], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 28], [0, 30], [0, 31], [0, 32], [0, 35], [0, 37], [0, 38], [1, 6], [1, 7], [1, 9], [1, 11], [1, 13], [1, 15], [1, 16], [1, 17], [1, 21], [1, 22], [1, 25], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 35], [1, 37], [1, 38], [1, 39], [2, 3], [2, 4], [2, 6], [2, 7], [2, 11], [2, 15], [2, 17], [2, 19], [2, 21], [2, 23], [2, 25], [2, 26], [2, 27], [2, 29], [2, 31], [2, 32], [2, 33], [2, 34], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [3, 6], [3, 7], [3, 14], [3, 15], [3, 18], [3, 19], [3, 20], [3, 21], [3, 22], [3, 26], [3, 27], [3, 28], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [4, 5], [4, 7], [4, 9], [4, 14], [4, 15], [4, 19], [4, 22], [4, 23], [4, 24], [4, 28], [4, 34], [4, 35], [4, 39], [5, 8], [5, 11], [5, 13], [5, 15], [5, 17], [5, 19], [5, 20], [5, 21], [5, 22], [5, 23], [5, 25], [5, 27], [5, 28], [5, 29], [5, 31], [5, 32], [5, 33], [5, 35], [5, 36], [5, 37], [5, 39], [6, 7], [6, 8], [6, 10], [6, 12], [6, 13], [6, 17], [6, 18], [6, 21], [6, 22], [6, 28], [6, 29], [6, 33], [6, 34], [6, 38], [7, 8], [7, 12], [7, 13], [7, 15], [7, 16], [7, 17], [7, 18], [7, 24], [7, 25], [7, 26], [7, 30], [7, 33], [7, 34], [7, 35], [7, 37], [8, 9], [8, 11], [8, 12], [8, 13], [8, 15], [8, 17], [8, 18], [8, 19], [8, 20], [8, 22], [8, 25], [8, 29], [8, 30], [8, 33], [8, 36], [9, 10], [9, 11], [9, 13], [9, 15], [9, 17], [9, 19], [9, 21], [9, 23], [9, 25], [9, 28], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 36], [9, 39], [10, 11], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 25], [10, 27], [10, 29], [10, 33], [10, 35], [10, 36], [10, 38], [10, 39], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 22], [11, 23], [11, 24], [11, 25], [11, 27], [11, 28], [11, 29], [11, 31], [11, 33], [11, 36], [11, 37], [11, 39], [12, 13], [12, 16], [12, 17], [12, 18], [12, 20], [12, 22], [12, 23], [12, 29], [12, 30], [12, 31], [12, 34], [12, 37], [12, 38], [13, 15], [13, 16], [13, 18], [13, 22], [13, 25], [13, 28], [13, 29], [13, 30], [13, 31], [13, 33], [13, 36], [13, 37], [14, 15], [14, 17], [14, 18], [14, 19], [14, 21], [14, 22], [14, 24], [14, 29], [14, 32], [14, 36], [14, 37], [14, 38], [14, 39], [15, 17], [15, 24], [15, 26], [15, 29], [15, 30], [15, 34], [15, 36], [15, 38], [15, 39], [16, 17], [16, 18], [16, 19], [16, 22], [16, 25], [16, 26], [16, 27], [16, 30], [16, 33], [16, 35], [16, 38], [17, 19], [17, 21], [17, 22], [17, 23], [17, 24], [17, 26], [17, 28], [17, 29], [17, 32], [17, 34], [17, 36], [17, 37], [17, 39], [18, 19], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 27], [18, 29], [18, 30], [18, 31], [18, 35], [18, 36], [18, 37], [18, 38], [19, 20], [19, 23], [19, 24], [19, 26], [19, 28], [19, 29], [19, 30], [19, 31], [19, 35], [19, 38], [20, 22], [20, 25], [20, 26], [20, 29], [20, 31], [20, 32], [20, 35], [20, 37], [20, 38], [20, 39], [21, 25], [21, 26], [21, 27], [21, 28], [21, 30], [21, 32], [21, 33], [21, 37], [21, 38], [22, 24], [22, 25], [22, 26], [22, 27], [22, 28], [22, 29], [22, 32], [22, 33], [22, 34], [22, 37], [22, 38], [22, 39], [23, 24], [23, 25], [23, 27], [23, 28], [23, 29], [23, 34], [23, 35], [23, 36], [23, 37], [23, 38], [24, 29], [24, 30], [24, 31], [24, 35], [24, 36], [24, 37], [25, 28], [25, 29], [25, 30], [25, 31], [25, 33], [25, 34], [25, 36], [25, 38], [26, 30], [26, 33], [26, 34], [26, 37], [26, 39], [27, 28], [27, 29], [27, 30], [27, 37], [27, 39], [28, 29], [28, 31], [28, 32], [28, 33], [28, 39], [29, 30], [29, 34], [29, 37], [30, 35], [30, 38], [31, 33], [31, 34], [31, 37], [31, 38], [32, 35], [32, 37], [32, 39], [33, 35], [33, 37], [34, 38], [35, 36], [35, 38], [35, 39], [36, 37], [36, 39], [37, 38], [37, 39]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l2-s2/instruction.md b/tasks/construct-mc-max-clique-l2-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..dc00b0a4a7070da6761bcfd7617db14c8c1f1718
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 40 vertices numbered 0..39 and 400 edges:
+(0,1), (0,2), (0,3), (0,4), (0,5), (0,6), (0,7), (0,9), (0,11), (0,12), (0,16), (0,18), (0,20), (0,21), (0,23), (0,24), (0,25), (0,28), (0,30), (0,31), (0,32), (0,35), (0,37), (0,38), (1,6), (1,7), (1,9), (1,11), (1,13), (1,15), (1,16), (1,17), (1,21), (1,22), (1,25), (1,28), (1,29), (1,30), (1,31), (1,33), (1,35), (1,37), (1,38), (1,39), (2,3), (2,4), (2,6), (2,7), (2,11), (2,15), (2,17), (2,19), (2,21), (2,23), (2,25), (2,26), (2,27), (2,29), (2,31), (2,32), (2,33), (2,34), (2,35), (2,36), (2,37), (2,38), (2,39), (3,6), (3,7), (3,14), (3,15), (3,18), (3,19), (3,20), (3,21), (3,22), (3,26), (3,27), (3,28), (3,34), (3,35), (3,36), (3,37), (3,38), (4,5), (4,7), (4,9), (4,14), (4,15), (4,19), (4,22), (4,23), (4,24), (4,28), (4,34), (4,35), (4,39), (5,8), (5,11), (5,13), (5,15), (5,17), (5,19), (5,20), (5,21), (5,22), (5,23), (5,25), (5,27), (5,28), (5,29), (5,31), (5,32), (5,33), (5,35), (5,36), (5,37), (5,39), (6,7), (6,8), (6,10), (6,12), (6,13), (6,17), (6,18), (6,21), (6,22), (6,28), (6,29), (6,33), (6,34), (6,38), (7,8), (7,12), (7,13), (7,15), (7,16), (7,17), (7,18), (7,24), (7,25), (7,26), (7,30), (7,33), (7,34), (7,35), (7,37), (8,9), (8,11), (8,12), (8,13), (8,15), (8,17), (8,18), (8,19), (8,20), (8,22), (8,25), (8,29), (8,30), (8,33), (8,36), (9,10), (9,11), (9,13), (9,15), (9,17), (9,19), (9,21), (9,23), (9,25), (9,28), (9,30), (9,31), (9,32), (9,33), (9,34), (9,36), (9,39), (10,11), (10,15), (10,16), (10,17), (10,18), (10,19), (10,20), (10,21), (10,25), (10,27), (10,29), (10,33), (10,35), (10,36), (10,38), (10,39), (11,13), (11,15), (11,16), (11,17), (11,18), (11,19), (11,22), (11,23), (11,24), (11,25), (11,27), (11,28), (11,29), (11,31), (11,33), (11,36), (11,37), (11,39), (12,13), (12,16), (12,17), (12,18), (12,20), (12,22), (12,23), (12,29), (12,30), (12,31), (12,34), (12,37), (12,38), (13,15), (13,16), (13,18), (13,22), (13,25), (13,28), (13,29), (13,30), (13,31), (13,33), (13,36), (13,37), (14,15), (14,17), (14,18), (14,19), (14,21), (14,22), (14,24), (14,29), (14,32), (14,36), (14,37), (14,38), (14,39), (15,17), (15,24), (15,26), (15,29), (15,30), (15,34), (15,36), (15,38), (15,39), (16,17), (16,18), (16,19), (16,22), (16,25), (16,26), (16,27), (16,30), (16,33), (16,35), (16,38), (17,19), (17,21), (17,22), (17,23), (17,24), (17,26), (17,28), (17,29), (17,32), (17,34), (17,36), (17,37), (17,39), (18,19), (18,21), (18,22), (18,23), (18,24), (18,25), (18,27), (18,29), (18,30), (18,31), (18,35), (18,36), (18,37), (18,38), (19,20), (19,23), (19,24), (19,26), (19,28), (19,29), (19,30), (19,31), (19,35), (19,38), (20,22), (20,25), (20,26), (20,29), (20,31), (20,32), (20,35), (20,37), (20,38), (20,39), (21,25), (21,26), (21,27), (21,28), (21,30), (21,32), (21,33), (21,37), (21,38), (22,24), (22,25), (22,26), (22,27), (22,28), (22,29), (22,32), (22,33), (22,34), (22,37), (22,38), (22,39), (23,24), (23,25), (23,27), (23,28), (23,29), (23,34), (23,35), (23,36), (23,37), (23,38), (24,29), (24,30), (24,31), (24,35), (24,36), (24,37), (25,28), (25,29), (25,30), (25,31), (25,33), (25,34), (25,36), (25,38), (26,30), (26,33), (26,34), (26,37), (26,39), (27,28), (27,29), (27,30), (27,37), (27,39), (28,29), (28,31), (28,32), (28,33), (28,39), (29,30), (29,34), (29,37), (30,35), (30,38), (31,33), (31,34), (31,37), (31,38), (32,35), (32,37), (32,39), (33,35), (33,37), (34,38), (35,36), (35,38), (35,39), (36,37), (36,39), (37,38), (37,39)
+
+Find a clique of size at least 8 in G: a set of at least 8 vertices that are pairwise adjacent.
+
+Answer format: {"clique": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-clique-l2-s2/solution/solve.sh b/tasks/construct-mc-max-clique-l2-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c550ff4f298e71a24e970aa9bfa4fdde0b436f32
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [1, 9, 11, 13, 25, 28, 31, 33]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-clique-l2-s2/task.toml b/tasks/construct-mc-max-clique-l2-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..26d20e4c89cb509aba0b8708189a6c96b0b9c723
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-clique-l2-s2"
+version = "0.2.0"
+description = "construct/mc_max_clique"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_clique"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_clique"
+problem_key = "graph_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "MathConstraint/max_clique"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-clique-l2-s2/tests/check.py b/tasks/construct-mc-max-clique-l2-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3f70dbd5b155a3514c2102aa4ad460201495210
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/tests/check.py
@@ -0,0 +1,18 @@
+"""Clique of size >= k in a given graph (MathConstraint max_clique decision version, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"clique has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) not in E:
+            raise Invalid(f"vertices {u} and {v} are not adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-clique-l2-s2/tests/instance.json b/tasks/construct-mc-max-clique-l2-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d89bac32e48a76ae6b7e7c63051a5eaea3157724
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 40, "k": 8, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 9], [0, 11], [0, 12], [0, 16], [0, 18], [0, 20], [0, 21], [0, 23], [0, 24], [0, 25], [0, 28], [0, 30], [0, 31], [0, 32], [0, 35], [0, 37], [0, 38], [1, 6], [1, 7], [1, 9], [1, 11], [1, 13], [1, 15], [1, 16], [1, 17], [1, 21], [1, 22], [1, 25], [1, 28], [1, 29], [1, 30], [1, 31], [1, 33], [1, 35], [1, 37], [1, 38], [1, 39], [2, 3], [2, 4], [2, 6], [2, 7], [2, 11], [2, 15], [2, 17], [2, 19], [2, 21], [2, 23], [2, 25], [2, 26], [2, 27], [2, 29], [2, 31], [2, 32], [2, 33], [2, 34], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [3, 6], [3, 7], [3, 14], [3, 15], [3, 18], [3, 19], [3, 20], [3, 21], [3, 22], [3, 26], [3, 27], [3, 28], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [4, 5], [4, 7], [4, 9], [4, 14], [4, 15], [4, 19], [4, 22], [4, 23], [4, 24], [4, 28], [4, 34], [4, 35], [4, 39], [5, 8], [5, 11], [5, 13], [5, 15], [5, 17], [5, 19], [5, 20], [5, 21], [5, 22], [5, 23], [5, 25], [5, 27], [5, 28], [5, 29], [5, 31], [5, 32], [5, 33], [5, 35], [5, 36], [5, 37], [5, 39], [6, 7], [6, 8], [6, 10], [6, 12], [6, 13], [6, 17], [6, 18], [6, 21], [6, 22], [6, 28], [6, 29], [6, 33], [6, 34], [6, 38], [7, 8], [7, 12], [7, 13], [7, 15], [7, 16], [7, 17], [7, 18], [7, 24], [7, 25], [7, 26], [7, 30], [7, 33], [7, 34], [7, 35], [7, 37], [8, 9], [8, 11], [8, 12], [8, 13], [8, 15], [8, 17], [8, 18], [8, 19], [8, 20], [8, 22], [8, 25], [8, 29], [8, 30], [8, 33], [8, 36], [9, 10], [9, 11], [9, 13], [9, 15], [9, 17], [9, 19], [9, 21], [9, 23], [9, 25], [9, 28], [9, 30], [9, 31], [9, 32], [9, 33], [9, 34], [9, 36], [9, 39], [10, 11], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 25], [10, 27], [10, 29], [10, 33], [10, 35], [10, 36], [10, 38], [10, 39], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 22], [11, 23], [11, 24], [11, 25], [11, 27], [11, 28], [11, 29], [11, 31], [11, 33], [11, 36], [11, 37], [11, 39], [12, 13], [12, 16], [12, 17], [12, 18], [12, 20], [12, 22], [12, 23], [12, 29], [12, 30], [12, 31], [12, 34], [12, 37], [12, 38], [13, 15], [13, 16], [13, 18], [13, 22], [13, 25], [13, 28], [13, 29], [13, 30], [13, 31], [13, 33], [13, 36], [13, 37], [14, 15], [14, 17], [14, 18], [14, 19], [14, 21], [14, 22], [14, 24], [14, 29], [14, 32], [14, 36], [14, 37], [14, 38], [14, 39], [15, 17], [15, 24], [15, 26], [15, 29], [15, 30], [15, 34], [15, 36], [15, 38], [15, 39], [16, 17], [16, 18], [16, 19], [16, 22], [16, 25], [16, 26], [16, 27], [16, 30], [16, 33], [16, 35], [16, 38], [17, 19], [17, 21], [17, 22], [17, 23], [17, 24], [17, 26], [17, 28], [17, 29], [17, 32], [17, 34], [17, 36], [17, 37], [17, 39], [18, 19], [18, 21], [18, 22], [18, 23], [18, 24], [18, 25], [18, 27], [18, 29], [18, 30], [18, 31], [18, 35], [18, 36], [18, 37], [18, 38], [19, 20], [19, 23], [19, 24], [19, 26], [19, 28], [19, 29], [19, 30], [19, 31], [19, 35], [19, 38], [20, 22], [20, 25], [20, 26], [20, 29], [20, 31], [20, 32], [20, 35], [20, 37], [20, 38], [20, 39], [21, 25], [21, 26], [21, 27], [21, 28], [21, 30], [21, 32], [21, 33], [21, 37], [21, 38], [22, 24], [22, 25], [22, 26], [22, 27], [22, 28], [22, 29], [22, 32], [22, 33], [22, 34], [22, 37], [22, 38], [22, 39], [23, 24], [23, 25], [23, 27], [23, 28], [23, 29], [23, 34], [23, 35], [23, 36], [23, 37], [23, 38], [24, 29], [24, 30], [24, 31], [24, 35], [24, 36], [24, 37], [25, 28], [25, 29], [25, 30], [25, 31], [25, 33], [25, 34], [25, 36], [25, 38], [26, 30], [26, 33], [26, 34], [26, 37], [26, 39], [27, 28], [27, 29], [27, 30], [27, 37], [27, 39], [28, 29], [28, 31], [28, 32], [28, 33], [28, 39], [29, 30], [29, 34], [29, 37], [30, 35], [30, 38], [31, 33], [31, 34], [31, 37], [31, 38], [32, 35], [32, 37], [32, 39], [33, 35], [33, 37], [34, 38], [35, 36], [35, 38], [35, 39], [36, 37], [36, 39], [37, 38], [37, 39]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l2-s2/tests/run.py b/tasks/construct-mc-max-clique-l2-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-clique-l2-s2/tests/test.sh b/tasks/construct-mc-max-clique-l2-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-clique-l2-s5/environment/Dockerfile b/tasks/construct-mc-max-clique-l2-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-clique-l2-s5/environment/instance.json b/tasks/construct-mc-max-clique-l2-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c7b265e854308de129354dd4d0b34c46a057ee61
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 40, "k": 8, "edges": [[0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 11], [0, 12], [0, 15], [0, 16], [0, 18], [0, 20], [0, 24], [0, 26], [0, 27], [0, 29], [0, 30], [0, 33], [0, 34], [0, 37], [0, 39], [1, 2], [1, 6], [1, 7], [1, 10], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 22], [1, 24], [1, 25], [1, 26], [1, 28], [1, 29], [1, 30], [1, 34], [1, 38], [2, 5], [2, 7], [2, 8], [2, 10], [2, 11], [2, 13], [2, 14], [2, 16], [2, 17], [2, 19], [2, 20], [2, 21], [2, 22], [2, 24], [2, 25], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 33], [2, 34], [2, 35], [2, 38], [3, 5], [3, 7], [3, 9], [3, 12], [3, 13], [3, 14], [3, 15], [3, 17], [3, 18], [3, 19], [3, 21], [3, 23], [3, 24], [3, 27], [3, 31], [3, 32], [3, 35], [3, 39], [4, 6], [4, 10], [4, 13], [4, 15], [4, 17], [4, 18], [4, 19], [4, 20], [4, 23], [4, 24], [4, 29], [4, 30], [4, 34], [4, 35], [4, 39], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 13], [5, 14], [5, 15], [5, 16], [5, 19], [5, 20], [5, 22], [5, 23], [5, 25], [5, 27], [5, 34], [5, 37], [5, 39], [6, 10], [6, 13], [6, 18], [6, 20], [6, 21], [6, 23], [6, 24], [6, 26], [6, 27], [6, 30], [6, 31], [6, 35], [6, 36], [6, 38], [6, 39], [7, 8], [7, 12], [7, 13], [7, 15], [7, 18], [7, 19], [7, 20], [7, 22], [7, 24], [7, 25], [7, 27], [7, 28], [7, 29], [7, 30], [7, 31], [7, 34], [7, 37], [7, 38], [8, 9], [8, 11], [8, 13], [8, 15], [8, 17], [8, 18], [8, 21], [8, 22], [8, 23], [8, 29], [8, 33], [8, 35], [8, 36], [8, 38], [8, 39], [9, 11], [9, 13], [9, 19], [9, 21], [9, 22], [9, 23], [9, 24], [9, 29], [9, 31], [9, 33], [9, 36], [9, 39], [10, 11], [10, 12], [10, 16], [10, 17], [10, 18], [10, 20], [10, 21], [10, 23], [10, 26], [10, 30], [10, 32], [10, 36], [10, 38], [11, 13], [11, 14], [11, 16], [11, 17], [11, 19], [11, 21], [11, 23], [11, 28], [11, 29], [11, 30], [11, 31], [11, 32], [11, 33], [11, 36], [11, 37], [11, 38], [11, 39], [12, 14], [12, 15], [12, 19], [12, 23], [12, 27], [12, 29], [12, 34], [12, 35], [12, 38], [13, 14], [13, 16], [13, 17], [13, 19], [13, 20], [13, 21], [13, 23], [13, 24], [13, 25], [13, 26], [13, 30], [13, 31], [13, 33], [13, 34], [13, 35], [13, 39], [14, 15], [14, 16], [14, 18], [14, 19], [14, 20], [14, 21], [14, 23], [14, 24], [14, 26], [14, 28], [14, 31], [14, 32], [14, 37], [14, 39], [15, 20], [15, 22], [15, 24], [15, 26], [15, 27], [15, 32], [15, 33], [15, 36], [15, 38], [15, 39], [16, 17], [16, 19], [16, 21], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 29], [16, 35], [16, 36], [16, 38], [16, 39], [17, 19], [17, 20], [17, 21], [17, 23], [17, 26], [17, 27], [17, 30], [17, 31], [17, 32], [17, 34], [17, 35], [17, 36], [17, 39], [18, 23], [18, 27], [18, 29], [18, 30], [18, 31], [18, 32], [18, 33], [18, 35], [18, 36], [18, 37], [18, 38], [19, 24], [19, 25], [19, 28], [19, 33], [19, 36], [19, 38], [20, 21], [20, 22], [20, 24], [20, 26], [20, 31], [20, 32], [20, 33], [20, 34], [20, 37], [20, 39], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 31], [21, 32], [21, 34], [21, 37], [22, 24], [22, 26], [22, 31], [22, 32], [22, 35], [22, 36], [22, 38], [23, 26], [23, 27], [23, 30], [23, 32], [23, 34], [23, 35], [23, 36], [23, 37], [23, 38], [24, 26], [24, 27], [24, 29], [24, 30], [24, 32], [24, 33], [24, 34], [24, 38], [25, 28], [25, 31], [25, 33], [25, 34], [25, 35], [25, 36], [25, 39], [26, 27], [26, 29], [26, 31], [26, 32], [26, 33], [26, 34], [26, 37], [26, 38], [26, 39], [27, 28], [27, 34], [27, 35], [27, 37], [27, 39], [28, 31], [28, 32], [28, 34], [28, 35], [28, 36], [28, 37], [28, 38], [28, 39], [29, 30], [29, 31], [29, 33], [29, 35], [29, 36], [29, 37], [30, 32], [30, 36], [30, 38], [31, 32], [31, 34], [31, 35], [31, 36], [32, 34], [32, 37], [32, 38], [33, 35], [33, 36], [33, 38], [33, 39], [34, 35], [34, 36], [34, 38], [34, 39], [36, 39], [38, 39]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l2-s5/instruction.md b/tasks/construct-mc-max-clique-l2-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..505bdcdb432afe3200f8833f1d36d39129bcc03e
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 40 vertices numbered 0..39 and 393 edges:
+(0,4), (0,5), (0,6), (0,8), (0,9), (0,11), (0,12), (0,15), (0,16), (0,18), (0,20), (0,24), (0,26), (0,27), (0,29), (0,30), (0,33), (0,34), (0,37), (0,39), (1,2), (1,6), (1,7), (1,10), (1,13), (1,14), (1,15), (1,17), (1,18), (1,22), (1,24), (1,25), (1,26), (1,28), (1,29), (1,30), (1,34), (1,38), (2,5), (2,7), (2,8), (2,10), (2,11), (2,13), (2,14), (2,16), (2,17), (2,19), (2,20), (2,21), (2,22), (2,24), (2,25), (2,26), (2,27), (2,29), (2,30), (2,31), (2,33), (2,34), (2,35), (2,38), (3,5), (3,7), (3,9), (3,12), (3,13), (3,14), (3,15), (3,17), (3,18), (3,19), (3,21), (3,23), (3,24), (3,27), (3,31), (3,32), (3,35), (3,39), (4,6), (4,10), (4,13), (4,15), (4,17), (4,18), (4,19), (4,20), (4,23), (4,24), (4,29), (4,30), (4,34), (4,35), (4,39), (5,6), (5,7), (5,8), (5,9), (5,10), (5,13), (5,14), (5,15), (5,16), (5,19), (5,20), (5,22), (5,23), (5,25), (5,27), (5,34), (5,37), (5,39), (6,10), (6,13), (6,18), (6,20), (6,21), (6,23), (6,24), (6,26), (6,27), (6,30), (6,31), (6,35), (6,36), (6,38), (6,39), (7,8), (7,12), (7,13), (7,15), (7,18), (7,19), (7,20), (7,22), (7,24), (7,25), (7,27), (7,28), (7,29), (7,30), (7,31), (7,34), (7,37), (7,38), (8,9), (8,11), (8,13), (8,15), (8,17), (8,18), (8,21), (8,22), (8,23), (8,29), (8,33), (8,35), (8,36), (8,38), (8,39), (9,11), (9,13), (9,19), (9,21), (9,22), (9,23), (9,24), (9,29), (9,31), (9,33), (9,36), (9,39), (10,11), (10,12), (10,16), (10,17), (10,18), (10,20), (10,21), (10,23), (10,26), (10,30), (10,32), (10,36), (10,38), (11,13), (11,14), (11,16), (11,17), (11,19), (11,21), (11,23), (11,28), (11,29), (11,30), (11,31), (11,32), (11,33), (11,36), (11,37), (11,38), (11,39), (12,14), (12,15), (12,19), (12,23), (12,27), (12,29), (12,34), (12,35), (12,38), (13,14), (13,16), (13,17), (13,19), (13,20), (13,21), (13,23), (13,24), (13,25), (13,26), (13,30), (13,31), (13,33), (13,34), (13,35), (13,39), (14,15), (14,16), (14,18), (14,19), (14,20), (14,21), (14,23), (14,24), (14,26), (14,28), (14,31), (14,32), (14,37), (14,39), (15,20), (15,22), (15,24), (15,26), (15,27), (15,32), (15,33), (15,36), (15,38), (15,39), (16,17), (16,19), (16,21), (16,23), (16,24), (16,25), (16,26), (16,27), (16,29), (16,35), (16,36), (16,38), (16,39), (17,19), (17,20), (17,21), (17,23), (17,26), (17,27), (17,30), (17,31), (17,32), (17,34), (17,35), (17,36), (17,39), (18,23), (18,27), (18,29), (18,30), (18,31), (18,32), (18,33), (18,35), (18,36), (18,37), (18,38), (19,24), (19,25), (19,28), (19,33), (19,36), (19,38), (20,21), (20,22), (20,24), (20,26), (20,31), (20,32), (20,33), (20,34), (20,37), (20,39), (21,25), (21,26), (21,27), (21,28), (21,29), (21,31), (21,32), (21,34), (21,37), (22,24), (22,26), (22,31), (22,32), (22,35), (22,36), (22,38), (23,26), (23,27), (23,30), (23,32), (23,34), (23,35), (23,36), (23,37), (23,38), (24,26), (24,27), (24,29), (24,30), (24,32), (24,33), (24,34), (24,38), (25,28), (25,31), (25,33), (25,34), (25,35), (25,36), (25,39), (26,27), (26,29), (26,31), (26,32), (26,33), (26,34), (26,37), (26,38), (26,39), (27,28), (27,34), (27,35), (27,37), (27,39), (28,31), (28,32), (28,34), (28,35), (28,36), (28,37), (28,38), (28,39), (29,30), (29,31), (29,33), (29,35), (29,36), (29,37), (30,32), (30,36), (30,38), (31,32), (31,34), (31,35), (31,36), (32,34), (32,37), (32,38), (33,35), (33,36), (33,38), (33,39), (34,35), (34,36), (34,38), (34,39), (36,39), (38,39)
+
+Find a clique of size at least 8 in G: a set of at least 8 vertices that are pairwise adjacent.
+
+Answer format: {"clique": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-clique-l2-s5/solution/solve.sh b/tasks/construct-mc-max-clique-l2-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2c1a94a9197b3369a65a9145a9bcda02a42a2aba
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [2, 13, 17, 20, 21, 26, 31, 34]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-clique-l2-s5/task.toml b/tasks/construct-mc-max-clique-l2-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ab4738148adda75f3d5a8b0468494651b8d69516
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-clique-l2-s5"
+version = "0.2.0"
+description = "construct/mc_max_clique"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_clique"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_clique"
+problem_key = "graph_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "MathConstraint/max_clique"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-clique-l2-s5/tests/check.py b/tasks/construct-mc-max-clique-l2-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3f70dbd5b155a3514c2102aa4ad460201495210
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/tests/check.py
@@ -0,0 +1,18 @@
+"""Clique of size >= k in a given graph (MathConstraint max_clique decision version, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"clique has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) not in E:
+            raise Invalid(f"vertices {u} and {v} are not adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-clique-l2-s5/tests/instance.json b/tasks/construct-mc-max-clique-l2-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c7b265e854308de129354dd4d0b34c46a057ee61
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 40, "k": 8, "edges": [[0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 11], [0, 12], [0, 15], [0, 16], [0, 18], [0, 20], [0, 24], [0, 26], [0, 27], [0, 29], [0, 30], [0, 33], [0, 34], [0, 37], [0, 39], [1, 2], [1, 6], [1, 7], [1, 10], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 22], [1, 24], [1, 25], [1, 26], [1, 28], [1, 29], [1, 30], [1, 34], [1, 38], [2, 5], [2, 7], [2, 8], [2, 10], [2, 11], [2, 13], [2, 14], [2, 16], [2, 17], [2, 19], [2, 20], [2, 21], [2, 22], [2, 24], [2, 25], [2, 26], [2, 27], [2, 29], [2, 30], [2, 31], [2, 33], [2, 34], [2, 35], [2, 38], [3, 5], [3, 7], [3, 9], [3, 12], [3, 13], [3, 14], [3, 15], [3, 17], [3, 18], [3, 19], [3, 21], [3, 23], [3, 24], [3, 27], [3, 31], [3, 32], [3, 35], [3, 39], [4, 6], [4, 10], [4, 13], [4, 15], [4, 17], [4, 18], [4, 19], [4, 20], [4, 23], [4, 24], [4, 29], [4, 30], [4, 34], [4, 35], [4, 39], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 13], [5, 14], [5, 15], [5, 16], [5, 19], [5, 20], [5, 22], [5, 23], [5, 25], [5, 27], [5, 34], [5, 37], [5, 39], [6, 10], [6, 13], [6, 18], [6, 20], [6, 21], [6, 23], [6, 24], [6, 26], [6, 27], [6, 30], [6, 31], [6, 35], [6, 36], [6, 38], [6, 39], [7, 8], [7, 12], [7, 13], [7, 15], [7, 18], [7, 19], [7, 20], [7, 22], [7, 24], [7, 25], [7, 27], [7, 28], [7, 29], [7, 30], [7, 31], [7, 34], [7, 37], [7, 38], [8, 9], [8, 11], [8, 13], [8, 15], [8, 17], [8, 18], [8, 21], [8, 22], [8, 23], [8, 29], [8, 33], [8, 35], [8, 36], [8, 38], [8, 39], [9, 11], [9, 13], [9, 19], [9, 21], [9, 22], [9, 23], [9, 24], [9, 29], [9, 31], [9, 33], [9, 36], [9, 39], [10, 11], [10, 12], [10, 16], [10, 17], [10, 18], [10, 20], [10, 21], [10, 23], [10, 26], [10, 30], [10, 32], [10, 36], [10, 38], [11, 13], [11, 14], [11, 16], [11, 17], [11, 19], [11, 21], [11, 23], [11, 28], [11, 29], [11, 30], [11, 31], [11, 32], [11, 33], [11, 36], [11, 37], [11, 38], [11, 39], [12, 14], [12, 15], [12, 19], [12, 23], [12, 27], [12, 29], [12, 34], [12, 35], [12, 38], [13, 14], [13, 16], [13, 17], [13, 19], [13, 20], [13, 21], [13, 23], [13, 24], [13, 25], [13, 26], [13, 30], [13, 31], [13, 33], [13, 34], [13, 35], [13, 39], [14, 15], [14, 16], [14, 18], [14, 19], [14, 20], [14, 21], [14, 23], [14, 24], [14, 26], [14, 28], [14, 31], [14, 32], [14, 37], [14, 39], [15, 20], [15, 22], [15, 24], [15, 26], [15, 27], [15, 32], [15, 33], [15, 36], [15, 38], [15, 39], [16, 17], [16, 19], [16, 21], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [16, 29], [16, 35], [16, 36], [16, 38], [16, 39], [17, 19], [17, 20], [17, 21], [17, 23], [17, 26], [17, 27], [17, 30], [17, 31], [17, 32], [17, 34], [17, 35], [17, 36], [17, 39], [18, 23], [18, 27], [18, 29], [18, 30], [18, 31], [18, 32], [18, 33], [18, 35], [18, 36], [18, 37], [18, 38], [19, 24], [19, 25], [19, 28], [19, 33], [19, 36], [19, 38], [20, 21], [20, 22], [20, 24], [20, 26], [20, 31], [20, 32], [20, 33], [20, 34], [20, 37], [20, 39], [21, 25], [21, 26], [21, 27], [21, 28], [21, 29], [21, 31], [21, 32], [21, 34], [21, 37], [22, 24], [22, 26], [22, 31], [22, 32], [22, 35], [22, 36], [22, 38], [23, 26], [23, 27], [23, 30], [23, 32], [23, 34], [23, 35], [23, 36], [23, 37], [23, 38], [24, 26], [24, 27], [24, 29], [24, 30], [24, 32], [24, 33], [24, 34], [24, 38], [25, 28], [25, 31], [25, 33], [25, 34], [25, 35], [25, 36], [25, 39], [26, 27], [26, 29], [26, 31], [26, 32], [26, 33], [26, 34], [26, 37], [26, 38], [26, 39], [27, 28], [27, 34], [27, 35], [27, 37], [27, 39], [28, 31], [28, 32], [28, 34], [28, 35], [28, 36], [28, 37], [28, 38], [28, 39], [29, 30], [29, 31], [29, 33], [29, 35], [29, 36], [29, 37], [30, 32], [30, 36], [30, 38], [31, 32], [31, 34], [31, 35], [31, 36], [32, 34], [32, 37], [32, 38], [33, 35], [33, 36], [33, 38], [33, 39], [34, 35], [34, 36], [34, 38], [34, 39], [36, 39], [38, 39]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l2-s5/tests/run.py b/tasks/construct-mc-max-clique-l2-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-clique-l2-s5/tests/test.sh b/tasks/construct-mc-max-clique-l2-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l2-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-clique-l6-s3/environment/Dockerfile b/tasks/construct-mc-max-clique-l6-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-clique-l6-s3/environment/instance.json b/tasks/construct-mc-max-clique-l6-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7843593b32b1c623e3527bfb44a985eb7400433a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/environment/instance.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l6-s3/instruction.md b/tasks/construct-mc-max-clique-l6-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..8c6a46f48babf4f2bbca8c0b141d85151e0b45f0
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/instruction.md
@@ -0,0 +1,8 @@
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+
+Find a clique of size at least 13 in G: a set of at least 13 vertices that are pairwise adjacent.
+
+Answer format: {"clique": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-clique-l6-s3/solution/solve.sh b/tasks/construct-mc-max-clique-l6-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9ee83973e9da0188c888013146df56b02c18f957
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [3, 10, 18, 19, 21, 31, 47, 60, 70, 82, 98, 102, 112]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-clique-l6-s3/task.toml b/tasks/construct-mc-max-clique-l6-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..f050af715a54992fd71ad21b7c5397ad325f6494
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-clique-l6-s3"
+version = "0.2.0"
+description = "construct/mc_max_clique"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_clique"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_clique"
+problem_key = "graph_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "MathConstraint/max_clique"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-clique-l6-s3/tests/check.py b/tasks/construct-mc-max-clique-l6-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3f70dbd5b155a3514c2102aa4ad460201495210
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/tests/check.py
@@ -0,0 +1,18 @@
+"""Clique of size >= k in a given graph (MathConstraint max_clique decision version, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"clique has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) not in E:
+            raise Invalid(f"vertices {u} and {v} are not adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-clique-l6-s3/tests/instance.json b/tasks/construct-mc-max-clique-l6-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..7843593b32b1c623e3527bfb44a985eb7400433a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 120, "k": 13, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 23], [0, 26], [0, 27], [0, 28], [0, 30], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 41], [0, 44], [0, 46], [0, 47], [0, 50], [0, 51], [0, 53], [0, 55], [0, 57], [0, 59], [0, 60], [0, 61], [0, 62], [0, 66], [0, 67], [0, 68], [0, 69], [0, 71], [0, 74], [0, 75], [0, 76], [0, 79], [0, 80], [0, 81], [0, 88], [0, 89], [0, 95], [0, 96], [0, 98], [0, 99], [0, 101], [0, 103], [0, 104], [0, 105], [0, 110], [0, 113], [0, 115], [0, 116], [0, 119], [1, 3], [1, 4], [1, 9], [1, 10], [1, 20], [1, 22], [1, 25], [1, 26], [1, 29], [1, 30], [1, 33], [1, 34], [1, 36], [1, 37], [1, 39], [1, 40], [1, 46], [1, 49], [1, 52], [1, 54], [1, 56], [1, 57], [1, 59], [1, 62], [1, 67], [1, 69], [1, 72], [1, 73], [1, 74], [1, 75], [1, 76], [1, 78], [1, 81], [1, 84], [1, 86], [1, 88], [1, 89], [1, 91], [1, 92], [1, 93], [1, 94], [1, 100], [1, 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119], [103, 106], [103, 108], [103, 111], [103, 113], [103, 119], [104, 105], [104, 106], [104, 108], [104, 110], [104, 111], [104, 114], [104, 115], [104, 116], [105, 107], [105, 108], [105, 110], [105, 112], [105, 113], [105, 116], [105, 117], [105, 119], [106, 108], [106, 109], [106, 110], [106, 113], [106, 114], [106, 115], [106, 116], [106, 118], [106, 119], [107, 108], [107, 109], [107, 110], [107, 112], [107, 113], [107, 114], [108, 109], [108, 112], [108, 114], [108, 115], [108, 116], [108, 117], [108, 118], [108, 119], [109, 111], [109, 115], [109, 116], [109, 118], [109, 119], [110, 111], [110, 113], [110, 114], [110, 117], [111, 114], [111, 115], [111, 117], [112, 113], [112, 117], [112, 118], [112, 119], [113, 115], [113, 116], [113, 117], [114, 115], [114, 117], [115, 119], [116, 117], [116, 118], [116, 119], [117, 119], [118, 119]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l6-s3/tests/run.py b/tasks/construct-mc-max-clique-l6-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-clique-l6-s3/tests/test.sh b/tasks/construct-mc-max-clique-l6-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-clique-l6-s4/environment/Dockerfile b/tasks/construct-mc-max-clique-l6-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-clique-l6-s4/environment/instance.json b/tasks/construct-mc-max-clique-l6-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..13b2dcde91598e584c81d1cbef19ad25c41658f5
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 120, "k": 13, "edges": [[0, 1], [0, 2], [0, 4], [0, 5], [0, 6], [0, 8], [0, 13], [0, 19], [0, 21], [0, 23], [0, 25], [0, 26], [0, 27], [0, 29], [0, 30], [0, 34], [0, 36], [0, 38], [0, 40], [0, 41], [0, 44], [0, 49], [0, 50], [0, 51], [0, 53], [0, 54], [0, 58], [0, 60], [0, 61], [0, 62], [0, 63], [0, 65], [0, 67], [0, 68], [0, 69], [0, 71], [0, 72], [0, 73], [0, 76], [0, 77], [0, 78], [0, 80], [0, 81], [0, 85], [0, 86], [0, 87], [0, 89], [0, 90], [0, 96], [0, 99], [0, 103], [0, 105], [0, 108], [0, 112], [0, 114], [0, 115], [0, 119], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 14], [1, 15], [1, 16], [1, 20], [1, 21], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 31], [1, 32], [1, 33], [1, 37], [1, 38], [1, 40], [1, 42], [1, 45], [1, 47], [1, 49], [1, 51], [1, 52], [1, 54], [1, 55], [1, 56], [1, 57], [1, 62], [1, 64], [1, 66], [1, 68], [1, 70], [1, 71], [1, 74], [1, 76], [1, 77], [1, 78], [1, 79], [1, 81], [1, 82], [1, 83], [1, 84], [1, 88], [1, 89], 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\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l6-s4/instruction.md b/tasks/construct-mc-max-clique-l6-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..304eda61ccc6db75eb1dbad5c4e3ffb1405bcea7
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/instruction.md
@@ -0,0 +1,8 @@
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+
+Find a clique of size at least 13 in G: a set of at least 13 vertices that are pairwise adjacent.
+
+Answer format: {"clique": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-clique-l6-s4/solution/solve.sh b/tasks/construct-mc-max-clique-l6-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..cafba0b8d1ae9077034698563b2bc7351f6489df
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [19, 29, 37, 43, 44, 52, 53, 57, 76, 80, 95, 98, 119]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-clique-l6-s4/task.toml b/tasks/construct-mc-max-clique-l6-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..96022340f7f9af383b9bc8c54b90151a96f47955
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-clique-l6-s4"
+version = "0.2.0"
+description = "construct/mc_max_clique"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_clique"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_clique"
+problem_key = "graph_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "MathConstraint/max_clique"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-clique-l6-s4/tests/check.py b/tasks/construct-mc-max-clique-l6-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3f70dbd5b155a3514c2102aa4ad460201495210
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/tests/check.py
@@ -0,0 +1,18 @@
+"""Clique of size >= k in a given graph (MathConstraint max_clique decision version, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"clique has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) not in E:
+            raise Invalid(f"vertices {u} and {v} are not adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-clique-l6-s4/tests/instance.json b/tasks/construct-mc-max-clique-l6-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..13b2dcde91598e584c81d1cbef19ad25c41658f5
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/tests/instance.json
@@ -0,0 +1 @@
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110], [109, 111], [109, 112], [109, 113], [109, 115], [109, 116], [109, 117], [109, 118], [110, 111], [110, 112], [110, 113], [110, 114], [110, 115], [110, 116], [110, 117], [110, 118], [110, 119], [111, 112], [111, 113], [111, 114], [111, 116], [111, 117], [111, 119], [112, 113], [112, 114], [112, 115], [112, 116], [112, 117], [112, 119], [113, 117], [113, 118], [114, 116], [114, 118], [115, 116], [115, 117], [115, 118], [116, 117], [117, 118], [118, 119]], "family": "mc_max_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-clique-l6-s4/tests/run.py b/tasks/construct-mc-max-clique-l6-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-clique-l6-s4/tests/test.sh b/tasks/construct-mc-max-clique-l6-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-clique-l6-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/environment/instance.json b/tasks/construct-mc-max-independent-set-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..adcb59698e10da4a7dede6b34af033c1868b48c0
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 7, "edges": [[0, 1], [0, 4], [0, 8], [0, 11], [0, 16], [1, 7], [1, 13], [1, 17], [1, 19], [2, 3], [2, 4], [2, 9], [2, 11], [2, 14], [2, 17], [3, 4], [3, 8], [3, 16], [4, 11], [4, 13], [4, 16], [5, 10], [5, 11], [5, 14], [5, 19], [6, 9], [6, 11], [6, 12], [6, 15], [8, 11], [8, 16], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 18], [10, 11], [10, 15], [11, 15], [11, 16], [11, 17], [12, 15], [12, 19], [13, 16], [13, 17], [13, 18], [13, 19], [14, 15], [14, 16], [14, 17], [15, 16], [16, 19], [18, 19]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/instruction.md b/tasks/construct-mc-max-independent-set-l1-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..be7e11ab38fd3ead1e8cd0832d939cae55c7ce79
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 20 vertices numbered 0..19 and 54 edges:
+(0,1), (0,4), (0,8), (0,11), (0,16), (1,7), (1,13), (1,17), (1,19), (2,3), (2,4), (2,9), (2,11), (2,14), (2,17), (3,4), (3,8), (3,16), (4,11), (4,13), (4,16), (5,10), (5,11), (5,14), (5,19), (6,9), (6,11), (6,12), (6,15), (8,11), (8,16), (9,11), (9,12), (9,13), (9,14), (9,16), (9,18), (10,11), (10,15), (11,15), (11,16), (11,17), (12,15), (12,19), (13,16), (13,17), (13,18), (13,19), (14,15), (14,16), (14,17), (15,16), (16,19), (18,19)
+
+Find an independent set of size at least 7 in G: a set of at least 7 vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/solution/solve.sh b/tasks/construct-mc-max-independent-set-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5c0edaebfa702a5dc691bca1e998e6975a4f8b2e
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [0, 3, 5, 7, 15, 17, 18]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/task.toml b/tasks/construct-mc-max-independent-set-l1-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..a9e085bd4c990c685877e20d82139fa06c6b8be3
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-independent-set-l1-s0"
+version = "0.2.0"
+description = "construct/mc_max_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "MathConstraint/max_independent_set"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/tests/check.py b/tasks/construct-mc-max-independent-set-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/tests/instance.json b/tasks/construct-mc-max-independent-set-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..adcb59698e10da4a7dede6b34af033c1868b48c0
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 7, "edges": [[0, 1], [0, 4], [0, 8], [0, 11], [0, 16], [1, 7], [1, 13], [1, 17], [1, 19], [2, 3], [2, 4], [2, 9], [2, 11], [2, 14], [2, 17], [3, 4], [3, 8], [3, 16], [4, 11], [4, 13], [4, 16], [5, 10], [5, 11], [5, 14], [5, 19], [6, 9], [6, 11], [6, 12], [6, 15], [8, 11], [8, 16], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 18], [10, 11], [10, 15], [11, 15], [11, 16], [11, 17], [12, 15], [12, 19], [13, 16], [13, 17], [13, 18], [13, 19], [14, 15], [14, 16], [14, 17], [15, 16], [16, 19], [18, 19]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/tests/run.py b/tasks/construct-mc-max-independent-set-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-independent-set-l1-s0/tests/test.sh b/tasks/construct-mc-max-independent-set-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l1-s7/instruction.md b/tasks/construct-mc-max-independent-set-l1-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4ab350b220ef6935b6a8cc9e3e73f84a58311ca1
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s7/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 20 vertices numbered 0..19 and 48 edges:
+(0,8), (1,6), (1,7), (1,9), (1,11), (1,13), (1,16), (2,4), (2,5), (2,10), (2,18), (3,6), (3,8), (3,16), (3,19), (4,9), (4,10), (4,19), (5,9), (5,10), (5,11), (5,13), (5,16), (5,17), (6,7), (6,12), (6,14), (6,17), (7,19), (8,10), (8,12), (8,16), (8,17), (9,11), (9,16), (9,19), (10,12), (10,14), (10,15), (10,16), (10,17), (11,16), (11,18), (12,16), (12,19), (13,17), (14,16), (15,18)
+
+Find an independent set of size at least 7 in G: a set of at least 7 vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-independent-set-l1-s7/task.toml b/tasks/construct-mc-max-independent-set-l1-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..8f4b2a11d2bb822d1aa83b8d61efe4dc2be7221d
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-independent-set-l1-s7"
+version = "0.2.0"
+description = "construct/mc_max_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "MathConstraint/max_independent_set"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l1-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/environment/instance.json b/tasks/construct-mc-max-independent-set-l1-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5def2abb4c8a1568d66517e9f8ac68bd37c1b953
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 7, "edges": [[0, 5], [0, 6], [0, 9], [0, 18], [1, 5], [1, 16], [1, 17], [1, 19], [2, 7], [2, 9], [2, 10], [2, 13], [2, 15], [2, 17], [3, 9], [3, 10], [4, 9], [4, 11], [4, 12], [4, 14], [4, 15], [4, 16], [4, 17], [5, 6], [6, 9], [6, 12], [6, 15], [7, 13], [7, 14], [7, 17], [8, 9], [8, 11], [8, 17], [9, 18], [9, 19], [10, 11], [10, 16], [10, 17], [11, 17], [11, 19], [12, 14], [12, 17], [12, 18], [13, 15], [14, 18], [15, 17], [15, 18], [15, 19], [18, 19]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/instruction.md b/tasks/construct-mc-max-independent-set-l1-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..774c17900674cc91c8e5670ff5d5a7d9f305b2e9
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 20 vertices numbered 0..19 and 49 edges:
+(0,5), (0,6), (0,9), (0,18), (1,5), (1,16), (1,17), (1,19), (2,7), (2,9), (2,10), (2,13), (2,15), (2,17), (3,9), (3,10), (4,9), (4,11), (4,12), (4,14), (4,15), (4,16), (4,17), (5,6), (6,9), (6,12), (6,15), (7,13), (7,14), (7,17), (8,9), (8,11), (8,17), (9,18), (9,19), (10,11), (10,16), (10,17), (11,17), (11,19), (12,14), (12,17), (12,18), (13,15), (14,18), (15,17), (15,18), (15,19), (18,19)
+
+Find an independent set of size at least 7 in G: a set of at least 7 vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/solution/solve.sh b/tasks/construct-mc-max-independent-set-l1-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f81e8b91a3ef8d9f3e31bfae5ba6bad501216f83
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [0, 2, 3, 8, 14, 16, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/task.toml b/tasks/construct-mc-max-independent-set-l1-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..d9d342aa16d659edf9d1bd54b284026579a9d7ec
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-independent-set-l1-s9"
+version = "0.2.0"
+description = "construct/mc_max_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "MathConstraint/max_independent_set"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/tests/check.py b/tasks/construct-mc-max-independent-set-l1-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/tests/instance.json b/tasks/construct-mc-max-independent-set-l1-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5def2abb4c8a1568d66517e9f8ac68bd37c1b953
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 20, "k": 7, "edges": [[0, 5], [0, 6], [0, 9], [0, 18], [1, 5], [1, 16], [1, 17], [1, 19], [2, 7], [2, 9], [2, 10], [2, 13], [2, 15], [2, 17], [3, 9], [3, 10], [4, 9], [4, 11], [4, 12], [4, 14], [4, 15], [4, 16], [4, 17], [5, 6], [6, 9], [6, 12], [6, 15], [7, 13], [7, 14], [7, 17], [8, 9], [8, 11], [8, 17], [9, 18], [9, 19], [10, 11], [10, 16], [10, 17], [11, 17], [11, 19], [12, 14], [12, 17], [12, 18], [13, 15], [14, 18], [15, 17], [15, 18], [15, 19], [18, 19]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/tests/run.py b/tasks/construct-mc-max-independent-set-l1-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-independent-set-l1-s9/tests/test.sh b/tasks/construct-mc-max-independent-set-l1-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l1-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/environment/instance.json b/tasks/construct-mc-max-independent-set-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b5ec0eeb7915c5273cf70826aa870b877e5540a8
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 16, "edges": [[0, 4], [0, 5], [0, 6], [0, 10], [0, 15], [0, 17], [0, 23], [0, 24], [0, 28], [0, 31], [0, 32], [0, 42], [0, 44], [0, 51], [0, 54], [0, 56], [0, 57], [0, 59], [0, 60], [0, 61], [0, 62], [0, 63], [0, 64], [0, 67], [0, 68], [0, 71], [0, 74], [0, 77], [0, 81], [0, 84], [0, 85], [1, 2], [1, 3], [1, 6], [1, 7], [1, 8], [1, 9], [1, 13], [1, 14], [1, 15], [1, 16], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 27], [1, 36], [1, 37], [1, 39], [1, 40], [1, 44], [1, 45], [1, 48], [1, 54], [1, 55], [1, 56], [1, 64], [1, 66], [1, 67], [1, 68], [1, 79], [1, 81], [1, 86], [1, 87], [2, 10], [2, 11], [2, 13], [2, 15], [2, 17], [2, 22], [2, 29], [2, 32], [2, 33], [2, 34], [2, 35], [2, 37], [2, 41], [2, 47], [2, 48], [2, 51], [2, 52], [2, 53], [2, 57], [2, 60], [2, 64], [2, 66], [2, 69], [2, 71], [2, 79], [2, 81], [2, 82], [2, 83], [2, 86], [2, 88], [3, 5], [3, 17], [3, 18], [3, 19], [3, 28], [3, 29], [3, 32], [3, 42], [3, 44], [3, 45], [3, 51], [3, 52], [3, 63], 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\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/instruction.md b/tasks/construct-mc-max-independent-set-l5-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..f96cf4f2a4ff6355c730cebda2a776a4465bfe18
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 90 vertices numbered 0..89 and 1203 edges:
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+
+Find an independent set of size at least 16 in G: a set of at least 16 vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/solution/solve.sh b/tasks/construct-mc-max-independent-set-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..05b7fd25d15416c53e4db138e5e23be485a8dff2
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [16, 24, 29, 31, 32, 41, 44, 45, 49, 55, 71, 78, 79, 80, 87, 89]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/task.toml b/tasks/construct-mc-max-independent-set-l5-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..b06f030502b7fc0c8cd96b7b94a96cacad061cda
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-independent-set-l5-s1"
+version = "0.2.0"
+description = "construct/mc_max_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "MathConstraint/max_independent_set"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/tests/check.py b/tasks/construct-mc-max-independent-set-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/tests/instance.json b/tasks/construct-mc-max-independent-set-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b5ec0eeb7915c5273cf70826aa870b877e5540a8
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 16, "edges": [[0, 4], [0, 5], [0, 6], [0, 10], [0, 15], [0, 17], [0, 23], [0, 24], [0, 28], [0, 31], [0, 32], [0, 42], [0, 44], [0, 51], [0, 54], [0, 56], [0, 57], [0, 59], [0, 60], [0, 61], [0, 62], [0, 63], [0, 64], [0, 67], [0, 68], [0, 71], [0, 74], [0, 77], [0, 81], [0, 84], [0, 85], [1, 2], [1, 3], [1, 6], [1, 7], [1, 8], [1, 9], [1, 13], [1, 14], [1, 15], [1, 16], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 27], [1, 36], [1, 37], [1, 39], [1, 40], [1, 44], [1, 45], [1, 48], [1, 54], [1, 55], [1, 56], [1, 64], [1, 66], [1, 67], [1, 68], [1, 79], [1, 81], [1, 86], [1, 87], [2, 10], [2, 11], [2, 13], [2, 15], [2, 17], [2, 22], [2, 29], [2, 32], [2, 33], [2, 34], [2, 35], [2, 37], [2, 41], [2, 47], [2, 48], [2, 51], [2, 52], [2, 53], [2, 57], [2, 60], [2, 64], [2, 66], [2, 69], [2, 71], [2, 79], [2, 81], [2, 82], [2, 83], [2, 86], [2, 88], [3, 5], [3, 17], [3, 18], [3, 19], [3, 28], [3, 29], [3, 32], [3, 42], [3, 44], [3, 45], [3, 51], [3, 52], [3, 63], [3, 69], [3, 75], [3, 76], [3, 83], [3, 84], [3, 87], [4, 5], [4, 6], [4, 9], [4, 12], [4, 15], [4, 17], [4, 26], [4, 30], [4, 31], [4, 34], [4, 36], [4, 42], [4, 46], [4, 47], [4, 49], [4, 56], [4, 64], [4, 68], [4, 74], [4, 77], [4, 79], [5, 12], [5, 15], [5, 16], [5, 17], [5, 18], [5, 23], [5, 26], [5, 27], [5, 28], [5, 30], [5, 31], [5, 36], [5, 37], [5, 40], [5, 45], [5, 46], [5, 48], [5, 51], [5, 58], [5, 61], [5, 63], [5, 66], [5, 67], [5, 68], [5, 69], [5, 70], [5, 72], [5, 81], [5, 84], [6, 10], [6, 11], [6, 13], [6, 14], [6, 16], [6, 18], [6, 20], [6, 23], [6, 29], [6, 31], [6, 33], [6, 37], [6, 45], [6, 48], [6, 53], [6, 56], [6, 59], [6, 64], [6, 68], [6, 70], [6, 73], [6, 76], [6, 82], [6, 86], [7, 8], [7, 10], [7, 12], [7, 15], [7, 16], [7, 19], [7, 21], [7, 25], [7, 27], [7, 34], [7, 35], [7, 36], [7, 39], [7, 46], [7, 53], [7, 55], [7, 61], [7, 62], [7, 66], [7, 72], [7, 74], [7, 75], [7, 80], [7, 81], [7, 82], [7, 86], [7, 88], [7, 89], [8, 9], [8, 12], [8, 13], [8, 17], [8, 20], [8, 22], [8, 25], [8, 33], [8, 36], [8, 40], [8, 50], [8, 51], [8, 52], [8, 55], [8, 57], [8, 62], [8, 66], [8, 79], [8, 81], [8, 82], [8, 85], [9, 15], [9, 17], [9, 19], [9, 21], [9, 29], [9, 31], [9, 33], [9, 34], [9, 35], [9, 36], [9, 42], [9, 43], [9, 47], [9, 49], [9, 53], [9, 55], [9, 56], [9, 59], [9, 60], [9, 62], [9, 64], [9, 66], [9, 70], [9, 78], [9, 79], [9, 82], [9, 84], [9, 88], [10, 11], [10, 15], [10, 19], [10, 21], [10, 23], [10, 26], [10, 30], [10, 33], [10, 35], [10, 38], [10, 40], [10, 41], [10, 42], [10, 44], [10, 48], [10, 49], [10, 53], [10, 54], [10, 57], [10, 59], [10, 67], [10, 69], [10, 70], [10, 76], [10, 78], [10, 79], [10, 83], [10, 84], [10, 88], [10, 89], [11, 17], [11, 19], [11, 20], [11, 21], [11, 22], [11, 25], [11, 27], [11, 39], [11, 40], [11, 43], [11, 44], [11, 45], [11, 50], [11, 51], [11, 52], [11, 53], [11, 54], [11, 55], [11, 63], [11, 67], [11, 72], [11, 74], [11, 75], [11, 77], [11, 78], [11, 84], [11, 85], [11, 87], [11, 88], [12, 13], [12, 14], [12, 16], [12, 26], [12, 29], [12, 36], [12, 39], [12, 40], [12, 44], [12, 45], [12, 48], [12, 57], [12, 58], [12, 62], [12, 63], [12, 68], [12, 73], [12, 75], [12, 78], [12, 79], [12, 81], [13, 17], [13, 18], [13, 21], [13, 22], [13, 23], [13, 25], [13, 28], [13, 29], [13, 37], [13, 39], [13, 40], [13, 43], [13, 49], [13, 51], [13, 52], [13, 53], [13, 58], [13, 60], [13, 62], [13, 66], [13, 67], [13, 68], [13, 69], [13, 73], [13, 74], [13, 76], [13, 78], [13, 80], [13, 82], [13, 84], [13, 87], [13, 88], [13, 89], [14, 16], [14, 19], [14, 20], [14, 22], [14, 26], [14, 29], [14, 30], [14, 37], [14, 40], [14, 45], [14, 49], [14, 50], [14, 51], [14, 53], [14, 55], [14, 58], [14, 61], [14, 62], [14, 65], [14, 67], [14, 73], [14, 74], [14, 76], [14, 83], [14, 85], [15, 24], [15, 29], [15, 30], [15, 31], [15, 32], [15, 36], [15, 37], [15, 44], [15, 48], [15, 51], [15, 54], [15, 55], [15, 59], [15, 60], [15, 61], [15, 63], [15, 64], [15, 67], [15, 74], [15, 75], [15, 76], [15, 85], [15, 86], [15, 87], [15, 88], [16, 18], [16, 21], [16, 26], [16, 36], [16, 42], [16, 50], [16, 56], [16, 58], [16, 65], [16, 69], [16, 74], [16, 81], [16, 82], [16, 83], [17, 24], [17, 27], [17, 28], [17, 31], [17, 32], [17, 33], [17, 46], [17, 59], [17, 61], [17, 66], [17, 68], [17, 71], [17, 75], [17, 77], [17, 78], [17, 81], [17, 83], [17, 84], [17, 88], [18, 24], [18, 28], [18, 34], [18, 40], [18, 41], [18, 43], [18, 44], [18, 45], [18, 47], [18, 49], [18, 50], [18, 53], [18, 54], [18, 56], [18, 57], [18, 58], [18, 62], [18, 64], [18, 67], [18, 71], [18, 76], [18, 78], [18, 79], [18, 82], [18, 86], [19, 20], [19, 21], [19, 26], [19, 27], [19, 28], [19, 32], [19, 33], [19, 35], [19, 37], [19, 40], [19, 43], [19, 44], [19, 55], [19, 62], [19, 67], [19, 68], [19, 74], [19, 76], [19, 77], [19, 78], [19, 84], [19, 86], [19, 87], [20, 22], [20, 36], [20, 42], [20, 44], [20, 48], [20, 51], [20, 56], [20, 61], [20, 66], [20, 67], [20, 68], [20, 70], [20, 72], [20, 74], [20, 75], [20, 86], [21, 22], [21, 24], [21, 25], [21, 35], [21, 40], [21, 59], [21, 61], [21, 64], [21, 69], [21, 74], [21, 79], [21, 80], [21, 82], [21, 84], [21, 85], [22, 31], [22, 33], [22, 34], [22, 37], [22, 39], [22, 47], [22, 52], [22, 54], [22, 58], [22, 60], [22, 61], [22, 63], [22, 67], [22, 72], [22, 73], [22, 75], [22, 84], [22, 88], [22, 89], [23, 25], [23, 29], [23, 31], [23, 32], [23, 33], [23, 36], [23, 38], [23, 41], [23, 42], [23, 45], [23, 46], [23, 49], [23, 50], [23, 52], [23, 67], [23, 69], [23, 70], [23, 71], [23, 75], [23, 76], [23, 79], [23, 80], [23, 81], [23, 86], [23, 88], [24, 26], [24, 28], [24, 35], [24, 38], [24, 39], [24, 46], [24, 53], [24, 58], [24, 61], [24, 63], [24, 66], [24, 69], [24, 74], [24, 77], [24, 81], [24, 83], [25, 30], [25, 34], [25, 39], [25, 41], [25, 43], [25, 52], [25, 54], [25, 56], [25, 61], [25, 64], [25, 70], [25, 71], [25, 77], [25, 86], [25, 87], [26, 27], [26, 39], [26, 42], [26, 45], [26, 46], [26, 53], [26, 54], [26, 56], [26, 58], 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[31, 68], [31, 69], [31, 72], [31, 73], [31, 74], [31, 76], [31, 82], [31, 85], [32, 34], [32, 36], [32, 37], [32, 38], [32, 42], [32, 43], [32, 46], [32, 51], [32, 52], [32, 58], [32, 59], [32, 60], [32, 62], [32, 65], [32, 67], [32, 68], [32, 72], [32, 77], [32, 82], [32, 83], [32, 86], [33, 35], [33, 38], [33, 40], [33, 45], [33, 47], [33, 52], [33, 54], [33, 56], [33, 59], [33, 61], [33, 66], [33, 69], [33, 71], [33, 73], [33, 74], [33, 76], [33, 81], [33, 82], [33, 84], [33, 85], [33, 87], [34, 37], [34, 38], [34, 43], [34, 44], [34, 48], [34, 49], [34, 51], [34, 54], [34, 55], [34, 65], [34, 72], [34, 76], [34, 83], [34, 89], [35, 37], [35, 40], [35, 56], [35, 62], [35, 77], [35, 87], [35, 88], [36, 41], [36, 45], [36, 49], [36, 50], [36, 52], [36, 57], [36, 58], [36, 63], [36, 64], [36, 65], [36, 70], [36, 77], [36, 78], [36, 80], [36, 81], [36, 82], [36, 88], [36, 89], [37, 41], [37, 42], [37, 47], [37, 48], [37, 49], [37, 50], [37, 52], [37, 54], [37, 67], [37, 75], [37, 76], 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[43, 81], [43, 84], [43, 85], [43, 86], [43, 87], [43, 88], [44, 46], [44, 47], [44, 51], [44, 62], [44, 64], [44, 67], [44, 75], [44, 83], [44, 86], [45, 48], [45, 52], [45, 56], [45, 57], [45, 59], [45, 61], [45, 62], [45, 63], [45, 67], [45, 68], [45, 70], [45, 83], [46, 51], [46, 53], [46, 54], [46, 59], [46, 62], [46, 68], [46, 69], [46, 78], [46, 81], [46, 82], [46, 84], [46, 87], [46, 89], [47, 49], [47, 56], [47, 60], [47, 62], [47, 65], [47, 67], [47, 69], [47, 72], [47, 78], [47, 79], [47, 80], [47, 81], [47, 84], [47, 86], [47, 89], [48, 50], [48, 60], [48, 61], [48, 65], [48, 66], [48, 70], [48, 75], [48, 77], [48, 82], [48, 83], [49, 52], [49, 56], [49, 57], [49, 59], [49, 61], [49, 63], [49, 64], [49, 73], [49, 77], [50, 51], [50, 53], [50, 54], [50, 68], [50, 70], [50, 76], [50, 79], [50, 88], [51, 52], [51, 55], [51, 58], [51, 64], [51, 69], [51, 79], [51, 83], [51, 86], [51, 89], [52, 61], [52, 70], [52, 73], [52, 75], [52, 77], [52, 80], [52, 81], [52, 84], [52, 85], [52, 88], [53, 55], [53, 59], [53, 65], [53, 68], [53, 75], [53, 79], [53, 81], [53, 86], [54, 55], [54, 56], [54, 60], [54, 64], [54, 65], [54, 70], [54, 77], [55, 56], [55, 57], [55, 59], [55, 60], [55, 61], [55, 62], [55, 64], [55, 65], [55, 66], [55, 67], [55, 68], [55, 69], [55, 72], [55, 75], [55, 77], [55, 83], [55, 86], [56, 58], [56, 60], [56, 63], [56, 65], [56, 68], [56, 71], [56, 74], [56, 77], [56, 79], [56, 84], [56, 86], [56, 89], [57, 59], [57, 60], [57, 61], [57, 63], [57, 79], [57, 83], [57, 85], [57, 86], [57, 87], [58, 61], [58, 63], [58, 65], [58, 84], [59, 67], [59, 70], [59, 72], [59, 82], [59, 84], [60, 65], [60, 69], [60, 73], [60, 74], [60, 78], [60, 81], [60, 82], [60, 83], [60, 84], [61, 63], [61, 68], [61, 69], [61, 70], [61, 74], [61, 77], [61, 78], [61, 80], [61, 83], [62, 63], [62, 64], [62, 65], [62, 77], [62, 78], [62, 79], [62, 81], [62, 82], [62, 84], [62, 88], [63, 68], [63, 71], [63, 75], [63, 81], [63, 86], [64, 74], [64, 77], [64, 80], [64, 87], [65, 70], [65, 73], [65, 77], [65, 85], [65, 86], [65, 87], [66, 73], [66, 74], [66, 81], [66, 83], [66, 85], [66, 86], [66, 87], [66, 89], [67, 70], [67, 75], [67, 77], [67, 81], [67, 83], [67, 84], [67, 86], [68, 75], [68, 83], [69, 75], [69, 76], [69, 77], [69, 78], [69, 79], [69, 81], [69, 83], [70, 73], [70, 76], [70, 78], [70, 81], [70, 89], [71, 73], [71, 77], [71, 81], [71, 82], [71, 84], [71, 85], [72, 73], [72, 81], [72, 82], [72, 83], [72, 86], [72, 89], [73, 77], [73, 78], [73, 80], [73, 82], [74, 76], [74, 77], [75, 78], [75, 85], [76, 78], [76, 84], [76, 87], [77, 78], [77, 82], [77, 85], [77, 86], [78, 84], [78, 86], [79, 82], [79, 83], [79, 84], [79, 85], [80, 86], [81, 86], [81, 88], [82, 86], [83, 86], [84, 85], [85, 86], [85, 88], [85, 89], [86, 88]], "family": "mc_max_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/tests/run.py b/tasks/construct-mc-max-independent-set-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-independent-set-l5-s1/tests/test.sh b/tasks/construct-mc-max-independent-set-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l5-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/environment/instance.json b/tasks/construct-mc-max-independent-set-l5-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..713051bb2ab4723acd2dc8991b8e30aeba162e85
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 16, "edges": [[0, 1], [0, 5], [0, 6], [0, 9], [0, 11], [0, 14], [0, 15], [0, 22], [0, 24], [0, 25], [0, 26], [0, 28], [0, 36], [0, 39], [0, 46], [0, 51], [0, 52], [0, 57], [0, 62], [0, 68], [0, 70], [0, 71], [0, 74], [0, 79], [0, 81], [0, 82], [0, 83], [0, 86], [1, 4], [1, 7], [1, 8], [1, 12], [1, 21], [1, 26], [1, 31], [1, 32], [1, 39], [1, 42], [1, 47], [1, 48], [1, 52], [1, 53], [1, 59], [1, 60], [1, 62], [1, 68], [1, 70], [1, 72], [1, 74], [1, 75], [1, 77], [1, 79], [1, 81], [1, 82], [1, 83], [2, 6], [2, 12], [2, 15], [2, 19], [2, 23], [2, 24], [2, 29], [2, 34], [2, 38], [2, 39], [2, 43], [2, 45], [2, 47], [2, 50], [2, 52], [2, 58], [2, 59], [2, 63], [2, 75], [2, 81], [2, 85], [3, 5], [3, 6], [3, 20], [3, 25], [3, 26], [3, 29], [3, 33], [3, 35], [3, 40], [3, 43], [3, 45], [3, 50], [3, 51], [3, 53], [3, 55], [3, 61], [3, 65], [3, 69], [3, 70], [3, 71], [3, 76], [3, 78], [3, 81], [3, 84], [4, 19], [4, 24], [4, 26], [4, 32], [4, 33], [4, 35], [4, 42], [4, 43], [4, 45], 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\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/instruction.md b/tasks/construct-mc-max-independent-set-l5-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3f4f5b8b6a38d0b844a21783060d17ce503500a5
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 90 vertices numbered 0..89 and 1115 edges:
+(0,1), (0,5), (0,6), (0,9), (0,11), (0,14), (0,15), (0,22), (0,24), (0,25), (0,26), (0,28), (0,36), (0,39), (0,46), (0,51), (0,52), (0,57), (0,62), (0,68), (0,70), (0,71), (0,74), (0,79), (0,81), (0,82), (0,83), (0,86), (1,4), (1,7), (1,8), (1,12), (1,21), (1,26), (1,31), (1,32), (1,39), (1,42), (1,47), (1,48), (1,52), (1,53), (1,59), (1,60), (1,62), (1,68), (1,70), (1,72), (1,74), (1,75), (1,77), (1,79), (1,81), (1,82), (1,83), (2,6), (2,12), (2,15), (2,19), (2,23), (2,24), (2,29), (2,34), (2,38), (2,39), (2,43), (2,45), (2,47), (2,50), (2,52), (2,58), (2,59), (2,63), (2,75), (2,81), (2,85), (3,5), (3,6), (3,20), (3,25), (3,26), (3,29), (3,33), (3,35), (3,40), (3,43), (3,45), (3,50), (3,51), (3,53), (3,55), (3,61), (3,65), (3,69), (3,70), (3,71), (3,76), (3,78), (3,81), (3,84), (4,19), (4,24), (4,26), (4,32), (4,33), (4,35), (4,42), (4,43), (4,45), (4,46), (4,51), (4,62), (4,67), (4,72), (4,73), (4,74), (4,75), (4,77), (4,78), (4,79), (4,80), (4,83), (4,84), (4,86), (5,8), (5,9), 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+
+Find an independent set of size at least 16 in G: a set of at least 16 vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/solution/solve.sh b/tasks/construct-mc-max-independent-set-l5-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f6f5135ea0952fdd81de01d15e228e9d60aa4f87
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [2, 9, 11, 13, 25, 35, 36, 37, 54, 61, 65, 68, 70, 76, 80, 88]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/task.toml b/tasks/construct-mc-max-independent-set-l5-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..b2a6b505cbd6ed63b9e6dab5c570216ff932ed40
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-independent-set-l5-s6"
+version = "0.2.0"
+description = "construct/mc_max_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "MathConstraint/max_independent_set"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/tests/check.py b/tasks/construct-mc-max-independent-set-l5-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/tests/instance.json b/tasks/construct-mc-max-independent-set-l5-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..713051bb2ab4723acd2dc8991b8e30aeba162e85
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 16, "edges": [[0, 1], [0, 5], [0, 6], [0, 9], [0, 11], [0, 14], [0, 15], [0, 22], [0, 24], [0, 25], [0, 26], [0, 28], [0, 36], [0, 39], [0, 46], [0, 51], [0, 52], [0, 57], [0, 62], [0, 68], [0, 70], [0, 71], [0, 74], [0, 79], [0, 81], [0, 82], [0, 83], [0, 86], [1, 4], [1, 7], [1, 8], [1, 12], [1, 21], [1, 26], [1, 31], [1, 32], [1, 39], [1, 42], [1, 47], [1, 48], [1, 52], [1, 53], [1, 59], [1, 60], [1, 62], [1, 68], [1, 70], [1, 72], [1, 74], [1, 75], [1, 77], [1, 79], [1, 81], [1, 82], [1, 83], [2, 6], [2, 12], [2, 15], [2, 19], [2, 23], [2, 24], [2, 29], [2, 34], [2, 38], [2, 39], [2, 43], [2, 45], [2, 47], [2, 50], [2, 52], [2, 58], [2, 59], [2, 63], [2, 75], [2, 81], [2, 85], [3, 5], [3, 6], [3, 20], [3, 25], [3, 26], [3, 29], [3, 33], [3, 35], [3, 40], [3, 43], [3, 45], [3, 50], [3, 51], [3, 53], [3, 55], [3, 61], [3, 65], [3, 69], [3, 70], [3, 71], [3, 76], [3, 78], [3, 81], [3, 84], [4, 19], [4, 24], [4, 26], [4, 32], [4, 33], [4, 35], [4, 42], [4, 43], [4, 45], 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\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/tests/run.py b/tasks/construct-mc-max-independent-set-l5-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-max-independent-set-l5-s6/tests/test.sh b/tasks/construct-mc-max-independent-set-l5-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/environment/Dockerfile b/tasks/construct-mc-max-independent-set-l5-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/environment/instance.json b/tasks/construct-mc-max-independent-set-l5-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fd6a1e42d601e94890bafea1647b73db60efd274
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/environment/instance.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/instruction.md b/tasks/construct-mc-max-independent-set-l5-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..6c41bb6c839806a9e9eee44e1c8bd0eb03981a97
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/instruction.md
@@ -0,0 +1,8 @@
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+
+Find an independent set of size at least 16 in G: a set of at least 16 vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/solution/solve.sh b/tasks/construct-mc-max-independent-set-l5-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f14ab4a440cba313d88f2d00fbe2cf35222df1c7
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [3, 6, 17, 27, 35, 36, 37, 38, 49, 52, 54, 55, 59, 75, 82, 84]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/task.toml b/tasks/construct-mc-max-independent-set-l5-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..00509cad94b5cfa1af610547a87bb9f8711967ee
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-max-independent-set-l5-s8"
+version = "0.2.0"
+description = "construct/mc_max_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "mc_max_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "mc_max_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "MathConstraint/max_independent_set"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/tests/check.py b/tasks/construct-mc-max-independent-set-l5-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..adce413e8578d996549583b990e4ff559f38ed41
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/tests/check.py
@@ -0,0 +1,18 @@
+"""Independent set of size >= k in a given graph (MathConstraint max_independent_set, CC-BY-4.0)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) < k:
+        raise Invalid(f"set has {len(S)} vertices, need at least {k}")
+    E = {(u, v) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(S), 2):
+        if (u, v) in E:
+            raise Invalid(f"vertices {u} and {v} are adjacent")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/tests/instance.json b/tasks/construct-mc-max-independent-set-l5-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fd6a1e42d601e94890bafea1647b73db60efd274
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 90, "k": 16, "edges": [[0, 7], [0, 9], [0, 14], [0, 17], [0, 18], [0, 28], [0, 33], [0, 35], [0, 41], [0, 42], [0, 45], [0, 55], [0, 61], [0, 63], [0, 65], [0, 80], [0, 85], [0, 86], [0, 87], [1, 4], [1, 5], [1, 9], [1, 10], [1, 16], [1, 21], [1, 28], [1, 29], [1, 33], [1, 34], [1, 37], [1, 41], [1, 42], [1, 43], [1, 48], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 66], [1, 69], [1, 75], [1, 76], [1, 79], [1, 85], [1, 89], [2, 3], [2, 5], [2, 8], [2, 9], [2, 10], [2, 12], [2, 13], [2, 16], [2, 19], [2, 20], [2, 21], [2, 29], [2, 36], [2, 37], [2, 39], [2, 45], [2, 50], [2, 53], [2, 59], [2, 62], [2, 64], [2, 68], [2, 69], [2, 72], [2, 75], [2, 78], [2, 87], [2, 89], [3, 8], [3, 9], [3, 10], [3, 12], [3, 18], [3, 20], [3, 26], [3, 28], [3, 29], [3, 32], [3, 33], [3, 42], [3, 51], [3, 53], [3, 57], [3, 58], [3, 60], [3, 77], [3, 89], [4, 6], [4, 23], [4, 24], [4, 26], [4, 27], [4, 32], [4, 33], [4, 43], [4, 44], [4, 49], [4, 50], [4, 53], [4, 54], [4, 56], [4, 62], [4, 67], 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\ No newline at end of file
diff --git a/tasks/construct-mc-max-independent-set-l5-s8/tests/run.py b/tasks/construct-mc-max-independent-set-l5-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-max-independent-set-l5-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-non-transitive-dice-l5-s1/instruction.md b/tasks/construct-mc-non-transitive-dice-l5-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..7c1e0d07106c31dbea48661ac025a6f60a2a055b
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-l5-s1/instruction.md
@@ -0,0 +1,7 @@
+Design 5 dice D_0, ..., D_4, each with 7 faces showing integers from 0..13 (values may repeat). Die D_i beats die D_j if, among the 49 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 24 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 5 for every i = 0..4.
+
+Find such dice.
+
+Answer format: {"dice": [[faces of D_0], ..., [faces of D_4]]}, each a list of 7 integers
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-non-transitive-dice-l5-s1/task.toml b/tasks/construct-mc-non-transitive-dice-l5-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..382f1f91cce60bff53ab3b5949a24fde329e94d7
--- /dev/null
+++ b/tasks/construct-mc-non-transitive-dice-l5-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-non-transitive-dice-l5-s1"
+version = "0.2.0"
+description = "construct/mc_non_transitive_dice"
+authors = []
+keywords = ["rlmath", "construct", "mc_non_transitive_dice"]
+
+[metadata]
+subset = "construct"
+family = "mc_non_transitive_dice"
+problem_key = "intransitive_dice"
+domain = "probability"
+tier = "competition"
+level = "5"
+source = "MathConstraint/non_transitive_dice"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-number-partitioning-l5-s2/instruction.md b/tasks/construct-mc-number-partitioning-l5-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a8253d79a896f297f7263ee8873d3b5eaac1ad86
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l5-s2/instruction.md
@@ -0,0 +1,7 @@
+Partition the integers 1, 2, ..., 53 into 3 disjoint subsets (numbered 0..2) that all have the same sum 477 (the total is 1431).
+
+Find such a partition.
+
+Answer format: {"x": [x_1, ..., x_53]}: a list of 53 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-number-partitioning-l5-s2/task.toml b/tasks/construct-mc-number-partitioning-l5-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..3669be8272d391879c40ede39a62ff9b82a2db24
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l5-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-number-partitioning-l5-s2"
+version = "0.2.0"
+description = "construct/mc_number_partitioning"
+authors = []
+keywords = ["rlmath", "construct", "mc_number_partitioning"]
+
+[metadata]
+subset = "construct"
+family = "mc_number_partitioning"
+problem_key = "equal_sum_partition_1_to_n"
+domain = "number_theory"
+tier = "competition"
+level = "5"
+source = "MathConstraint/number_partitioning"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-number-partitioning-l5-s5/instruction.md b/tasks/construct-mc-number-partitioning-l5-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..88b39904bad66058cd7edf2660f8e4c11539c9bd
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l5-s5/instruction.md
@@ -0,0 +1,7 @@
+Partition the integers 1, 2, ..., 66 into 3 disjoint subsets (numbered 0..2) that all have the same sum 737 (the total is 2211).
+
+Find such a partition.
+
+Answer format: {"x": [x_1, ..., x_66]}: a list of 66 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-number-partitioning-l5-s5/task.toml b/tasks/construct-mc-number-partitioning-l5-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..0cc095048a292ea6421c712589174fa9384a6b86
--- /dev/null
+++ b/tasks/construct-mc-number-partitioning-l5-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-number-partitioning-l5-s5"
+version = "0.2.0"
+description = "construct/mc_number_partitioning"
+authors = []
+keywords = ["rlmath", "construct", "mc_number_partitioning"]
+
+[metadata]
+subset = "construct"
+family = "mc_number_partitioning"
+problem_key = "equal_sum_partition_1_to_n"
+domain = "number_theory"
+tier = "competition"
+level = "5"
+source = "MathConstraint/number_partitioning"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ortholatin-l3-s3/instruction.md b/tasks/construct-mc-ortholatin-l3-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..df7daf83cfca0a8ab7f388f86813347e180c3773
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l3-s3/instruction.md
@@ -0,0 +1,5 @@
+Construct a pair of orthogonal Latin squares of order 12: two 12x12 arrays X and Y with entries in 0..11 such that every row and every column of X is a permutation of 0..11, the same holds for Y, and the 144 ordered pairs (X[i][j], Y[i][j]) are all distinct.
+
+Answer format: {"X": [[row 0], ..., [row 11]], "Y": [[row 0], ..., [row 11]]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-ortholatin-l3-s3/task.toml b/tasks/construct-mc-ortholatin-l3-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..f309c29301ab0cde67cbf31239fa1bc1d6abc334
--- /dev/null
+++ b/tasks/construct-mc-ortholatin-l3-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-ortholatin-l3-s3"
+version = "0.2.0"
+description = "construct/mc_ortholatin"
+authors = []
+keywords = ["rlmath", "construct", "mc_ortholatin"]
+
+[metadata]
+subset = "construct"
+family = "mc_ortholatin"
+problem_key = "orthogonal_latin_squares"
+domain = "combinatorics"
+tier = "competition"
+level = "3"
+source = "MathConstraint/ortholatin"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l3-s3/instruction.md b/tasks/construct-mc-pysms-chromatic-girth-l3-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c20a2d2a0619dbb9f085d89d2f316d1765f3c51d
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l3-s3/instruction.md
@@ -0,0 +1,8 @@
+Construct a simple undirected graph on the 19 vertices 0..18 such that:
+  - the graph has at least 25 edges
+  - the chromatic number is at most 5: the vertices can be coloured with colours 0..4 so that adjacent vertices get different colours (you must also give such a colouring)
+  - the girth is at least 5: the graph has no cycle of length less than 5 (a graph without cycles qualifies)
+
+Answer format: {"edges": [[u, v], ...], "coloring": [c_0, ..., c_18]} where each edge is a pair of distinct vertices in 0..18, listed once; coloring[i] is the colour (0..4) of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-chromatic-girth-l3-s3/task.toml b/tasks/construct-mc-pysms-chromatic-girth-l3-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..69e037da392ca6f978b248505c610b7c46156de6
--- /dev/null
+++ b/tasks/construct-mc-pysms-chromatic-girth-l3-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-chromatic-girth-l3-s3"
+version = "0.2.0"
+description = "construct/mc_pysms_chromatic_girth"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_chromatic_girth"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_chromatic_girth"
+problem_key = "graph_existence_chromatic_girth"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "MathConstraint/pysms_chromatic_girth"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/environment/Dockerfile b/tasks/construct-mc-pysms-graph-builder-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/environment/instance.json b/tasks/construct-mc-pysms-graph-builder-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5570d52a08a8611951c921872f050159cbf49e42
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 14, "required_edges": [], "max_degree": 6, "min_degree": 4, "max_chromatic_number": 4, "min_chromatic_number": 3, "min_edges": 21, "max_edges": 37, "family": "mc_pysms_graph_builder", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/instruction.md b/tasks/construct-mc-pysms-graph-builder-l4-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..d47cbf99ac9624adc1556479e88efa6bd75db1e3
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/instruction.md
@@ -0,0 +1,9 @@
+Construct a simple undirected graph on the 14 vertices 0..13 such that:
+  - every vertex has degree between 4 and 6 (inclusive)
+  - the number of edges is between 21 and 37 (inclusive)
+  - the chromatic number is at most 4: the vertices can be coloured with colours 0..3 so that adjacent vertices get different colours (you must also give such a colouring)
+  - the chromatic number is at least 3 (the graph has no proper colouring with 2 colours)
+
+Answer format: {"edges": [[u, v], ...], "coloring": [c_0, ..., c_13]} where each edge is a pair of distinct vertices in 0..13, listed once; coloring[i] is the colour (0..3) of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/solution/solve.sh b/tasks/construct-mc-pysms-graph-builder-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..93c60d4df265ed7a7b079828701c3e5257e222df
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 10], [0, 11], [0, 12], [0, 13], [1, 6], [1, 7], [1, 8], [1, 9], [1, 13], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 13], [4, 5], [4, 8], [4, 9], [5, 6], [5, 9], [5, 12], [6, 7], [6, 8], [6, 12], [7, 12], [7, 13], [8, 11], [10, 11], [10, 12], [10, 13], [11, 12], [11, 13]], "coloring": [1, 0, 0, 0, 2, 1, 3, 1, 1, 3, 3, 0, 2, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/task.toml b/tasks/construct-mc-pysms-graph-builder-l4-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..72e5c337147b340efe62416d6e7b8d86ab4418c4
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-graph-builder-l4-s1"
+version = "0.2.0"
+description = "construct/mc_pysms_graph_builder"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_graph_builder"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_graph_builder"
+problem_key = "graph_existence_graph_builder"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "MathConstraint/pysms_graph_builder"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/check.py b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/instance.json b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5570d52a08a8611951c921872f050159cbf49e42
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 14, "required_edges": [], "max_degree": 6, "min_degree": 4, "max_chromatic_number": 4, "min_chromatic_number": 3, "min_edges": 21, "max_edges": 37, "family": "mc_pysms_graph_builder", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/run.py b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/test.sh b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-graph-builder-l4-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/environment/Dockerfile b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/environment/instance.json b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..417a2bb0d0524df1d72f71050c58f24f0e123cfd
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 8, "required_edges": [], "max_independent_set": 2, "min_connectivity": 1, "family": "mc_pysms_independent_connectivity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/instruction.md b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..9c8c90cb65aadbbd54479f1199dcc544bf1372d1
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/instruction.md
@@ -0,0 +1,7 @@
+Construct a simple undirected graph on the 8 vertices 0..7 such that:
+  - the graph contains no independent set of size 3 (maximum independent set size at most 2)
+  - the vertex-connectivity is at least 1: deleting any set of fewer than 1 vertices leaves a connected graph
+
+Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..7, listed once
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/solution/solve.sh b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a411bb51ad0fd830529a244c60057cdaa691261e
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/task.toml b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..1759f6748c973fcacbbfd2fc9a3188215756cb60
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-independent-connectivity-l1-s1"
+version = "0.2.0"
+description = "construct/mc_pysms_independent_connectivity"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_independent_connectivity"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_independent_connectivity"
+problem_key = "graph_existence_independent_connectivity"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "MathConstraint/pysms_independent_connectivity"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/check.py b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/instance.json b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..417a2bb0d0524df1d72f71050c58f24f0e123cfd
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 8, "required_edges": [], "max_independent_set": 2, "min_connectivity": 1, "family": "mc_pysms_independent_connectivity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/run.py b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/test.sh b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l1-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/environment/Dockerfile b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/environment/instance.json b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..94a255a8015b5577634cd44daaa69211801c4213
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 20, "required_edges": [], "max_independent_set": 3, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/instruction.md b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c125bc1c14d989aca5d5b7cd41f80386d42dcc1e
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/instruction.md
@@ -0,0 +1,7 @@
+Construct a simple undirected graph on the 20 vertices 0..19 such that:
+  - the graph contains no independent set of size 4 (maximum independent set size at most 3)
+  - the vertex-connectivity is at least 4: deleting any set of fewer than 4 vertices leaves a connected graph
+
+Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..19, listed once
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/solution/solve.sh b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b4a4550b0ce568fa2a7f31bf686bba3e6d39e0fe
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 19], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 17], [6, 18], [6, 19], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 17], [9, 18], [9, 19], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [14, 15], [14, 16], [14, 17], [14, 18], [14, 19], [15, 16], [15, 17], [15, 18], [15, 19], [16, 17], [16, 18], [16, 19], [17, 18], [17, 19], [18, 19]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/task.toml b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..9220e96d5e01125a8ae06bb073fb8d86ec481d4c
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-independent-connectivity-l5-s0"
+version = "0.2.0"
+description = "construct/mc_pysms_independent_connectivity"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_independent_connectivity"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_independent_connectivity"
+problem_key = "graph_existence_independent_connectivity"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "MathConstraint/pysms_independent_connectivity"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/check.py b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/instance.json b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..94a255a8015b5577634cd44daaa69211801c4213
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 20, "required_edges": [], "max_independent_set": 3, "min_connectivity": 4, "family": "mc_pysms_independent_connectivity", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/run.py b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/test.sh b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-independent-connectivity-l5-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/environment/Dockerfile b/tasks/construct-mc-pysms-min-girth-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/environment/instance.json b/tasks/construct-mc-pysms-min-girth-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4eb8cc375e1bcce0f5a2cc0887283385252ca244
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 8, "required_edges": [], "min_girth": 6, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/instruction.md b/tasks/construct-mc-pysms-min-girth-l1-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..2e8f620701a238d678831b3fefe68e953906df50
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/instruction.md
@@ -0,0 +1,6 @@
+Construct a simple undirected graph on the 8 vertices 0..7 such that:
+  - the girth is at least 6: the graph has no cycle of length less than 6 (a graph without cycles qualifies)
+
+Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..7, listed once
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/solution/solve.sh b/tasks/construct-mc-pysms-min-girth-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..dbb85483c38085ee05b4c5ad65d28d5ab5157660
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/task.toml b/tasks/construct-mc-pysms-min-girth-l1-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..3366d7c779537c7569239820604f6c4b2f321aa1
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-min-girth-l1-s0"
+version = "0.2.0"
+description = "construct/mc_pysms_min_girth"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_min_girth"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_min_girth"
+problem_key = "graph_existence_min_girth"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "MathConstraint/pysms_min_girth"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/tests/check.py b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/tests/instance.json b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4eb8cc375e1bcce0f5a2cc0887283385252ca244
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 8, "required_edges": [], "min_girth": 6, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/tests/run.py b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-min-girth-l1-s0/tests/test.sh b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l1-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/environment/Dockerfile b/tasks/construct-mc-pysms-min-girth-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/environment/instance.json b/tasks/construct-mc-pysms-min-girth-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..451e2a61cccb67c1028766aadec18df2d9c8522a
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 16, "required_edges": [[11, 15], [3, 15], [5, 15]], "min_girth": 8, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/instruction.md b/tasks/construct-mc-pysms-min-girth-l5-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3fada50487cf6621dc85393efc670bf22ada6b89
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/instruction.md
@@ -0,0 +1,7 @@
+Construct a simple undirected graph on the 16 vertices 0..15 such that:
+  - the girth is at least 8: the graph has no cycle of length less than 8 (a graph without cycles qualifies)
+  - it contains each of the following edges: (11,15), (3,15), (5,15)
+
+Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..15, listed once
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/solution/solve.sh b/tasks/construct-mc-pysms-min-girth-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..52434ade2eca518b13864ef731b50c0013a703bd
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 15], [1, 15], [2, 15], [3, 15], [4, 15], [5, 15], [6, 15], [7, 15], [8, 15], [9, 15], [10, 15], [11, 15], [12, 15], [13, 15], [14, 15]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/task.toml b/tasks/construct-mc-pysms-min-girth-l5-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..92b5b9320a8723a15a60b682e2d49a85c0a636ea
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-min-girth-l5-s1"
+version = "0.2.0"
+description = "construct/mc_pysms_min_girth"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_min_girth"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_min_girth"
+problem_key = "graph_existence_min_girth"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "MathConstraint/pysms_min_girth"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/tests/check.py b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/tests/instance.json b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..451e2a61cccb67c1028766aadec18df2d9c8522a
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 16, "required_edges": [[11, 15], [3, 15], [5, 15]], "min_girth": 8, "family": "mc_pysms_min_girth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/tests/run.py b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-min-girth-l5-s1/tests/test.sh b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-min-girth-l5-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/environment/Dockerfile b/tasks/construct-mc-pysms-mtf-l3-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/environment/instance.json b/tasks/construct-mc-pysms-mtf-l3-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0d92303db396795dedc6f8812f1c84f99ffddec1
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/environment/instance.json
@@ -0,0 +1 @@
+{"vertices": 10, "required_edges": [], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/instruction.md b/tasks/construct-mc-pysms-mtf-l3-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c448de732a62c6bf3db9c51b31714224e76a1dfa
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/instruction.md
@@ -0,0 +1,6 @@
+Construct a simple undirected graph on the 10 vertices 0..9 such that:
+  - the graph is maximal triangle-free: it contains no triangle, and adding any missing edge would create one (every two non-adjacent vertices have a common neighbour)
+
+Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..9, listed once
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/solution/solve.sh b/tasks/construct-mc-pysms-mtf-l3-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c85e671a548b9b7e2f9e6a3362fb213ef4e2d2ff
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"edges": [[0, 8], [0, 9], [1, 8], [1, 9], [2, 8], [2, 9], [3, 8], [3, 9], [4, 8], [4, 9], [5, 8], [5, 9], [6, 8], [6, 9], [7, 8], [7, 9]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/task.toml b/tasks/construct-mc-pysms-mtf-l3-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..259c67848016d44fb76a062cfbd951bf010f46df
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-mtf-l3-s2"
+version = "0.2.0"
+description = "construct/mc_pysms_mtf"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_mtf"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_mtf"
+problem_key = "maximal_triangle_free_graph"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "MathConstraint/pysms_mtf"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/tests/check.py b/tasks/construct-mc-pysms-mtf-l3-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..4ab0b12508cf59b733f007a9d1f50831aec9efdf
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/tests/check.py
@@ -0,0 +1,151 @@
+"""Graph-existence constraints (MathConstraint pysms_* problem types, CC-BY-4.0). The answer is a graph on
+the stated vertex set, plus a proper colouring when a chromatic-number upper bound is asked for. Every
+constraint present in the instance is checked exactly (no stored answer is compared).
+
+Upstream note: upstream verifies by fixing the edge variables in the pysms CNF and calling CaDiCaL; the
+min-chromatic-number bound of pysms_graph_builder is only a raw smsg solver parameter, not a clause, so the
+upstream verifier ignored it. It is enforced here. Edge endpoints are also type-checked (upstream accepted
+floats/bools that compare in range)."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def _has_clique(adj, n, k):
+    def rec(cand, size):
+        if size == k:
+            return True
+        while cand:
+            if size + bin(cand).count("1") < k:
+                return False
+            v = cand.bit_length() - 1
+            cand &= ~(1 << v)
+            if rec(cand & adj[v], size + 1):
+                return True
+        return False
+    return rec((1 << n) - 1, 0)
+
+
+def _connected(adj, n, removed):
+    alive = [v for v in range(n) if not removed >> v & 1]
+    if len(alive) <= 1:
+        return True
+    mask = sum(1 << v for v in alive)
+    seen = 1 << alive[0]
+    stack = [alive[0]]
+    while stack:
+        v = stack.pop()
+        new = adj[v] & mask & ~seen
+        seen |= new
+        while new:
+            u = new.bit_length() - 1
+            new &= ~(1 << u)
+            stack.append(u)
+    return seen == mask
+
+
+def _girth(adj, n):
+    best = None
+    for r in range(n):
+        dist, par, q = {r: 0}, {r: -1}, [r]
+        for v in q:
+            nb = adj[v]
+            while nb:
+                u = nb.bit_length() - 1
+                nb &= ~(1 << u)
+                if u not in dist:
+                    dist[u], par[u] = dist[v] + 1, v
+                    q.append(u)
+                elif par[v] != u:
+                    c = dist[u] + dist[v] + 1
+                    best = c if best is None else min(best, c)
+    return best  # None = acyclic
+
+
+def _colourable(adj, n, k):
+    col = [-1] * n
+    order = sorted(range(n), key=lambda v: -bin(adj[v]).count("1"))
+
+    def rec(i):
+        if i == n:
+            return True
+        v = order[i]
+        used = {col[u] for u in range(n) if adj[v] >> u & 1 and col[u] >= 0}
+        for c in range(k):
+            if c not in used:
+                col[v] = c
+                if rec(i + 1):
+                    return True
+        col[v] = -1
+        return False
+    return rec(0)
+
+
+def check(inst, ans):
+    n = inst["vertices"]
+    E = ans.get("edges")
+    if not isinstance(E, list):
+        raise Invalid("edges must be a list of [u, v] pairs")
+    edges = set()
+    for e in E:
+        u, v = int_list(e, 2, 0, n - 1, "edge")
+        if u == v:
+            raise Invalid(f"self-loop at {u}")
+        e2 = (min(u, v), max(u, v))
+        if e2 in edges:
+            raise Invalid(f"duplicate edge {e2}")
+        edges.add(e2)
+    adj = [0] * n
+    for u, v in edges:
+        adj[u] |= 1 << v
+        adj[v] |= 1 << u
+    deg = [bin(a).count("1") for a in adj]
+    for u, v in inst.get("required_edges", []):
+        if (min(u, v), max(u, v)) not in edges:
+            raise Invalid(f"required edge ({u},{v}) is missing")
+    c = inst.get
+    if c("min_degree") is not None and min(deg) < c("min_degree"):
+        raise Invalid(f"minimum degree {min(deg)} < {c('min_degree')}")
+    if c("max_degree") is not None and max(deg) > c("max_degree"):
+        raise Invalid(f"maximum degree {max(deg)} > {c('max_degree')}")
+    if c("min_edges") is not None and len(edges) < c("min_edges"):
+        raise Invalid(f"{len(edges)} edges < {c('min_edges')}")
+    if c("max_edges") is not None and len(edges) > c("max_edges"):
+        raise Invalid(f"{len(edges)} edges > {c('max_edges')}")
+    if c("max_clique") is not None and _has_clique(adj, n, c("max_clique") + 1):
+        raise Invalid(f"graph contains a clique of size {c('max_clique') + 1}")
+    if c("max_independent_set") is not None:
+        full = (1 << n) - 1
+        comp = [full & ~adj[v] & ~(1 << v) for v in range(n)]
+        if _has_clique(comp, n, c("max_independent_set") + 1):
+            raise Invalid(f"graph contains an independent set of size {c('max_independent_set') + 1}")
+    if c("min_girth") is not None:
+        g = _girth(adj, n)
+        if g is not None and g < c("min_girth"):
+            raise Invalid(f"graph has a cycle of length {g} < {c('min_girth')}")
+    if c("min_connectivity") is not None:
+        k = c("min_connectivity")
+        if n <= k:
+            raise Invalid("too few vertices for this connectivity")
+        for s in range(k):
+            for I in itertools.combinations(range(n), s):
+                if not _connected(adj, n, sum(1 << v for v in I)):
+                    raise Invalid(f"deleting vertices {list(I)} disconnects the graph")
+    if c("mtf"):
+        for u, v in itertools.combinations(range(n), 2):
+            if adj[u] >> v & 1:
+                if adj[u] & adj[v]:
+                    raise Invalid(f"triangle on edge ({u},{v})")
+            elif not adj[u] & adj[v]:
+                raise Invalid(f"non-adjacent {u}, {v} have no common neighbour (edge could be added)")
+    if c("max_chromatic_number") is not None:
+        k = c("max_chromatic_number")
+        col = int_list(ans.get("coloring"), n, 0, k - 1, "coloring")
+        for u, v in edges:
+            if col[u] == col[v]:
+                raise Invalid(f"coloring: edge ({u},{v}) is monochromatic")
+    if c("min_chromatic_number") is not None and c("min_chromatic_number") >= 2:
+        m = c("min_chromatic_number")
+        if not edges or _colourable(adj, n, m - 1):
+            raise Invalid(f"graph is {m - 1}-colourable, chromatic number must be at least {m}")
+    return None, {"num_edges": len(edges)}
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/tests/instance.json b/tasks/construct-mc-pysms-mtf-l3-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0d92303db396795dedc6f8812f1c84f99ffddec1
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/tests/instance.json
@@ -0,0 +1 @@
+{"vertices": 10, "required_edges": [], "mtf": true, "family": "mc_pysms_mtf", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/tests/run.py b/tasks/construct-mc-pysms-mtf-l3-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-pysms-mtf-l3-s2/tests/test.sh b/tasks/construct-mc-pysms-mtf-l3-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-pysms-mtf-l3-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-pysms-num-edges-bounds-l3-s1/instruction.md b/tasks/construct-mc-pysms-num-edges-bounds-l3-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..935f21eb1657189a9f9de2a24204dd9d1e3ca60f
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-bounds-l3-s1/instruction.md
@@ -0,0 +1,6 @@
+Construct a simple undirected graph on the 14 vertices 0..13 such that:
+  - the number of edges is between 33 and 33 (inclusive)
+
+Answer format: {"edges": [[u, v], ...]} where each edge is a pair of distinct vertices in 0..13, listed once
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-pysms-num-edges-bounds-l3-s1/task.toml b/tasks/construct-mc-pysms-num-edges-bounds-l3-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..3ba47552fd928a99de458509da98890e47981f3c
--- /dev/null
+++ b/tasks/construct-mc-pysms-num-edges-bounds-l3-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-num-edges-bounds-l3-s1"
+version = "0.2.0"
+description = "construct/mc_pysms_num_edges_bounds"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_num_edges_bounds"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_num_edges_bounds"
+problem_key = "graph_existence_num_edges_bounds"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "MathConstraint/pysms_num_edges_bounds"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ramsey-l1-s0/environment/Dockerfile b/tasks/construct-mc-ramsey-l1-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-ramsey-l1-s0/environment/instance.json b/tasks/construct-mc-ramsey-l1-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca554d22f90cbe644a5fd7c4850e0ae5b7cf6f2e
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 8, "r": 3, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l1-s0/instruction.md b/tasks/construct-mc-ramsey-l1-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..741981d38096007192bd47e255152fa24e9ff099
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/instruction.md
@@ -0,0 +1,5 @@
+Colour each of the 28 edges of the complete graph K_8 (vertices 0..7) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
+
+Answer format: {"colors": [c_0, ..., c_27]}, one entry (0 or 1) per edge (i, j) with 0 <= i < j < 8, in lexicographic order ((0,1), (0,2), ..., (0,7), (1,2), ..., (6,7)).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-ramsey-l1-s0/solution/solve.sh b/tasks/construct-mc-ramsey-l1-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7814971933684c55ba6462d376606ceb6c0f38da
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ramsey-l1-s0/task.toml b/tasks/construct-mc-ramsey-l1-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..a7822f00c0b01745654044243a526abb95bc9a7e
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-ramsey-l1-s0"
+version = "0.2.0"
+description = "construct/mc_ramsey"
+authors = []
+keywords = ["rlmath", "construct", "mc_ramsey"]
+
+[metadata]
+subset = "construct"
+family = "mc_ramsey"
+problem_key = "ramsey_two_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "1"
+source = "MathConstraint/ramsey"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ramsey-l1-s0/tests/check.py b/tasks/construct-mc-ramsey-l1-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/tests/check.py
@@ -0,0 +1,31 @@
+"""Two-colouring of the edges of K_n with no colour-0 K_r and no colour-1 K_s (MathConstraint ramsey,
+CC-BY-4.0). Adapted from pilot/grader.py check_ramsey; adds the optional fixed edge colours."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, r, s = inst["n"], inst["r"], inst["s"]
+    edges = list(itertools.combinations(range(n), 2))
+    col = int_list(ans.get("colors"), len(edges), 0, 1, "colors")
+    for name, i, v in inst.get("fixed", []):
+        if col[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    c = {e: col[i] for i, e in enumerate(edges)}
+    for k, colour in ((r, 0), (s, 1)):
+        adj = {v: {u for u in range(n) if u != v and c[(min(u, v), max(u, v))] == colour} for v in range(n)}
+
+        def grow(size, cand):
+            if size == k:
+                return True
+            if size + len(cand) < k:
+                return False
+            for v in sorted(cand):
+                if grow(size + 1, {u for u in cand if u > v} & adj[v]):
+                    return True
+            return False
+
+        if grow(0, set(range(n))):
+            raise Invalid(f"monochromatic K_{k} in colour {colour}")
+    return None, {}
diff --git a/tasks/construct-mc-ramsey-l1-s0/tests/instance.json b/tasks/construct-mc-ramsey-l1-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca554d22f90cbe644a5fd7c4850e0ae5b7cf6f2e
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 8, "r": 3, "s": 4, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l1-s0/tests/run.py b/tasks/construct-mc-ramsey-l1-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-ramsey-l1-s0/tests/test.sh b/tasks/construct-mc-ramsey-l1-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-ramsey-l1-s7/environment/Dockerfile b/tasks/construct-mc-ramsey-l1-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-ramsey-l1-s7/environment/instance.json b/tasks/construct-mc-ramsey-l1-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1a48b3ef5b73ad7357c620b64385e4c1a94596c1
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 8, "r": 4, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l1-s7/instruction.md b/tasks/construct-mc-ramsey-l1-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..977bb3977ffbbcda95896ac0f33a61399775339a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/instruction.md
@@ -0,0 +1,5 @@
+Colour each of the 28 edges of the complete graph K_8 (vertices 0..7) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
+
+Answer format: {"colors": [c_0, ..., c_27]}, one entry (0 or 1) per edge (i, j) with 0 <= i < j < 8, in lexicographic order ((0,1), (0,2), ..., (0,7), (1,2), ..., (6,7)).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-ramsey-l1-s7/solution/solve.sh b/tasks/construct-mc-ramsey-l1-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b6b6ab5786cb04c89c7f696e69c6bed107a7037f
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ramsey-l1-s7/task.toml b/tasks/construct-mc-ramsey-l1-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..6c26f581c18a0a9f0d0603ceba33d33c7d2acba3
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-ramsey-l1-s7"
+version = "0.2.0"
+description = "construct/mc_ramsey"
+authors = []
+keywords = ["rlmath", "construct", "mc_ramsey"]
+
+[metadata]
+subset = "construct"
+family = "mc_ramsey"
+problem_key = "ramsey_two_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "1"
+source = "MathConstraint/ramsey"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ramsey-l1-s7/tests/check.py b/tasks/construct-mc-ramsey-l1-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/tests/check.py
@@ -0,0 +1,31 @@
+"""Two-colouring of the edges of K_n with no colour-0 K_r and no colour-1 K_s (MathConstraint ramsey,
+CC-BY-4.0). Adapted from pilot/grader.py check_ramsey; adds the optional fixed edge colours."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, r, s = inst["n"], inst["r"], inst["s"]
+    edges = list(itertools.combinations(range(n), 2))
+    col = int_list(ans.get("colors"), len(edges), 0, 1, "colors")
+    for name, i, v in inst.get("fixed", []):
+        if col[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    c = {e: col[i] for i, e in enumerate(edges)}
+    for k, colour in ((r, 0), (s, 1)):
+        adj = {v: {u for u in range(n) if u != v and c[(min(u, v), max(u, v))] == colour} for v in range(n)}
+
+        def grow(size, cand):
+            if size == k:
+                return True
+            if size + len(cand) < k:
+                return False
+            for v in sorted(cand):
+                if grow(size + 1, {u for u in cand if u > v} & adj[v]):
+                    return True
+            return False
+
+        if grow(0, set(range(n))):
+            raise Invalid(f"monochromatic K_{k} in colour {colour}")
+    return None, {}
diff --git a/tasks/construct-mc-ramsey-l1-s7/tests/instance.json b/tasks/construct-mc-ramsey-l1-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1a48b3ef5b73ad7357c620b64385e4c1a94596c1
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 8, "r": 4, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l1-s7/tests/run.py b/tasks/construct-mc-ramsey-l1-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-ramsey-l1-s7/tests/test.sh b/tasks/construct-mc-ramsey-l1-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-ramsey-l1-s9/instruction.md b/tasks/construct-mc-ramsey-l1-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..495bdff329079c1183a439d4bd20332f19dceea9
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s9/instruction.md
@@ -0,0 +1,5 @@
+Colour each of the 10 edges of the complete graph K_5 (vertices 0..4) with colour 0 or 1 so that there is no set of 3 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
+
+Answer format: {"colors": [c_0, ..., c_9]}, one entry (0 or 1) per edge (i, j) with 0 <= i < j < 5, in lexicographic order ((0,1), (0,2), ..., (0,4), (1,2), ..., (3,4)).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-ramsey-l1-s9/task.toml b/tasks/construct-mc-ramsey-l1-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..c3da0327116000b910ac9b6a9a5a0471c83d83fe
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l1-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-ramsey-l1-s9"
+version = "0.2.0"
+description = "construct/mc_ramsey"
+authors = []
+keywords = ["rlmath", "construct", "mc_ramsey"]
+
+[metadata]
+subset = "construct"
+family = "mc_ramsey"
+problem_key = "ramsey_two_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "1"
+source = "MathConstraint/ramsey"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ramsey-l5-s1/environment/Dockerfile b/tasks/construct-mc-ramsey-l5-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-ramsey-l5-s1/environment/instance.json b/tasks/construct-mc-ramsey-l5-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..da8cf92a56496c05cd836ff4e70d00d9c03493c0
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 24, "r": 4, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l5-s1/instruction.md b/tasks/construct-mc-ramsey-l5-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..5b9775380e8987d780d6fae45b33288329474cf5
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/instruction.md
@@ -0,0 +1,5 @@
+Colour each of the 276 edges of the complete graph K_24 (vertices 0..23) with colour 0 or 1 so that there is no set of 4 vertices whose connecting edges all have colour 0, and no set of 5 vertices whose connecting edges all have colour 1.
+
+Answer format: {"colors": [c_0, ..., c_275]}, one entry (0 or 1) per edge (i, j) with 0 <= i < j < 24, in lexicographic order ((0,1), (0,2), ..., (0,23), (1,2), ..., (22,23)).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-ramsey-l5-s1/solution/solve.sh b/tasks/construct-mc-ramsey-l5-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7c62f34406fb732e5869482f7ae1b39637736595
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ramsey-l5-s1/task.toml b/tasks/construct-mc-ramsey-l5-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..f033a34a3a88f80ba486d57d1b24670396daddb3
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-ramsey-l5-s1"
+version = "0.2.0"
+description = "construct/mc_ramsey"
+authors = []
+keywords = ["rlmath", "construct", "mc_ramsey"]
+
+[metadata]
+subset = "construct"
+family = "mc_ramsey"
+problem_key = "ramsey_two_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/ramsey"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ramsey-l5-s1/tests/check.py b/tasks/construct-mc-ramsey-l5-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/tests/check.py
@@ -0,0 +1,31 @@
+"""Two-colouring of the edges of K_n with no colour-0 K_r and no colour-1 K_s (MathConstraint ramsey,
+CC-BY-4.0). Adapted from pilot/grader.py check_ramsey; adds the optional fixed edge colours."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, r, s = inst["n"], inst["r"], inst["s"]
+    edges = list(itertools.combinations(range(n), 2))
+    col = int_list(ans.get("colors"), len(edges), 0, 1, "colors")
+    for name, i, v in inst.get("fixed", []):
+        if col[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    c = {e: col[i] for i, e in enumerate(edges)}
+    for k, colour in ((r, 0), (s, 1)):
+        adj = {v: {u for u in range(n) if u != v and c[(min(u, v), max(u, v))] == colour} for v in range(n)}
+
+        def grow(size, cand):
+            if size == k:
+                return True
+            if size + len(cand) < k:
+                return False
+            for v in sorted(cand):
+                if grow(size + 1, {u for u in cand if u > v} & adj[v]):
+                    return True
+            return False
+
+        if grow(0, set(range(n))):
+            raise Invalid(f"monochromatic K_{k} in colour {colour}")
+    return None, {}
diff --git a/tasks/construct-mc-ramsey-l5-s1/tests/instance.json b/tasks/construct-mc-ramsey-l5-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..da8cf92a56496c05cd836ff4e70d00d9c03493c0
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 24, "r": 4, "s": 5, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l5-s1/tests/run.py b/tasks/construct-mc-ramsey-l5-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-ramsey-l5-s1/tests/test.sh b/tasks/construct-mc-ramsey-l5-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-ramsey-l5-s6/instruction.md b/tasks/construct-mc-ramsey-l5-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..937b0cb2d66b29b561d60bf17c84c821d38fe647
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s6/instruction.md
@@ -0,0 +1,5 @@
+Colour each of the 253 edges of the complete graph K_23 (vertices 0..22) with colour 0 or 1 so that there is no set of 5 vertices whose connecting edges all have colour 0, and no set of 4 vertices whose connecting edges all have colour 1.
+
+Answer format: {"colors": [c_0, ..., c_252]}, one entry (0 or 1) per edge (i, j) with 0 <= i < j < 23, in lexicographic order ((0,1), (0,2), ..., (0,22), (1,2), ..., (21,22)).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-ramsey-l5-s6/task.toml b/tasks/construct-mc-ramsey-l5-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5330d126717a623365d20222f76924aaae8e9184
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-ramsey-l5-s6"
+version = "0.2.0"
+description = "construct/mc_ramsey"
+authors = []
+keywords = ["rlmath", "construct", "mc_ramsey"]
+
+[metadata]
+subset = "construct"
+family = "mc_ramsey"
+problem_key = "ramsey_two_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/ramsey"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ramsey-l5-s8/environment/Dockerfile b/tasks/construct-mc-ramsey-l5-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-ramsey-l5-s8/environment/instance.json b/tasks/construct-mc-ramsey-l5-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e93701a172550ef82d3cf7d1492ada7b8e01a4aa
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/environment/instance.json
@@ -0,0 +1 @@
+{"n": 26, "r": 8, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l5-s8/instruction.md b/tasks/construct-mc-ramsey-l5-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..5f59f813d00f6c1ef8f0e14426c2805d16de839a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/instruction.md
@@ -0,0 +1,5 @@
+Colour each of the 325 edges of the complete graph K_26 (vertices 0..25) with colour 0 or 1 so that there is no set of 8 vertices whose connecting edges all have colour 0, and no set of 3 vertices whose connecting edges all have colour 1.
+
+Answer format: {"colors": [c_0, ..., c_324]}, one entry (0 or 1) per edge (i, j) with 0 <= i < j < 26, in lexicographic order ((0,1), (0,2), ..., (0,25), (1,2), ..., (24,25)).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-ramsey-l5-s8/solution/solve.sh b/tasks/construct-mc-ramsey-l5-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ed7698d3e256b803c881e166493524537269c291
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-ramsey-l5-s8/task.toml b/tasks/construct-mc-ramsey-l5-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..b01b757f69c7e1cb7ae9de661b09896ac1d96a40
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-ramsey-l5-s8"
+version = "0.2.0"
+description = "construct/mc_ramsey"
+authors = []
+keywords = ["rlmath", "construct", "mc_ramsey"]
+
+[metadata]
+subset = "construct"
+family = "mc_ramsey"
+problem_key = "ramsey_two_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/ramsey"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-ramsey-l5-s8/tests/check.py b/tasks/construct-mc-ramsey-l5-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..53526c0bc87af6298219d3e1eac5f95f01b57541
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/tests/check.py
@@ -0,0 +1,31 @@
+"""Two-colouring of the edges of K_n with no colour-0 K_r and no colour-1 K_s (MathConstraint ramsey,
+CC-BY-4.0). Adapted from pilot/grader.py check_ramsey; adds the optional fixed edge colours."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, r, s = inst["n"], inst["r"], inst["s"]
+    edges = list(itertools.combinations(range(n), 2))
+    col = int_list(ans.get("colors"), len(edges), 0, 1, "colors")
+    for name, i, v in inst.get("fixed", []):
+        if col[i] != v:
+            raise Invalid(f"fixed value {name}[{i}] = {v} not respected")
+    c = {e: col[i] for i, e in enumerate(edges)}
+    for k, colour in ((r, 0), (s, 1)):
+        adj = {v: {u for u in range(n) if u != v and c[(min(u, v), max(u, v))] == colour} for v in range(n)}
+
+        def grow(size, cand):
+            if size == k:
+                return True
+            if size + len(cand) < k:
+                return False
+            for v in sorted(cand):
+                if grow(size + 1, {u for u in cand if u > v} & adj[v]):
+                    return True
+            return False
+
+        if grow(0, set(range(n))):
+            raise Invalid(f"monochromatic K_{k} in colour {colour}")
+    return None, {}
diff --git a/tasks/construct-mc-ramsey-l5-s8/tests/instance.json b/tasks/construct-mc-ramsey-l5-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e93701a172550ef82d3cf7d1492ada7b8e01a4aa
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/tests/instance.json
@@ -0,0 +1 @@
+{"n": 26, "r": 8, "s": 3, "fixed": [], "family": "mc_ramsey", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-ramsey-l5-s8/tests/run.py b/tasks/construct-mc-ramsey-l5-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-ramsey-l5-s8/tests/test.sh b/tasks/construct-mc-ramsey-l5-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-ramsey-l5-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-social-golfers-l4-s2/environment/Dockerfile b/tasks/construct-mc-social-golfers-l4-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-social-golfers-l4-s2/environment/instance.json b/tasks/construct-mc-social-golfers-l4-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a0730c40f4b37b19433e35bcd04bdd6486e7e92
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n_groups": 6, "group_size": 3, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l4-s2/instruction.md b/tasks/construct-mc-social-golfers-l4-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4005d852fd101a7a7fa19f6b52e612c7883cbef0
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/instruction.md
@@ -0,0 +1,7 @@
+Schedule 18 golfers (numbered 0..17) for 7 weeks. Every week the golfers are split into 6 groups (numbered 0..5) of exactly 3 golfers each. No two golfers may play in the same group in more than one week.
+
+Find such a schedule.
+
+Answer format: {"schedule": [week_0, ..., week_6]} where week_t is a list of 18 integers and week_t[p] (in 0..5) is the group of golfer p in week t
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-social-golfers-l4-s2/solution/solve.sh b/tasks/construct-mc-social-golfers-l4-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3f54893604b59320eb1a612ed44c4f9145b64c97
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"schedule": [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [2, 1, 0, 1, 5, 3, 0, 4, 2, 2, 4, 1, 5, 0, 3, 3, 4, 5], [5, 2, 4, 5, 3, 2, 2, 0, 4, 3, 5, 1, 4, 0, 1, 3, 1, 0], [0, 5, 1, 1, 0, 2, 4, 3, 2, 4, 5, 3, 5, 0, 4, 3, 2, 1], [1, 0, 5, 3, 5, 2, 1, 3, 4, 2, 4, 5, 2, 0, 3, 1, 0, 4], [5, 0, 4, 1, 2, 3, 2, 5, 1, 0, 4, 3, 5, 3, 4, 1, 2, 0], [3, 0, 1, 2, 0, 1, 5, 1, 0, 2, 4, 5, 5, 4, 3, 4, 2, 3]]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-social-golfers-l4-s2/task.toml b/tasks/construct-mc-social-golfers-l4-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..16ae93ef82d885ac3ac488645e81fa6cb990c4b0
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-social-golfers-l4-s2"
+version = "0.2.0"
+description = "construct/mc_social_golfers"
+authors = []
+keywords = ["rlmath", "construct", "mc_social_golfers"]
+
+[metadata]
+subset = "construct"
+family = "mc_social_golfers"
+problem_key = "social_golfer"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "MathConstraint/social_golfers"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-social-golfers-l4-s2/tests/check.py b/tasks/construct-mc-social-golfers-l4-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..73977815b7b6094a8491075b6dc2ae1293e44930
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/tests/check.py
@@ -0,0 +1,25 @@
+"""Social golfer problem (MathConstraint social_golfers, CSPLib prob010, CC-BY-4.0): each week partition
+the g*s players into g groups of size s; no two players share a group in more than one week."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    g, s, w = inst["n_groups"], inst["group_size"], inst["n_weeks"]
+    P = g * s
+    sched = ans.get("schedule")
+    if not isinstance(sched, list) or len(sched) != w:
+        raise Invalid(f"schedule must be a list of {w} weeks")
+    met = set()
+    for wk, row in enumerate(sched):
+        row = int_list(row, P, 0, g - 1, f"week {wk}")
+        groups = [[p for p in range(P) if row[p] == grp] for grp in range(g)]
+        for grp, mem in enumerate(groups):
+            if len(mem) != s:
+                raise Invalid(f"week {wk}: group {grp} has {len(mem)} players, need {s}")
+            for i in range(s):
+                for j in range(i + 1, s):
+                    pr = (mem[i], mem[j])
+                    if pr in met:
+                        raise Invalid(f"players {pr} play together in more than one week")
+                    met.add(pr)
+    return None, {}
diff --git a/tasks/construct-mc-social-golfers-l4-s2/tests/instance.json b/tasks/construct-mc-social-golfers-l4-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a0730c40f4b37b19433e35bcd04bdd6486e7e92
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n_groups": 6, "group_size": 3, "n_weeks": 7, "family": "mc_social_golfers", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-social-golfers-l4-s2/tests/run.py b/tasks/construct-mc-social-golfers-l4-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-social-golfers-l4-s2/tests/test.sh b/tasks/construct-mc-social-golfers-l4-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-social-golfers-l4-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-van-der-waerden-l5-s3/instruction.md b/tasks/construct-mc-van-der-waerden-l5-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4a295eac7b8a288d2144d37f45c2a6231aa29949
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l5-s3/instruction.md
@@ -0,0 +1,7 @@
+Colour the integers 1, 2, ..., 65 with 4 colours (numbered 0..3) so that there is no monochromatic arithmetic progression of length 3: no a >= 1, d >= 1 with a + 2*d <= 65 such that a, a+d, ..., a+2*d all have the same colour.
+
+Find such a colouring.
+
+Answer format: {"colors": [c_1, ..., c_65]}: 65 integers in 0..3; the i-th entry (0-indexed) is the colour of the integer i+1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-van-der-waerden-l5-s3/task.toml b/tasks/construct-mc-van-der-waerden-l5-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ede6cd69aa37b894faa03c92e323d60f0e0cfe89
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l5-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-van-der-waerden-l5-s3"
+version = "0.2.0"
+description = "construct/mc_van_der_waerden"
+authors = []
+keywords = ["rlmath", "construct", "mc_van_der_waerden"]
+
+[metadata]
+subset = "construct"
+family = "mc_van_der_waerden"
+problem_key = "van_der_waerden_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/van_der_waerden"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-van-der-waerden-l5-s4/instruction.md b/tasks/construct-mc-van-der-waerden-l5-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..d6f6b9b0771777db11b46f2feccd155e8ba9f513
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l5-s4/instruction.md
@@ -0,0 +1,7 @@
+Colour the integers 1, 2, ..., 200 with 3 colours (numbered 0..2) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 200 such that a, a+d, ..., a+3*d all have the same colour.
+
+Find such a colouring.
+
+Answer format: {"colors": [c_1, ..., c_200]}: 200 integers in 0..2; the i-th entry (0-indexed) is the colour of the integer i+1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-van-der-waerden-l5-s4/task.toml b/tasks/construct-mc-van-der-waerden-l5-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..679b2e5ccead5e99ee03f65962c1683e7fd59032
--- /dev/null
+++ b/tasks/construct-mc-van-der-waerden-l5-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-van-der-waerden-l5-s4"
+version = "0.2.0"
+description = "construct/mc_van_der_waerden"
+authors = []
+keywords = ["rlmath", "construct", "mc_van_der_waerden"]
+
+[metadata]
+subset = "construct"
+family = "mc_van_der_waerden"
+problem_key = "van_der_waerden_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/van_der_waerden"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/environment/Dockerfile b/tasks/construct-mc-vertex-cover-l4-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/environment/instance.json b/tasks/construct-mc-vertex-cover-l4-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..95faa4715aaa723dd735a7e3d2858f47d82e84f5
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/environment/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 41, "edges": [[0, 2], [0, 4], [0, 12], [0, 13], [0, 15], [0, 23], [0, 27], [0, 38], [0, 44], [0, 49], [0, 54], [1, 2], [1, 4], [1, 9], [1, 22], [1, 24], [1, 25], [1, 34], [1, 35], [1, 39], [1, 43], [1, 51], [1, 56], [1, 58], [2, 14], [2, 21], [2, 24], [2, 25], [2, 30], [2, 51], [2, 53], [2, 57], [2, 59], [3, 11], [3, 16], [3, 18], [3, 30], [3, 31], [3, 33], [3, 37], [3, 42], [3, 44], [3, 52], [4, 7], [4, 9], [4, 11], [4, 12], [4, 14], [4, 17], [4, 44], [4, 57], [4, 58], [5, 13], [5, 16], [5, 22], [5, 25], [5, 34], [5, 37], [5, 44], [5, 46], [5, 50], [5, 53], [5, 56], [6, 7], [6, 9], [6, 20], [6, 21], [6, 52], [7, 11], [7, 13], [7, 16], [7, 20], [7, 21], [7, 33], [7, 35], [7, 36], [7, 38], [7, 42], [7, 46], [7, 52], [7, 53], [7, 54], [7, 56], [7, 58], [8, 10], [8, 13], [8, 26], [8, 35], [8, 39], [8, 41], [8, 42], [8, 44], [8, 47], [8, 48], [8, 50], [8, 59], [9, 14], [9, 24], [9, 25], [9, 32], [9, 33], [9, 39], [9, 45], [10, 11], [10, 20], [10, 33], [10, 34], [10, 37], [10, 39], [10, 43], [10, 47], [10, 56], [10, 58], [10, 59], [11, 12], [11, 16], [11, 17], [11, 20], [11, 24], [11, 26], [11, 27], [11, 28], [11, 45], [11, 48], [11, 55], [11, 56], [12, 15], [12, 16], [12, 18], [12, 19], [12, 24], [12, 26], [12, 29], [12, 40], [12, 47], [12, 53], [13, 15], [13, 22], [13, 35], [13, 41], [13, 52], [14, 25], [14, 29], [14, 36], [14, 37], [14, 41], [14, 52], [15, 21], [15, 28], [15, 35], [15, 39], [15, 40], [15, 41], [16, 21], [16, 24], [16, 28], [16, 32], [16, 35], [16, 52], [16, 54], [17, 21], [17, 25], [17, 30], [17, 31], [17, 35], [17, 44], [17, 46], [17, 47], [17, 54], [17, 56], [18, 48], [18, 49], [18, 52], [18, 58], [19, 22], [19, 29], [19, 30], [19, 33], [19, 35], [19, 48], [20, 35], [20, 40], [20, 51], [20, 52], [21, 29], [21, 35], [21, 36], [21, 37], [21, 48], [21, 51], [21, 58], [22, 25], [22, 31], [22, 32], [22, 46], [22, 50], [22, 52], [22, 54], [22, 58], [23, 25], [23, 29], [23, 35], [23, 57], [23, 58], [23, 59], [24, 31], [24, 32], [24, 38], [24, 41], [25, 31], [25, 33], [25, 34], [25, 37], [25, 43], [25, 48], [25, 55], [25, 59], [26, 33], [26, 38], [26, 51], [26, 53], [26, 56], [27, 29], [27, 32], [27, 33], [27, 41], [27, 52], [27, 59], [28, 31], [28, 44], [28, 45], [28, 53], [29, 48], [29, 49], [29, 51], [29, 56], [30, 33], [30, 36], [30, 46], [30, 49], [31, 33], [31, 40], [31, 52], [32, 36], [32, 37], [32, 48], [32, 50], [32, 51], [32, 56], [32, 57], [32, 58], [33, 43], [33, 44], [33, 47], [33, 59], [34, 48], [34, 50], [34, 53], [34, 56], [34, 57], [35, 39], [35, 41], [35, 44], [35, 52], [36, 38], [36, 45], [36, 52], [37, 55], [38, 43], [38, 44], [38, 47], [38, 48], [38, 50], [38, 55], [38, 59], [39, 45], [39, 53], [40, 47], [40, 48], [40, 55], [41, 47], [41, 48], [41, 51], [41, 58], [42, 53], [42, 58], [43, 51], [43, 52], [43, 57], [44, 50], [44, 52], [44, 55], [45, 48], [45, 53], [45, 56], [46, 55], [46, 56], [46, 57], [46, 58], [47, 49], [48, 51], [48, 54], [49, 53], [49, 56], [49, 58], [50, 51], [50, 56], [51, 58], [52, 53], [52, 58], [55, 59]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/instruction.md b/tasks/construct-mc-vertex-cover-l4-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..db6e2d40f0cd39f5e389b88c5a5eecfb2097c659
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 60 vertices numbered 0..59 and 311 edges:
+(0,2), (0,4), (0,12), (0,13), (0,15), (0,23), (0,27), (0,38), (0,44), (0,49), (0,54), (1,2), (1,4), (1,9), (1,22), (1,24), (1,25), (1,34), (1,35), (1,39), (1,43), (1,51), (1,56), (1,58), (2,14), (2,21), (2,24), (2,25), (2,30), (2,51), (2,53), (2,57), (2,59), (3,11), (3,16), (3,18), (3,30), (3,31), (3,33), (3,37), (3,42), (3,44), (3,52), (4,7), (4,9), (4,11), (4,12), (4,14), (4,17), (4,44), (4,57), (4,58), (5,13), (5,16), (5,22), (5,25), (5,34), (5,37), (5,44), (5,46), (5,50), (5,53), (5,56), (6,7), (6,9), (6,20), (6,21), (6,52), (7,11), (7,13), (7,16), (7,20), (7,21), (7,33), (7,35), (7,36), (7,38), (7,42), (7,46), (7,52), (7,53), (7,54), (7,56), (7,58), (8,10), (8,13), (8,26), (8,35), (8,39), (8,41), (8,42), (8,44), (8,47), (8,48), (8,50), (8,59), (9,14), (9,24), (9,25), (9,32), (9,33), (9,39), (9,45), (10,11), (10,20), (10,33), (10,34), (10,37), (10,39), (10,43), (10,47), (10,56), (10,58), (10,59), (11,12), (11,16), (11,17), (11,20), (11,24), (11,26), (11,27), (11,28), (11,45), (11,48), (11,55), (11,56), (12,15), (12,16), (12,18), (12,19), (12,24), (12,26), (12,29), (12,40), (12,47), (12,53), (13,15), (13,22), (13,35), (13,41), (13,52), (14,25), (14,29), (14,36), (14,37), (14,41), (14,52), (15,21), (15,28), (15,35), (15,39), (15,40), (15,41), (16,21), (16,24), (16,28), (16,32), (16,35), (16,52), (16,54), (17,21), (17,25), (17,30), (17,31), (17,35), (17,44), (17,46), (17,47), (17,54), (17,56), (18,48), (18,49), (18,52), (18,58), (19,22), (19,29), (19,30), (19,33), (19,35), (19,48), (20,35), (20,40), (20,51), (20,52), (21,29), (21,35), (21,36), (21,37), (21,48), (21,51), (21,58), (22,25), (22,31), (22,32), (22,46), (22,50), (22,52), (22,54), (22,58), (23,25), (23,29), (23,35), (23,57), (23,58), (23,59), (24,31), (24,32), (24,38), (24,41), (25,31), (25,33), (25,34), (25,37), (25,43), (25,48), (25,55), (25,59), (26,33), (26,38), (26,51), (26,53), (26,56), (27,29), (27,32), (27,33), (27,41), (27,52), (27,59), (28,31), (28,44), (28,45), (28,53), (29,48), (29,49), (29,51), (29,56), (30,33), (30,36), (30,46), (30,49), (31,33), (31,40), (31,52), (32,36), (32,37), (32,48), (32,50), (32,51), (32,56), (32,57), (32,58), (33,43), (33,44), (33,47), (33,59), (34,48), (34,50), (34,53), (34,56), (34,57), (35,39), (35,41), (35,44), (35,52), (36,38), (36,45), (36,52), (37,55), (38,43), (38,44), (38,47), (38,48), (38,50), (38,55), (38,59), (39,45), (39,53), (40,47), (40,48), (40,55), (41,47), (41,48), (41,51), (41,58), (42,53), (42,58), (43,51), (43,52), (43,57), (44,50), (44,52), (44,55), (45,48), (45,53), (45,56), (46,55), (46,56), (46,57), (46,58), (47,49), (48,51), (48,54), (49,53), (49,56), (49,58), (50,51), (50,56), (51,58), (52,53), (52,58), (55,59)
+
+Find a vertex cover of G with at most 41 vertices: a set of vertices that contains at least one endpoint of every edge.
+
+Answer format: {"cover": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/solution/solve.sh b/tasks/construct-mc-vertex-cover-l4-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c8c54b0f733166c790e96391f0ad13355d01c198
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 1, 3, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 32, 33, 34, 35, 38, 40, 41, 44, 45, 48, 49, 51, 52, 53, 55, 56, 57, 58, 59]}
+RLMATH_EOF
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/task.toml b/tasks/construct-mc-vertex-cover-l4-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..b2c48c971e97849e1d5a666aafe01fd2fc9e63bf
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-vertex-cover-l4-s3"
+version = "0.2.0"
+description = "construct/mc_vertex_cover"
+authors = []
+keywords = ["rlmath", "construct", "mc_vertex_cover"]
+
+[metadata]
+subset = "construct"
+family = "mc_vertex_cover"
+problem_key = "graph_vertex_cover"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "MathConstraint/vertex_cover"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/tests/check.py b/tasks/construct-mc-vertex-cover-l4-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..e3accb3da1c773fd2126b8b5b0a97b099e29c83b
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/tests/check.py
@@ -0,0 +1,16 @@
+"""Vertex cover of size <= k in a given graph (MathConstraint vertex_cover, CC-BY-4.0)."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    S = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(S)) != len(S):
+        raise Invalid("repeated vertex")
+    if len(S) > k:
+        raise Invalid(f"cover has {len(S)} vertices, at most {k} allowed")
+    C = set(S)
+    for u, v in inst["edges"]:
+        if u not in C and v not in C:
+            raise Invalid(f"edge ({u},{v}) is not covered")
+    return None, {"size": len(S)}
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/tests/instance.json b/tasks/construct-mc-vertex-cover-l4-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..95faa4715aaa723dd735a7e3d2858f47d82e84f5
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/tests/instance.json
@@ -0,0 +1 @@
+{"n": 60, "k": 41, "edges": [[0, 2], [0, 4], [0, 12], [0, 13], [0, 15], [0, 23], [0, 27], [0, 38], [0, 44], [0, 49], [0, 54], [1, 2], [1, 4], [1, 9], [1, 22], [1, 24], [1, 25], [1, 34], [1, 35], [1, 39], [1, 43], [1, 51], [1, 56], [1, 58], [2, 14], [2, 21], [2, 24], [2, 25], [2, 30], [2, 51], [2, 53], [2, 57], [2, 59], [3, 11], [3, 16], [3, 18], [3, 30], [3, 31], [3, 33], [3, 37], [3, 42], [3, 44], [3, 52], [4, 7], [4, 9], [4, 11], [4, 12], [4, 14], [4, 17], [4, 44], [4, 57], [4, 58], [5, 13], [5, 16], [5, 22], [5, 25], [5, 34], [5, 37], [5, 44], [5, 46], [5, 50], [5, 53], [5, 56], [6, 7], [6, 9], [6, 20], [6, 21], [6, 52], [7, 11], [7, 13], [7, 16], [7, 20], [7, 21], [7, 33], [7, 35], [7, 36], [7, 38], [7, 42], [7, 46], [7, 52], [7, 53], [7, 54], [7, 56], [7, 58], [8, 10], [8, 13], [8, 26], [8, 35], [8, 39], [8, 41], [8, 42], [8, 44], [8, 47], [8, 48], [8, 50], [8, 59], [9, 14], [9, 24], [9, 25], [9, 32], [9, 33], [9, 39], [9, 45], [10, 11], [10, 20], [10, 33], [10, 34], [10, 37], [10, 39], [10, 43], [10, 47], [10, 56], [10, 58], [10, 59], [11, 12], [11, 16], [11, 17], [11, 20], [11, 24], [11, 26], [11, 27], [11, 28], [11, 45], [11, 48], [11, 55], [11, 56], [12, 15], [12, 16], [12, 18], [12, 19], [12, 24], [12, 26], [12, 29], [12, 40], [12, 47], [12, 53], [13, 15], [13, 22], [13, 35], [13, 41], [13, 52], [14, 25], [14, 29], [14, 36], [14, 37], [14, 41], [14, 52], [15, 21], [15, 28], [15, 35], [15, 39], [15, 40], [15, 41], [16, 21], [16, 24], [16, 28], [16, 32], [16, 35], [16, 52], [16, 54], [17, 21], [17, 25], [17, 30], [17, 31], [17, 35], [17, 44], [17, 46], [17, 47], [17, 54], [17, 56], [18, 48], [18, 49], [18, 52], [18, 58], [19, 22], [19, 29], [19, 30], [19, 33], [19, 35], [19, 48], [20, 35], [20, 40], [20, 51], [20, 52], [21, 29], [21, 35], [21, 36], [21, 37], [21, 48], [21, 51], [21, 58], [22, 25], [22, 31], [22, 32], [22, 46], [22, 50], [22, 52], [22, 54], [22, 58], [23, 25], [23, 29], [23, 35], [23, 57], [23, 58], [23, 59], [24, 31], [24, 32], [24, 38], [24, 41], [25, 31], [25, 33], [25, 34], [25, 37], [25, 43], [25, 48], [25, 55], [25, 59], [26, 33], [26, 38], [26, 51], [26, 53], [26, 56], [27, 29], [27, 32], [27, 33], [27, 41], [27, 52], [27, 59], [28, 31], [28, 44], [28, 45], [28, 53], [29, 48], [29, 49], [29, 51], [29, 56], [30, 33], [30, 36], [30, 46], [30, 49], [31, 33], [31, 40], [31, 52], [32, 36], [32, 37], [32, 48], [32, 50], [32, 51], [32, 56], [32, 57], [32, 58], [33, 43], [33, 44], [33, 47], [33, 59], [34, 48], [34, 50], [34, 53], [34, 56], [34, 57], [35, 39], [35, 41], [35, 44], [35, 52], [36, 38], [36, 45], [36, 52], [37, 55], [38, 43], [38, 44], [38, 47], [38, 48], [38, 50], [38, 55], [38, 59], [39, 45], [39, 53], [40, 47], [40, 48], [40, 55], [41, 47], [41, 48], [41, 51], [41, 58], [42, 53], [42, 58], [43, 51], [43, 52], [43, 57], [44, 50], [44, 52], [44, 55], [45, 48], [45, 53], [45, 56], [46, 55], [46, 56], [46, 57], [46, 58], [47, 49], [48, 51], [48, 54], [49, 53], [49, 56], [49, 58], [50, 51], [50, 56], [51, 58], [52, 53], [52, 58], [55, 59]], "family": "mc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/tests/run.py b/tasks/construct-mc-vertex-cover-l4-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-mc-vertex-cover-l4-s3/tests/test.sh b/tasks/construct-mc-vertex-cover-l4-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-mc-vertex-cover-l4-s4/instruction.md b/tasks/construct-mc-vertex-cover-l4-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..9fa233e03099ef971f98aaa5d7400d2e49a2b7e3
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s4/instruction.md
@@ -0,0 +1,8 @@
+Graph G with 60 vertices numbered 0..59 and 334 edges:
+(0,11), (0,18), (0,20), (0,22), (0,24), (0,25), (0,34), (0,38), (0,40), (0,42), (0,43), (0,46), (0,52), (0,55), (1,2), (1,7), (1,8), (1,19), (1,26), (1,27), (1,28), (1,50), (1,51), (1,54), (2,11), (2,15), (2,17), (2,18), (2,20), (2,21), (2,26), (2,36), (2,44), (2,50), (2,54), (2,55), (2,57), (2,59), (3,12), (3,26), (3,32), (3,34), (3,35), (3,42), (3,47), (3,49), (3,51), (3,56), (3,58), (4,5), (4,15), (4,26), (4,49), (5,10), (5,20), (5,26), (5,27), (5,29), (5,34), (5,42), (5,47), (5,48), (6,9), (6,13), (6,15), (6,18), (6,23), (6,30), (6,31), (6,50), (6,56), (7,8), (7,10), (7,15), (7,27), (7,33), (7,34), (7,35), (7,37), (7,39), (7,41), (7,42), (7,46), (7,52), (7,53), (8,10), (8,15), (8,18), (8,19), (8,24), (8,27), (8,32), (8,38), (8,43), (8,46), (8,51), (8,52), (8,59), (9,11), (9,17), (9,22), (9,24), (9,27), (9,37), (9,39), (9,43), (9,47), (9,50), (9,54), (9,55), (9,58), (10,13), (10,16), (10,17), (10,23), (10,25), (10,26), (10,36), (10,56), (11,17), (11,23), (11,24), (11,25), (11,26), (11,29), (11,33), (11,37), (11,45), (11,49), (12,16), (12,17), (12,18), (12,19), (12,27), (12,28), (12,46), (12,51), (12,52), (13,22), (13,27), (13,28), (13,49), (13,53), (13,57), (14,17), (14,24), (14,27), (14,28), (14,29), (14,31), (14,33), (14,43), (14,47), (15,16), (15,18), (15,19), (15,32), (15,34), (15,35), (15,45), (15,50), (15,51), (15,54), (15,56), (16,22), (16,24), (16,26), (16,31), (16,32), (16,44), (16,54), (16,58), (17,18), (17,22), (17,25), (17,31), (17,38), (17,41), (17,45), (17,46), (18,19), (18,20), (18,24), (18,27), (18,37), (18,38), (18,40), (18,47), (18,48), (18,53), (19,36), (19,37), (19,41), (19,48), (20,45), (21,22), (21,23), (21,24), (21,31), (21,36), (21,43), (21,51), (21,56), (21,57), (21,58), (22,29), (22,35), (22,36), (22,38), (22,40), (22,50), (22,51), (22,52), (22,55), (23,26), (23,34), (23,38), (23,39), (23,45), (23,51), (24,25), (24,27), (24,33), (24,43), (24,44), (24,48), (24,55), (24,58), (25,26), (25,40), (25,44), (25,48), (25,49), (25,53), (25,57), (26,32), (26,34), (26,38), (26,44), (26,48), (26,54), (26,56), (26,59), (27,29), (27,30), (27,33), (27,37), (27,42), (27,51), (27,56), (27,57), (28,39), (28,46), (28,51), (28,52), (29,32), (29,42), (29,54), (29,57), (29,58), (29,59), (30,31), (30,36), (30,42), (30,54), (31,47), (31,49), (31,57), (32,33), (32,36), (32,45), (32,53), (32,57), (33,36), (33,58), (33,59), (34,35), (34,47), (35,41), (35,45), (35,46), (35,50), (35,58), (36,43), (36,44), (36,52), (36,54), (37,47), (37,49), (37,52), (37,54), (37,59), (38,45), (38,51), (39,49), (39,54), (39,58), (40,48), (40,55), (40,59), (41,47), (41,49), (42,58), (43,44), (43,47), (43,54), (43,55), (44,50), (45,52), (45,53), (45,56), (45,57), (45,59), (46,47), (46,51), (46,58), (47,48), (47,51), (47,54), (47,57), (47,59), (48,56), (49,52), (49,56), (50,56), (51,54), (51,58), (52,53), (52,58), (53,54), (54,55), (55,57), (56,58), (57,59)
+
+Find a vertex cover of G with at most 41 vertices: a set of vertices that contains at least one endpoint of every edge.
+
+Answer format: {"cover": [v_1, v_2, ...]} (distinct vertex numbers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-mc-vertex-cover-l4-s4/task.toml b/tasks/construct-mc-vertex-cover-l4-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..a3b6ca4007fc83c45093759e08205ea76cd12ec3
--- /dev/null
+++ b/tasks/construct-mc-vertex-cover-l4-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-vertex-cover-l4-s4"
+version = "0.2.0"
+description = "construct/mc_vertex_cover"
+authors = []
+keywords = ["rlmath", "construct", "mc_vertex_cover"]
+
+[metadata]
+subset = "construct"
+family = "mc_vertex_cover"
+problem_key = "graph_vertex_cover"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "MathConstraint/vertex_cover"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-3col-l4-s3/instruction.md b/tasks/construct-nppc-3col-l4-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..fb9dca6c12a0e4f18077a95ddc3e72101e4fec13
--- /dev/null
+++ b/tasks/construct-nppc-3col-l4-s3/instruction.md
@@ -0,0 +1,8 @@
+Graph with 30 vertices labelled 0..29 and edge list
+[[0, 5], [0, 7], [0, 10], [0, 13], [0, 23], [1, 2], [1, 6], [1, 16], [1, 20], [1, 24], [1, 28], [2, 13], [2, 19], [2, 21], [2, 22], [3, 4], [3, 5], [3, 22], [3, 25], [3, 26], [3, 28], [4, 7], [4, 9], [4, 12], [4, 17], [4, 21], [5, 12], [5, 23], [6, 15], [6, 19], [6, 21], [7, 15], [7, 19], [7, 21], [8, 13], [8, 14], [8, 24], [8, 26], [9, 23], [10, 15], [10, 16], [11, 13], [11, 18], [11, 21], [11, 22], [11, 26], [12, 18], [12, 22], [13, 19], [13, 23], [13, 27], [13, 29], [14, 18], [14, 19], [14, 21], [14, 26], [15, 22], [16, 21], [16, 29], [17, 20], [17, 24], [17, 26], [18, 24], [19, 22], [19, 25], [20, 27], [21, 22], [21, 25], [21, 27], [21, 28], [22, 23], [22, 24], [22, 27], [22, 28], [22, 29], [24, 25], [25, 27], [25, 28], [25, 29], [28, 29]]
+
+Give a proper colouring with colours 0, 1, 2: adjacent vertices must get different colours.
+
+Answer format: {"coloring": [c_0, ..., c_29]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-3col-l4-s3/task.toml b/tasks/construct-nppc-3col-l4-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..107ac973536eb36757c757bad39446bcbfba7370
--- /dev/null
+++ b/tasks/construct-nppc-3col-l4-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-3col-l4-s3"
+version = "0.2.0"
+description = "construct/nppc_three_coloring"
+authors = []
+keywords = ["rlmath", "construct", "nppc_three_coloring"]
+
+[metadata]
+subset = "construct"
+family = "nppc_three_coloring"
+problem_key = "graph_3_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "NPPC/graph_three_colorability"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-3col-l4-s4/instruction.md b/tasks/construct-nppc-3col-l4-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3f32020bc12c568f6f77f30728bf872ceebaa7c4
--- /dev/null
+++ b/tasks/construct-nppc-3col-l4-s4/instruction.md
@@ -0,0 +1,8 @@
+Graph with 30 vertices labelled 0..29 and edge list
+[[0, 3], [0, 5], [0, 10], [0, 14], [0, 18], [0, 29], [1, 3], [1, 15], [2, 6], [2, 10], [2, 11], [2, 14], [2, 15], [2, 26], [3, 9], [3, 12], [3, 16], [3, 27], [4, 6], [4, 14], [4, 15], [4, 20], [4, 21], [4, 23], [4, 25], [5, 16], [5, 17], [5, 24], [5, 25], [6, 7], [6, 13], [6, 21], [6, 23], [6, 27], [7, 14], [7, 17], [7, 27], [7, 28], [8, 9], [8, 12], [8, 13], [8, 20], [8, 24], [9, 10], [9, 17], [9, 21], [9, 26], [9, 27], [10, 24], [11, 26], [12, 14], [12, 15], [12, 26], [12, 28], [12, 29], [13, 15], [13, 24], [14, 17], [14, 24], [15, 22], [15, 23], [15, 26], [15, 27], [16, 17], [16, 26], [17, 26], [17, 27], [18, 22], [18, 23], [19, 24], [19, 27], [20, 26], [20, 27], [21, 22], [22, 24], [22, 26], [22, 29], [23, 24], [23, 25], [24, 26]]
+
+Give a proper colouring with colours 0, 1, 2: adjacent vertices must get different colours.
+
+Answer format: {"coloring": [c_0, ..., c_29]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-3col-l4-s4/task.toml b/tasks/construct-nppc-3col-l4-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..50a5039b4bf39d0d687e3b59dbaec81ca3874f6c
--- /dev/null
+++ b/tasks/construct-nppc-3col-l4-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-3col-l4-s4"
+version = "0.2.0"
+description = "construct/nppc_three_coloring"
+authors = []
+keywords = ["rlmath", "construct", "nppc_three_coloring"]
+
+[metadata]
+subset = "construct"
+family = "nppc_three_coloring"
+problem_key = "graph_3_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "NPPC/graph_three_colorability"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/environment/instance.json b/tasks/construct-nppc-bandwidth-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..723f69888ea10ad91fc0a106b8394c63cbac1c43
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 3, "edges": [[0, 2], [1, 3], [2, 3], [3, 4], [3, 7], [4, 6], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/instruction.md b/tasks/construct-nppc-bandwidth-l2-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..59a38ca5b8becc07a41280b20912d7624decb476
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 8 vertices labelled 0..7 and 8 edges:
+[[0, 2], [1, 3], [2, 3], [3, 4], [3, 7], [4, 6], [5, 6], [6, 7]]
+
+Find a linear layout of bandwidth at most 3: assign to each vertex v a distinct position p[v] in 0..7 (a permutation) such that |p[u] - p[v]| <= 3 for every edge (u, v).
+
+Answer format: {"layout": [p_0, p_1, ..., p_7]} where p_v is the position of vertex v.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/solution/solve.sh b/tasks/construct-nppc-bandwidth-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..73dd9f31e1529ddde1d5f3224e646ad81d160405
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [0, 6, 1, 4, 3, 7, 5, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/task.toml b/tasks/construct-nppc-bandwidth-l2-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..28e825ee81756aa85aa7d976cba4c1c8da29961d
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-bandwidth-l2-s1"
+version = "0.2.0"
+description = "construct/nppc_bandwidth"
+authors = []
+keywords = ["rlmath", "construct", "nppc_bandwidth"]
+
+[metadata]
+subset = "construct"
+family = "nppc_bandwidth"
+problem_key = "graph_bandwidth"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "NPPC/bandwidth"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/tests/check.py b/tasks/construct-nppc-bandwidth-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/tests/instance.json b/tasks/construct-nppc-bandwidth-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..723f69888ea10ad91fc0a106b8394c63cbac1c43
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 3, "edges": [[0, 2], [1, 3], [2, 3], [3, 4], [3, 7], [4, 6], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/tests/run.py b/tasks/construct-nppc-bandwidth-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l2-s1/tests/test.sh b/tasks/construct-nppc-bandwidth-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l2-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/environment/instance.json b/tasks/construct-nppc-bandwidth-l2-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..27dd20936d96e7acab021be3deedccd20eb7204c
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 3, "edges": [[0, 5], [0, 7], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/instruction.md b/tasks/construct-nppc-bandwidth-l2-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b3aa58175592166c81a97424415ba689a8aad8f2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 8 vertices labelled 0..7 and 8 edges:
+[[0, 5], [0, 7], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]]
+
+Find a linear layout of bandwidth at most 3: assign to each vertex v a distinct position p[v] in 0..7 (a permutation) such that |p[u] - p[v]| <= 3 for every edge (u, v).
+
+Answer format: {"layout": [p_0, p_1, ..., p_7]} where p_v is the position of vertex v.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/solution/solve.sh b/tasks/construct-nppc-bandwidth-l2-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ca268b156584a2193224dfb41b8ea890593f1667
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [0, 4, 6, 7, 5, 2, 1, 3]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/task.toml b/tasks/construct-nppc-bandwidth-l2-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ec05db43371eb4f77815e35850fddc33b87766df
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-bandwidth-l2-s6"
+version = "0.2.0"
+description = "construct/nppc_bandwidth"
+authors = []
+keywords = ["rlmath", "construct", "nppc_bandwidth"]
+
+[metadata]
+subset = "construct"
+family = "nppc_bandwidth"
+problem_key = "graph_bandwidth"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "NPPC/bandwidth"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/tests/check.py b/tasks/construct-nppc-bandwidth-l2-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/tests/instance.json b/tasks/construct-nppc-bandwidth-l2-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..27dd20936d96e7acab021be3deedccd20eb7204c
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 3, "edges": [[0, 5], [0, 7], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/tests/run.py b/tasks/construct-nppc-bandwidth-l2-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l2-s6/tests/test.sh b/tasks/construct-nppc-bandwidth-l2-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/environment/instance.json b/tasks/construct-nppc-bandwidth-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2eb560152fe51c52229844c9bd8ea3d50fce7011
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 3, "edges": [[0, 3], [1, 2], [2, 3], [3, 4], [3, 5], [4, 5], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/instruction.md b/tasks/construct-nppc-bandwidth-l2-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..0833ad37a0bb0053ed9ff8af96665c331ad81896
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 8 vertices labelled 0..7 and 8 edges:
+[[0, 3], [1, 2], [2, 3], [3, 4], [3, 5], [4, 5], [5, 6], [6, 7]]
+
+Find a linear layout of bandwidth at most 3: assign to each vertex v a distinct position p[v] in 0..7 (a permutation) such that |p[u] - p[v]| <= 3 for every edge (u, v).
+
+Answer format: {"layout": [p_0, p_1, ..., p_7]} where p_v is the position of vertex v.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/solution/solve.sh b/tasks/construct-nppc-bandwidth-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..47b382af0dd03ea9a09acc3d95674aa72633b6b5
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [1, 7, 5, 4, 6, 3, 0, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/task.toml b/tasks/construct-nppc-bandwidth-l2-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5fcea20cc459ade3c250409b840e968cc131e2fc
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-bandwidth-l2-s8"
+version = "0.2.0"
+description = "construct/nppc_bandwidth"
+authors = []
+keywords = ["rlmath", "construct", "nppc_bandwidth"]
+
+[metadata]
+subset = "construct"
+family = "nppc_bandwidth"
+problem_key = "graph_bandwidth"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "NPPC/bandwidth"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/tests/check.py b/tasks/construct-nppc-bandwidth-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/tests/instance.json b/tasks/construct-nppc-bandwidth-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2eb560152fe51c52229844c9bd8ea3d50fce7011
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "bandwidth": 3, "edges": [[0, 3], [1, 2], [2, 3], [3, 4], [3, 5], [4, 5], [5, 6], [6, 7]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/tests/run.py b/tasks/construct-nppc-bandwidth-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l2-s8/tests/test.sh b/tasks/construct-nppc-bandwidth-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l2-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/environment/instance.json b/tasks/construct-nppc-bandwidth-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c37466faaf15b4f1b6cd3678471f778f1eac9482
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "bandwidth": 5, "edges": [[0, 9], [0, 17], [0, 24], [0, 26], [0, 28], [0, 40], [1, 8], [1, 11], [1, 36], [1, 46], [1, 61], [1, 70], [1, 71], [2, 4], [2, 14], [2, 15], [2, 25], [2, 35], [2, 42], [2, 52], [2, 62], [3, 12], [3, 69], [3, 71], [3, 76], [4, 14], [4, 35], [4, 55], [5, 20], [5, 49], [5, 76], [6, 7], [6, 22], [6, 39], [6, 47], [6, 65], [6, 75], [7, 22], [7, 47], [7, 50], [7, 58], [7, 77], [8, 11], [8, 69], [8, 70], [8, 71], [9, 17], [9, 28], [9, 34], [9, 37], [9, 78], [10, 13], [10, 19], [10, 22], [10, 47], [10, 58], [11, 12], [11, 38], [11, 46], [12, 16], [12, 38], [12, 69], [13, 19], [13, 39], [13, 58], [14, 31], [14, 32], [14, 42], [14, 52], [14, 55], [14, 62], [14, 67], [15, 18], [15, 25], [15, 30], [15, 31], [15, 35], [15, 52], [16, 38], [16, 49], [16, 69], [16, 71], [16, 76], [17, 21], [17, 28], [17, 34], [17, 37], [17, 53], [17, 60], [18, 30], [18, 36], [18, 46], [18, 61], [19, 27], [20, 23], [20, 45], [20, 68], [20, 72], [21, 28], [21, 57], [21, 62], [22, 39], [22, 44], [22, 47], [23, 66], [23, 68], [23, 72], [24, 26], [24, 29], [24, 41], [24, 63], [24, 73], [24, 79], [25, 30], [25, 33], [25, 35], [26, 29], [26, 40], [26, 51], [27, 39], [28, 29], [28, 34], [28, 37], [28, 53], [29, 37], [29, 51], [29, 78], [30, 33], [30, 46], [31, 33], [32, 42], [32, 57], [32, 60], [32, 67], [33, 36], [33, 52], [33, 64], [34, 37], [34, 48], [34, 57], [34, 60], [34, 67], [35, 42], [36, 46], [37, 48], [37, 78], [38, 49], [38, 69], [38, 76], [39, 44], [39, 77], [40, 41], [40, 63], [40, 78], [40, 79], [41, 51], [41, 59], [41, 78], [41, 79], [42, 55], [42, 60], [42, 62], [42, 67], [43, 45], [43, 49], [43, 68], [43, 72], [44, 47], [45, 49], [45, 68], [45, 72], [46, 61], [47, 50], [47, 58], [47, 77], [48, 53], [48, 57], [49, 72], [49, 74], [49, 76], [50, 54], [50, 56], [50, 65], [50, 75], [51, 54], [51, 63], [52, 64], [53, 57], [54, 56], [54, 73], [54, 75], [54, 79], [55, 57], [55, 60], [55, 67], [56, 59], [56, 65], [56, 75], [57, 60], [57, 67], [59, 63], [59, 65], [59, 73], [59, 77], [60, 62], [60, 67], [61, 64], [61, 70], [62, 67], [63, 65], [65, 73], [65, 77], [66, 68], [66, 72], [68, 72], [69, 70], [69, 71], [69, 74], [71, 74], [72, 76], [73, 75], [74, 76], [75, 77], [75, 79]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/instruction.md b/tasks/construct-nppc-bandwidth-l6-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..d768f64f73eac27a24e3aa5a62e8153b0e5545c7
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 80 vertices labelled 0..79 and 224 edges:
+[[0, 9], [0, 17], [0, 24], [0, 26], [0, 28], [0, 40], [1, 8], [1, 11], [1, 36], [1, 46], [1, 61], [1, 70], [1, 71], [2, 4], [2, 14], [2, 15], [2, 25], [2, 35], [2, 42], [2, 52], [2, 62], [3, 12], [3, 69], [3, 71], [3, 76], [4, 14], [4, 35], [4, 55], [5, 20], [5, 49], [5, 76], [6, 7], [6, 22], [6, 39], [6, 47], [6, 65], [6, 75], [7, 22], [7, 47], [7, 50], [7, 58], [7, 77], [8, 11], [8, 69], [8, 70], [8, 71], [9, 17], [9, 28], [9, 34], [9, 37], [9, 78], [10, 13], [10, 19], [10, 22], [10, 47], [10, 58], [11, 12], [11, 38], [11, 46], [12, 16], [12, 38], [12, 69], [13, 19], [13, 39], [13, 58], [14, 31], [14, 32], [14, 42], [14, 52], [14, 55], [14, 62], [14, 67], [15, 18], [15, 25], [15, 30], [15, 31], [15, 35], [15, 52], [16, 38], [16, 49], [16, 69], [16, 71], [16, 76], [17, 21], [17, 28], [17, 34], [17, 37], [17, 53], [17, 60], [18, 30], [18, 36], [18, 46], [18, 61], [19, 27], [20, 23], [20, 45], [20, 68], [20, 72], [21, 28], [21, 57], [21, 62], [22, 39], [22, 44], [22, 47], [23, 66], [23, 68], [23, 72], [24, 26], [24, 29], [24, 41], [24, 63], [24, 73], [24, 79], [25, 30], [25, 33], [25, 35], [26, 29], [26, 40], [26, 51], [27, 39], [28, 29], [28, 34], [28, 37], [28, 53], [29, 37], [29, 51], [29, 78], [30, 33], [30, 46], [31, 33], [32, 42], [32, 57], [32, 60], [32, 67], [33, 36], [33, 52], [33, 64], [34, 37], [34, 48], [34, 57], [34, 60], [34, 67], [35, 42], [36, 46], [37, 48], [37, 78], [38, 49], [38, 69], [38, 76], [39, 44], [39, 77], [40, 41], [40, 63], [40, 78], [40, 79], [41, 51], [41, 59], [41, 78], [41, 79], [42, 55], [42, 60], [42, 62], [42, 67], [43, 45], [43, 49], [43, 68], [43, 72], [44, 47], [45, 49], [45, 68], [45, 72], [46, 61], [47, 50], [47, 58], [47, 77], [48, 53], [48, 57], [49, 72], [49, 74], [49, 76], [50, 54], [50, 56], [50, 65], [50, 75], [51, 54], [51, 63], [52, 64], [53, 57], [54, 56], [54, 73], [54, 75], [54, 79], [55, 57], [55, 60], [55, 67], [56, 59], [56, 65], [56, 75], [57, 60], [57, 67], [59, 63], [59, 65], [59, 73], [59, 77], [60, 62], [60, 67], [61, 64], [61, 70], [62, 67], [63, 65], [65, 73], [65, 77], [66, 68], [66, 72], [68, 72], [69, 70], [69, 71], [69, 74], [71, 74], [72, 76], [73, 75], [74, 76], [75, 77], [75, 79]]
+
+Find a linear layout of bandwidth at most 5: assign to each vertex v a distinct position p[v] in 0..79 (a permutation) such that |p[u] - p[v]| <= 5 for every edge (u, v).
+
+Answer format: {"layout": [p_0, p_1, ..., p_79]} where p_v is the position of vertex v.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/solution/solve.sh b/tasks/construct-nppc-bandwidth-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c4ec6bb9738916ef2407b3a307ea80848c499f23
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [28, 60, 46, 68, 45, 74, 10, 9, 61, 29, 3, 62, 63, 2, 44, 51, 67, 33, 56, 0, 76, 36, 7, 79, 23, 50, 25, 1, 31, 27, 54, 48, 40, 53, 34, 47, 57, 30, 66, 6, 24, 21, 43, 72, 5, 73, 58, 8, 35, 71, 12, 22, 49, 32, 17, 42, 13, 37, 4, 16, 38, 55, 41, 20, 52, 15, 78, 39, 77, 64, 59, 65, 75, 18, 69, 14, 70, 11, 26, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/task.toml b/tasks/construct-nppc-bandwidth-l6-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..124c2b460c2719c52848a26d2e9ddae2ff698528
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-bandwidth-l6-s0"
+version = "0.2.0"
+description = "construct/nppc_bandwidth"
+authors = []
+keywords = ["rlmath", "construct", "nppc_bandwidth"]
+
+[metadata]
+subset = "construct"
+family = "nppc_bandwidth"
+problem_key = "graph_bandwidth"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "NPPC/bandwidth"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/tests/check.py b/tasks/construct-nppc-bandwidth-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/tests/instance.json b/tasks/construct-nppc-bandwidth-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c37466faaf15b4f1b6cd3678471f778f1eac9482
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "bandwidth": 5, "edges": [[0, 9], [0, 17], [0, 24], [0, 26], [0, 28], [0, 40], [1, 8], [1, 11], [1, 36], [1, 46], [1, 61], [1, 70], [1, 71], [2, 4], [2, 14], [2, 15], [2, 25], [2, 35], [2, 42], [2, 52], [2, 62], [3, 12], [3, 69], [3, 71], [3, 76], [4, 14], [4, 35], [4, 55], [5, 20], [5, 49], [5, 76], [6, 7], [6, 22], [6, 39], [6, 47], [6, 65], [6, 75], [7, 22], [7, 47], [7, 50], [7, 58], [7, 77], [8, 11], [8, 69], [8, 70], [8, 71], [9, 17], [9, 28], [9, 34], [9, 37], [9, 78], [10, 13], [10, 19], [10, 22], [10, 47], [10, 58], [11, 12], [11, 38], [11, 46], [12, 16], [12, 38], [12, 69], [13, 19], [13, 39], [13, 58], [14, 31], [14, 32], [14, 42], [14, 52], [14, 55], [14, 62], [14, 67], [15, 18], [15, 25], [15, 30], [15, 31], [15, 35], [15, 52], [16, 38], [16, 49], [16, 69], [16, 71], [16, 76], [17, 21], [17, 28], [17, 34], [17, 37], [17, 53], [17, 60], [18, 30], [18, 36], [18, 46], [18, 61], [19, 27], [20, 23], [20, 45], [20, 68], [20, 72], [21, 28], [21, 57], [21, 62], [22, 39], [22, 44], [22, 47], [23, 66], [23, 68], [23, 72], [24, 26], [24, 29], [24, 41], [24, 63], [24, 73], [24, 79], [25, 30], [25, 33], [25, 35], [26, 29], [26, 40], [26, 51], [27, 39], [28, 29], [28, 34], [28, 37], [28, 53], [29, 37], [29, 51], [29, 78], [30, 33], [30, 46], [31, 33], [32, 42], [32, 57], [32, 60], [32, 67], [33, 36], [33, 52], [33, 64], [34, 37], [34, 48], [34, 57], [34, 60], [34, 67], [35, 42], [36, 46], [37, 48], [37, 78], [38, 49], [38, 69], [38, 76], [39, 44], [39, 77], [40, 41], [40, 63], [40, 78], [40, 79], [41, 51], [41, 59], [41, 78], [41, 79], [42, 55], [42, 60], [42, 62], [42, 67], [43, 45], [43, 49], [43, 68], [43, 72], [44, 47], [45, 49], [45, 68], [45, 72], [46, 61], [47, 50], [47, 58], [47, 77], [48, 53], [48, 57], [49, 72], [49, 74], [49, 76], [50, 54], [50, 56], [50, 65], [50, 75], [51, 54], [51, 63], [52, 64], [53, 57], [54, 56], [54, 73], [54, 75], [54, 79], [55, 57], [55, 60], [55, 67], [56, 59], [56, 65], [56, 75], [57, 60], [57, 67], [59, 63], [59, 65], [59, 73], [59, 77], [60, 62], [60, 67], [61, 64], [61, 70], [62, 67], [63, 65], [65, 73], [65, 77], [66, 68], [66, 72], [68, 72], [69, 70], [69, 71], [69, 74], [71, 74], [72, 76], [73, 75], [74, 76], [75, 77], [75, 79]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/tests/run.py b/tasks/construct-nppc-bandwidth-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l6-s0/tests/test.sh b/tasks/construct-nppc-bandwidth-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/environment/instance.json b/tasks/construct-nppc-bandwidth-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4cd889c5df22f33dd167ef066838479c0588954a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "bandwidth": 5, "edges": [[0, 10], [0, 46], [0, 53], [0, 74], [0, 75], [1, 11], [1, 20], [1, 28], [1, 37], [1, 51], [1, 76], [1, 78], [2, 3], [2, 12], [2, 16], [2, 54], [2, 60], [2, 64], [2, 77], [3, 12], [3, 24], [3, 25], [3, 54], [3, 58], [3, 60], [4, 15], [4, 18], [4, 19], [4, 48], [4, 55], [4, 56], [5, 7], [5, 8], [5, 9], [5, 57], [5, 61], [5, 65], [6, 18], [6, 68], [7, 9], [7, 30], [7, 46], [7, 57], [7, 61], [7, 65], [7, 67], [8, 9], [8, 21], [8, 31], [8, 61], [8, 65], [8, 73], [9, 21], [9, 31], [9, 57], [9, 61], [9, 73], [10, 23], [10, 30], [10, 36], [10, 46], [10, 67], [10, 75], [11, 17], [11, 20], [11, 37], [11, 44], [11, 47], [11, 50], [11, 76], [12, 17], [12, 35], [12, 47], [12, 60], [13, 14], [13, 22], [13, 29], [13, 33], [13, 41], [13, 63], [14, 22], [14, 29], [14, 33], [14, 41], [14, 66], [14, 71], [15, 19], [15, 29], [15, 38], [15, 48], [15, 55], [16, 24], [16, 34], [16, 49], [16, 60], [16, 64], [17, 35], [17, 37], [17, 47], [17, 58], [17, 76], [18, 19], [18, 40], [18, 52], [18, 55], [18, 56], [18, 68], [19, 52], [19, 55], [19, 69], [19, 79], [20, 28], [20, 51], [20, 76], [20, 78], [21, 31], [21, 73], [22, 26], [22, 39], [22, 71], [23, 30], [23, 46], [23, 67], [23, 70], [23, 74], [24, 25], [24, 71], [25, 45], [25, 54], [25, 60], [25, 64], [25, 72], [26, 29], [26, 48], [26, 63], [27, 32], [27, 40], [27, 59], [27, 68], [27, 69], [28, 36], [28, 53], [28, 74], [28, 76], [29, 38], [29, 48], [29, 63], [30, 46], [30, 57], [30, 65], [30, 67], [30, 75], [31, 43], [31, 57], [31, 65], [31, 73], [32, 40], [32, 42], [32, 59], [33, 34], [33, 41], [33, 49], [33, 66], [33, 72], [34, 41], [34, 64], [35, 37], [35, 54], [35, 77], [36, 51], [36, 53], [36, 78], [37, 44], [37, 47], [37, 76], [37, 77], [38, 39], [38, 52], [38, 63], [38, 79], [39, 48], [39, 63], [40, 42], [40, 59], [41, 49], [41, 63], [42, 62], [43, 73], [44, 50], [44, 51], [44, 76], [44, 78], [45, 47], [45, 60], [46, 53], [46, 57], [46, 70], [47, 50], [47, 77], [48, 52], [49, 64], [49, 66], [49, 71], [49, 72], [50, 51], [51, 70], [51, 78], [52, 55], [53, 70], [53, 74], [53, 78], [54, 58], [54, 60], [54, 77], [55, 56], [55, 59], [55, 79], [56, 59], [57, 61], [57, 65], [58, 77], [59, 68], [60, 64], [60, 72], [61, 65], [61, 73], [62, 68], [63, 66], [64, 71], [64, 72], [65, 67], [66, 71], [67, 75], [68, 69], [70, 74], [70, 78], [71, 72], [74, 78]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/instruction.md b/tasks/construct-nppc-bandwidth-l6-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..5c4c16453d2146b46084fabdb89f91599e68a518
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 80 vertices labelled 0..79 and 238 edges:
+[[0, 10], [0, 46], [0, 53], [0, 74], [0, 75], [1, 11], [1, 20], [1, 28], [1, 37], [1, 51], [1, 76], [1, 78], [2, 3], [2, 12], [2, 16], [2, 54], [2, 60], [2, 64], [2, 77], [3, 12], [3, 24], [3, 25], [3, 54], [3, 58], [3, 60], [4, 15], [4, 18], [4, 19], [4, 48], [4, 55], [4, 56], [5, 7], [5, 8], [5, 9], [5, 57], [5, 61], [5, 65], [6, 18], [6, 68], [7, 9], [7, 30], [7, 46], [7, 57], [7, 61], [7, 65], [7, 67], [8, 9], [8, 21], [8, 31], [8, 61], [8, 65], [8, 73], [9, 21], [9, 31], [9, 57], [9, 61], [9, 73], [10, 23], [10, 30], [10, 36], [10, 46], [10, 67], [10, 75], [11, 17], [11, 20], [11, 37], [11, 44], [11, 47], [11, 50], [11, 76], [12, 17], [12, 35], [12, 47], [12, 60], [13, 14], [13, 22], [13, 29], [13, 33], [13, 41], [13, 63], [14, 22], [14, 29], [14, 33], [14, 41], [14, 66], [14, 71], [15, 19], [15, 29], [15, 38], [15, 48], [15, 55], [16, 24], [16, 34], [16, 49], [16, 60], [16, 64], [17, 35], [17, 37], [17, 47], [17, 58], [17, 76], [18, 19], [18, 40], [18, 52], [18, 55], [18, 56], [18, 68], [19, 52], [19, 55], [19, 69], [19, 79], [20, 28], [20, 51], [20, 76], [20, 78], [21, 31], [21, 73], [22, 26], [22, 39], [22, 71], [23, 30], [23, 46], [23, 67], [23, 70], [23, 74], [24, 25], [24, 71], [25, 45], [25, 54], [25, 60], [25, 64], [25, 72], [26, 29], [26, 48], [26, 63], [27, 32], [27, 40], [27, 59], [27, 68], [27, 69], [28, 36], [28, 53], [28, 74], [28, 76], [29, 38], [29, 48], [29, 63], [30, 46], [30, 57], [30, 65], [30, 67], [30, 75], [31, 43], [31, 57], [31, 65], [31, 73], [32, 40], [32, 42], [32, 59], [33, 34], [33, 41], [33, 49], [33, 66], [33, 72], [34, 41], [34, 64], [35, 37], [35, 54], [35, 77], [36, 51], [36, 53], [36, 78], [37, 44], [37, 47], [37, 76], [37, 77], [38, 39], [38, 52], [38, 63], [38, 79], [39, 48], [39, 63], [40, 42], [40, 59], [41, 49], [41, 63], [42, 62], [43, 73], [44, 50], [44, 51], [44, 76], [44, 78], [45, 47], [45, 60], [46, 53], [46, 57], [46, 70], [47, 50], [47, 77], [48, 52], [49, 64], [49, 66], [49, 71], [49, 72], [50, 51], [51, 70], [51, 78], [52, 55], [53, 70], [53, 74], [53, 78], [54, 58], [54, 60], [54, 77], [55, 56], [55, 59], [55, 79], [56, 59], [57, 61], [57, 65], [58, 77], [59, 68], [60, 64], [60, 72], [61, 65], [61, 73], [62, 68], [63, 66], [64, 71], [64, 72], [65, 67], [66, 71], [67, 75], [68, 69], [70, 74], [70, 78], [71, 72], [74, 78]]
+
+Find a linear layout of bandwidth at most 5: assign to each vertex v a distinct position p[v] in 0..79 (a permutation) such that |p[u] - p[v]| <= 5 for every edge (u, v).
+
+Answer format: {"layout": [p_0, p_1, ..., p_79]} where p_v is the position of vertex v.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/solution/solve.sh b/tasks/construct-nppc-bandwidth-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..90f9c0c3b58100d194ac250dcb4a0f2298768aa6
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [63, 53, 38, 39, 14, 72, 6, 69, 76, 74, 64, 49, 42, 23, 25, 16, 35, 47, 9, 11, 54, 78, 24, 62, 34, 36, 21, 3, 56, 20, 66, 75, 2, 28, 30, 46, 59, 48, 17, 19, 4, 26, 0, 79, 52, 40, 65, 45, 18, 31, 50, 55, 13, 61, 41, 12, 10, 70, 44, 7, 37, 73, 1, 22, 33, 71, 27, 67, 5, 8, 60, 29, 32, 77, 58, 68, 51, 43, 57, 15]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/task.toml b/tasks/construct-nppc-bandwidth-l6-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..85c4fa73270a556d0440f9612979f74d1377553c
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-bandwidth-l6-s7"
+version = "0.2.0"
+description = "construct/nppc_bandwidth"
+authors = []
+keywords = ["rlmath", "construct", "nppc_bandwidth"]
+
+[metadata]
+subset = "construct"
+family = "nppc_bandwidth"
+problem_key = "graph_bandwidth"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "NPPC/bandwidth"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/tests/check.py b/tasks/construct-nppc-bandwidth-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/tests/instance.json b/tasks/construct-nppc-bandwidth-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4cd889c5df22f33dd167ef066838479c0588954a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "bandwidth": 5, "edges": [[0, 10], [0, 46], [0, 53], [0, 74], [0, 75], [1, 11], [1, 20], [1, 28], [1, 37], [1, 51], [1, 76], [1, 78], [2, 3], [2, 12], [2, 16], [2, 54], [2, 60], [2, 64], [2, 77], [3, 12], [3, 24], [3, 25], [3, 54], [3, 58], [3, 60], [4, 15], [4, 18], [4, 19], [4, 48], [4, 55], [4, 56], [5, 7], [5, 8], [5, 9], [5, 57], [5, 61], [5, 65], [6, 18], [6, 68], [7, 9], [7, 30], [7, 46], [7, 57], [7, 61], [7, 65], [7, 67], [8, 9], [8, 21], [8, 31], [8, 61], [8, 65], [8, 73], [9, 21], [9, 31], [9, 57], [9, 61], [9, 73], [10, 23], [10, 30], [10, 36], [10, 46], [10, 67], [10, 75], [11, 17], [11, 20], [11, 37], [11, 44], [11, 47], [11, 50], [11, 76], [12, 17], [12, 35], [12, 47], [12, 60], [13, 14], [13, 22], [13, 29], [13, 33], [13, 41], [13, 63], [14, 22], [14, 29], [14, 33], [14, 41], [14, 66], [14, 71], [15, 19], [15, 29], [15, 38], [15, 48], [15, 55], [16, 24], [16, 34], [16, 49], [16, 60], [16, 64], [17, 35], [17, 37], [17, 47], [17, 58], [17, 76], [18, 19], [18, 40], [18, 52], [18, 55], [18, 56], [18, 68], [19, 52], [19, 55], [19, 69], [19, 79], [20, 28], [20, 51], [20, 76], [20, 78], [21, 31], [21, 73], [22, 26], [22, 39], [22, 71], [23, 30], [23, 46], [23, 67], [23, 70], [23, 74], [24, 25], [24, 71], [25, 45], [25, 54], [25, 60], [25, 64], [25, 72], [26, 29], [26, 48], [26, 63], [27, 32], [27, 40], [27, 59], [27, 68], [27, 69], [28, 36], [28, 53], [28, 74], [28, 76], [29, 38], [29, 48], [29, 63], [30, 46], [30, 57], [30, 65], [30, 67], [30, 75], [31, 43], [31, 57], [31, 65], [31, 73], [32, 40], [32, 42], [32, 59], [33, 34], [33, 41], [33, 49], [33, 66], [33, 72], [34, 41], [34, 64], [35, 37], [35, 54], [35, 77], [36, 51], [36, 53], [36, 78], [37, 44], [37, 47], [37, 76], [37, 77], [38, 39], [38, 52], [38, 63], [38, 79], [39, 48], [39, 63], [40, 42], [40, 59], [41, 49], [41, 63], [42, 62], [43, 73], [44, 50], [44, 51], [44, 76], [44, 78], [45, 47], [45, 60], [46, 53], [46, 57], [46, 70], [47, 50], [47, 77], [48, 52], [49, 64], [49, 66], [49, 71], [49, 72], [50, 51], [51, 70], [51, 78], [52, 55], [53, 70], [53, 74], [53, 78], [54, 58], [54, 60], [54, 77], [55, 56], [55, 59], [55, 79], [56, 59], [57, 61], [57, 65], [58, 77], [59, 68], [60, 64], [60, 72], [61, 65], [61, 73], [62, 68], [63, 66], [64, 71], [64, 72], [65, 67], [66, 71], [67, 75], [68, 69], [70, 74], [70, 78], [71, 72], [74, 78]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/tests/run.py b/tasks/construct-nppc-bandwidth-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l6-s7/tests/test.sh b/tasks/construct-nppc-bandwidth-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/environment/Dockerfile b/tasks/construct-nppc-bandwidth-l6-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/environment/instance.json b/tasks/construct-nppc-bandwidth-l6-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..03037aed544a73c6b7ef85863cce1087fcc5c237
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "bandwidth": 5, "edges": [[0, 1], [0, 3], [0, 5], [0, 17], [0, 32], [0, 74], [1, 3], [1, 17], [1, 32], [2, 5], [2, 6], [2, 33], [2, 38], [2, 39], [2, 48], [2, 57], [3, 32], [4, 9], [4, 24], [4, 29], [4, 36], [4, 45], [4, 66], [4, 75], [5, 17], [5, 38], [5, 48], [5, 57], [5, 67], [6, 33], [6, 39], [6, 46], [7, 12], [7, 19], [7, 63], [7, 68], [7, 70], [7, 79], [8, 19], [8, 27], [8, 60], [8, 63], [9, 15], [9, 24], [9, 29], [9, 40], [9, 50], [9, 54], [9, 66], [9, 69], [10, 11], [10, 31], [10, 58], [10, 62], [10, 69], [10, 77], [11, 31], [11, 33], [11, 42], [11, 62], [11, 77], [12, 19], [12, 65], [12, 79], [13, 14], [13, 22], [13, 28], [13, 37], [13, 49], [13, 51], [13, 53], [13, 55], [14, 28], [14, 37], [14, 56], [14, 65], [14, 78], [15, 21], [15, 24], [15, 29], [15, 50], [15, 54], [15, 69], [16, 24], [16, 29], [16, 36], [16, 43], [16, 45], [16, 66], [17, 32], [17, 34], [18, 20], [18, 27], [18, 30], [18, 44], [18, 47], [18, 60], [18, 72], [19, 23], [19, 26], [19, 60], [19, 63], [19, 79], [20, 25], [20, 72], [21, 31], [21, 50], [21, 54], [21, 69], [22, 28], [22, 36], [22, 37], [22, 49], [22, 51], [22, 55], [23, 26], [23, 59], [23, 63], [23, 79], [24, 29], [24, 40], [24, 66], [25, 27], [26, 63], [26, 65], [26, 70], [26, 71], [27, 30], [27, 44], [27, 59], [27, 60], [27, 72], [28, 37], [28, 41], [28, 53], [28, 78], [29, 35], [29, 50], [29, 66], [30, 44], [30, 60], [30, 72], [31, 42], [31, 58], [31, 62], [31, 77], [32, 34], [32, 67], [33, 38], [33, 39], [33, 76], [34, 38], [34, 67], [35, 40], [35, 66], [36, 43], [36, 45], [36, 49], [36, 55], [37, 41], [37, 51], [37, 52], [37, 78], [38, 48], [39, 42], [39, 46], [39, 58], [40, 50], [40, 54], [41, 51], [41, 64], [41, 65], [41, 71], [42, 46], [42, 73], [42, 76], [43, 45], [43, 49], [43, 53], [43, 66], [43, 75], [44, 59], [44, 60], [44, 72], [45, 49], [45, 55], [45, 75], [46, 58], [47, 72], [48, 57], [49, 51], [49, 55], [50, 54], [50, 61], [51, 53], [51, 78], [52, 56], [52, 65], [52, 68], [52, 70], [52, 71], [53, 55], [54, 61], [54, 69], [55, 75], [56, 64], [56, 70], [56, 71], [57, 74], [58, 61], [58, 73], [58, 77], [59, 60], [60, 72], [61, 62], [61, 69], [61, 77], [62, 73], [62, 77], [63, 68], [64, 65], [64, 78], [65, 68], [65, 71], [66, 75], [67, 74], [68, 70], [68, 79], [69, 77], [70, 71], [70, 79], [73, 76], [73, 77]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/instruction.md b/tasks/construct-nppc-bandwidth-l6-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..f8293fb7265c7cb36616bfd60dd159556f36d3a3
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 80 vertices labelled 0..79 and 233 edges:
+[[0, 1], [0, 3], [0, 5], [0, 17], [0, 32], [0, 74], [1, 3], [1, 17], [1, 32], [2, 5], [2, 6], [2, 33], [2, 38], [2, 39], [2, 48], [2, 57], [3, 32], [4, 9], [4, 24], [4, 29], [4, 36], [4, 45], [4, 66], [4, 75], [5, 17], [5, 38], [5, 48], [5, 57], [5, 67], [6, 33], [6, 39], [6, 46], [7, 12], [7, 19], [7, 63], [7, 68], [7, 70], [7, 79], [8, 19], [8, 27], [8, 60], [8, 63], [9, 15], [9, 24], [9, 29], [9, 40], [9, 50], [9, 54], [9, 66], [9, 69], [10, 11], [10, 31], [10, 58], [10, 62], [10, 69], [10, 77], [11, 31], [11, 33], [11, 42], [11, 62], [11, 77], [12, 19], [12, 65], [12, 79], [13, 14], [13, 22], [13, 28], [13, 37], [13, 49], [13, 51], [13, 53], [13, 55], [14, 28], [14, 37], [14, 56], [14, 65], [14, 78], [15, 21], [15, 24], [15, 29], [15, 50], [15, 54], [15, 69], [16, 24], [16, 29], [16, 36], [16, 43], [16, 45], [16, 66], [17, 32], [17, 34], [18, 20], [18, 27], [18, 30], [18, 44], [18, 47], [18, 60], [18, 72], [19, 23], [19, 26], [19, 60], [19, 63], [19, 79], [20, 25], [20, 72], [21, 31], [21, 50], [21, 54], [21, 69], [22, 28], [22, 36], [22, 37], [22, 49], [22, 51], [22, 55], [23, 26], [23, 59], [23, 63], [23, 79], [24, 29], [24, 40], [24, 66], [25, 27], [26, 63], [26, 65], [26, 70], [26, 71], [27, 30], [27, 44], [27, 59], [27, 60], [27, 72], [28, 37], [28, 41], [28, 53], [28, 78], [29, 35], [29, 50], [29, 66], [30, 44], [30, 60], [30, 72], [31, 42], [31, 58], [31, 62], [31, 77], [32, 34], [32, 67], [33, 38], [33, 39], [33, 76], [34, 38], [34, 67], [35, 40], [35, 66], [36, 43], [36, 45], [36, 49], [36, 55], [37, 41], [37, 51], [37, 52], [37, 78], [38, 48], [39, 42], [39, 46], [39, 58], [40, 50], [40, 54], [41, 51], [41, 64], [41, 65], [41, 71], [42, 46], [42, 73], [42, 76], [43, 45], [43, 49], [43, 53], [43, 66], [43, 75], [44, 59], [44, 60], [44, 72], [45, 49], [45, 55], [45, 75], [46, 58], [47, 72], [48, 57], [49, 51], [49, 55], [50, 54], [50, 61], [51, 53], [51, 78], [52, 56], [52, 65], [52, 68], [52, 70], [52, 71], [53, 55], [54, 61], [54, 69], [55, 75], [56, 64], [56, 70], [56, 71], [57, 74], [58, 61], [58, 73], [58, 77], [59, 60], [60, 72], [61, 62], [61, 69], [61, 77], [62, 73], [62, 77], [63, 68], [64, 65], [64, 78], [65, 68], [65, 71], [66, 75], [67, 74], [68, 70], [68, 79], [69, 77], [70, 71], [70, 79], [73, 76], [73, 77]]
+
+Find a linear layout of bandwidth at most 5: assign to each vertex v a distinct position p[v] in 0..79 (a permutation) such that |p[u] - p[v]| <= 5 for every edge (u, v).
+
+Answer format: {"layout": [p_0, p_1, ..., p_79]} where p_v is the position of vertex v.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/solution/solve.sh b/tasks/construct-nppc-bandwidth-l6-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..6f34ef464f951a73ef38cb0bd2405b67c2156899
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"layout": [4, 2, 12, 0, 37, 7, 13, 64, 70, 33, 25, 20, 62, 48, 53, 31, 39, 6, 76, 67, 77, 27, 47, 68, 34, 78, 63, 74, 50, 35, 73, 22, 1, 15, 5, 36, 42, 52, 10, 16, 32, 54, 17, 43, 71, 41, 18, 79, 11, 46, 30, 49, 56, 45, 28, 44, 57, 9, 21, 69, 72, 26, 23, 66, 55, 58, 38, 3, 61, 29, 60, 59, 75, 19, 8, 40, 14, 24, 51, 65]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/task.toml b/tasks/construct-nppc-bandwidth-l6-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..260800408116bf6531e68503cadc628a0d14632c
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-bandwidth-l6-s9"
+version = "0.2.0"
+description = "construct/nppc_bandwidth"
+authors = []
+keywords = ["rlmath", "construct", "nppc_bandwidth"]
+
+[metadata]
+subset = "construct"
+family = "nppc_bandwidth"
+problem_key = "graph_bandwidth"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "NPPC/bandwidth"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/tests/check.py b/tasks/construct-nppc-bandwidth-l6-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f847cded257e6c404063dfafde33fa44163afa2
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/tests/check.py
@@ -0,0 +1,14 @@
+"""Bandwidth <= b: layout must be a permutation of 0..n-1 with |p[u]-p[v]| <= b on every edge."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, b = inst["num_nodes"], inst["bandwidth"]
+    # upstream NPPC verifier compares sorted(layout) to range(n), which also accepts floats/bools
+    p = int_list(ans.get("layout"), n, 0, n - 1, "layout")
+    if len(set(p)) != n:
+        raise Invalid("layout is not a permutation of 0..n-1")
+    for u, v in inst["edges"]:
+        if abs(p[u] - p[v]) > b:
+            raise Invalid(f"edge ({u},{v}) has stretch {abs(p[u] - p[v])} > {b}")
+    return None, {}
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/tests/instance.json b/tasks/construct-nppc-bandwidth-l6-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..03037aed544a73c6b7ef85863cce1087fcc5c237
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "bandwidth": 5, "edges": [[0, 1], [0, 3], [0, 5], [0, 17], [0, 32], [0, 74], [1, 3], [1, 17], [1, 32], [2, 5], [2, 6], [2, 33], [2, 38], [2, 39], [2, 48], [2, 57], [3, 32], [4, 9], [4, 24], [4, 29], [4, 36], [4, 45], [4, 66], [4, 75], [5, 17], [5, 38], [5, 48], [5, 57], [5, 67], [6, 33], [6, 39], [6, 46], [7, 12], [7, 19], [7, 63], [7, 68], [7, 70], [7, 79], [8, 19], [8, 27], [8, 60], [8, 63], [9, 15], [9, 24], [9, 29], [9, 40], [9, 50], [9, 54], [9, 66], [9, 69], [10, 11], [10, 31], [10, 58], [10, 62], [10, 69], [10, 77], [11, 31], [11, 33], [11, 42], [11, 62], [11, 77], [12, 19], [12, 65], [12, 79], [13, 14], [13, 22], [13, 28], [13, 37], [13, 49], [13, 51], [13, 53], [13, 55], [14, 28], [14, 37], [14, 56], [14, 65], [14, 78], [15, 21], [15, 24], [15, 29], [15, 50], [15, 54], [15, 69], [16, 24], [16, 29], [16, 36], [16, 43], [16, 45], [16, 66], [17, 32], [17, 34], [18, 20], [18, 27], [18, 30], [18, 44], [18, 47], [18, 60], [18, 72], [19, 23], [19, 26], [19, 60], [19, 63], [19, 79], [20, 25], [20, 72], [21, 31], [21, 50], [21, 54], [21, 69], [22, 28], [22, 36], [22, 37], [22, 49], [22, 51], [22, 55], [23, 26], [23, 59], [23, 63], [23, 79], [24, 29], [24, 40], [24, 66], [25, 27], [26, 63], [26, 65], [26, 70], [26, 71], [27, 30], [27, 44], [27, 59], [27, 60], [27, 72], [28, 37], [28, 41], [28, 53], [28, 78], [29, 35], [29, 50], [29, 66], [30, 44], [30, 60], [30, 72], [31, 42], [31, 58], [31, 62], [31, 77], [32, 34], [32, 67], [33, 38], [33, 39], [33, 76], [34, 38], [34, 67], [35, 40], [35, 66], [36, 43], [36, 45], [36, 49], [36, 55], [37, 41], [37, 51], [37, 52], [37, 78], [38, 48], [39, 42], [39, 46], [39, 58], [40, 50], [40, 54], [41, 51], [41, 64], [41, 65], [41, 71], [42, 46], [42, 73], [42, 76], [43, 45], [43, 49], [43, 53], [43, 66], [43, 75], [44, 59], [44, 60], [44, 72], [45, 49], [45, 55], [45, 75], [46, 58], [47, 72], [48, 57], [49, 51], [49, 55], [50, 54], [50, 61], [51, 53], [51, 78], [52, 56], [52, 65], [52, 68], [52, 70], [52, 71], [53, 55], [54, 61], [54, 69], [55, 75], [56, 64], [56, 70], [56, 71], [57, 74], [58, 61], [58, 73], [58, 77], [59, 60], [60, 72], [61, 62], [61, 69], [61, 77], [62, 73], [62, 77], [63, 68], [64, 65], [64, 78], [65, 68], [65, 71], [66, 75], [67, 74], [68, 70], [68, 79], [69, 77], [70, 71], [70, 79], [73, 76], [73, 77]], "family": "nppc_bandwidth", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/tests/run.py b/tasks/construct-nppc-bandwidth-l6-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-bandwidth-l6-s9/tests/test.sh b/tasks/construct-nppc-bandwidth-l6-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-bandwidth-l6-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-clique-l3-s1/environment/Dockerfile b/tasks/construct-nppc-clique-l3-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-clique-l3-s1/environment/instance.json b/tasks/construct-nppc-clique-l3-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a66473624d5768199de908903576714e84eda860
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "k": 10, "edges": [[0, 1], [0, 3], [0, 7], [0, 8], [0, 11], [0, 17], [1, 2], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 18], [1, 19], [2, 4], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 19], [3, 5], [3, 6], [3, 8], [3, 16], [3, 17], [4, 7], [4, 8], [4, 11], [4, 13], [4, 17], [4, 18], [5, 8], [5, 10], [5, 13], [5, 16], [5, 19], [6, 9], [6, 11], [6, 13], [6, 16], [6, 18], [7, 8], [7, 9], [7, 10], [7, 12], [7, 13], [7, 14], [7, 15], [7, 19], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 17], [8, 18], [8, 19], [9, 10], [9, 11], [9, 12], [9, 13], [9, 15], [9, 18], [9, 19], [10, 11], [10, 12], [10, 13], [10, 15], [10, 19], [11, 12], [12, 13], [12, 15], [12, 17], [12, 19], [13, 14], [13, 15], [13, 19], [14, 16], [14, 18], [14, 19], [15, 18], [15, 19], [16, 17], [17, 19], [18, 19]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l3-s1/instruction.md b/tasks/construct-nppc-clique-l3-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..ab60acb037a14b02f5de6b91eaab64db59656e37
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 20 vertices labelled 0..19 and 97 edges:
+[[0, 1], [0, 3], [0, 7], [0, 8], [0, 11], [0, 17], [1, 2], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 18], [1, 19], [2, 4], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 19], [3, 5], [3, 6], [3, 8], [3, 16], [3, 17], [4, 7], [4, 8], [4, 11], [4, 13], [4, 17], [4, 18], [5, 8], [5, 10], [5, 13], [5, 16], [5, 19], [6, 9], [6, 11], [6, 13], [6, 16], [6, 18], [7, 8], [7, 9], [7, 10], [7, 12], [7, 13], [7, 14], [7, 15], [7, 19], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 17], [8, 18], [8, 19], [9, 10], [9, 11], [9, 12], [9, 13], [9, 15], [9, 18], [9, 19], [10, 11], [10, 12], [10, 13], [10, 15], [10, 19], [11, 12], [12, 13], [12, 15], [12, 17], [12, 19], [13, 14], [13, 15], [13, 19], [14, 16], [14, 18], [14, 19], [15, 18], [15, 19], [16, 17], [17, 19], [18, 19]]
+
+Find a clique of size at least 10: a set of distinct vertices every two of which are joined by an edge.
+
+Answer format: {"clique": [v_1, v_2, ...]} (at least 10 distinct integers in 0..19).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-clique-l3-s1/solution/solve.sh b/tasks/construct-nppc-clique-l3-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..24686638807a4583eff4f736107a8b3121a59a7e
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [1, 2, 7, 8, 9, 10, 12, 13, 15, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l3-s1/task.toml b/tasks/construct-nppc-clique-l3-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..45135a5c462454b2055aff3bddf4ea17f9a6ff1b
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-clique-l3-s1"
+version = "0.2.0"
+description = "construct/nppc_clique"
+authors = []
+keywords = ["rlmath", "construct", "nppc_clique"]
+
+[metadata]
+subset = "construct"
+family = "nppc_clique"
+problem_key = "graph_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/clique"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-clique-l3-s1/tests/check.py b/tasks/construct-nppc-clique-l3-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/tests/check.py
@@ -0,0 +1,19 @@
+"""Clique of size >= k. Accepts any valid clique."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    # upstream NPPC verifier checks len(list) >= k but only tests pairs u < v, so [v, v, ..., v] passed
+    if len(set(c)) != len(c):
+        raise Invalid("clique contains duplicates")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(c), 2):
+        if (u, v) not in es:
+            raise Invalid(f"no edge between {u} and {v}")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-clique-l3-s1/tests/instance.json b/tasks/construct-nppc-clique-l3-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a66473624d5768199de908903576714e84eda860
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "k": 10, "edges": [[0, 1], [0, 3], [0, 7], [0, 8], [0, 11], [0, 17], [1, 2], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 18], [1, 19], [2, 4], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 17], [2, 19], [3, 5], [3, 6], [3, 8], [3, 16], [3, 17], [4, 7], [4, 8], [4, 11], [4, 13], [4, 17], [4, 18], [5, 8], [5, 10], [5, 13], [5, 16], [5, 19], [6, 9], [6, 11], [6, 13], [6, 16], [6, 18], [7, 8], [7, 9], [7, 10], [7, 12], [7, 13], [7, 14], [7, 15], [7, 19], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 17], [8, 18], [8, 19], [9, 10], [9, 11], [9, 12], [9, 13], [9, 15], [9, 18], [9, 19], [10, 11], [10, 12], [10, 13], [10, 15], [10, 19], [11, 12], [12, 13], [12, 15], [12, 17], [12, 19], [13, 14], [13, 15], [13, 19], [14, 16], [14, 18], [14, 19], [15, 18], [15, 19], [16, 17], [17, 19], [18, 19]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l3-s1/tests/run.py b/tasks/construct-nppc-clique-l3-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-clique-l3-s1/tests/test.sh b/tasks/construct-nppc-clique-l3-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-clique-l3-s6/environment/Dockerfile b/tasks/construct-nppc-clique-l3-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-clique-l3-s6/environment/instance.json b/tasks/construct-nppc-clique-l3-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..958040d3b6791cb741ac6a7c3d774ff4b24767b5
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "k": 10, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 19], [1, 3], [1, 5], [1, 7], [1, 8], [1, 11], [1, 18], [2, 3], [2, 9], [2, 10], [2, 11], [2, 13], [2, 15], [2, 16], [2, 17], [2, 18], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 18], [3, 19], [4, 5], [4, 6], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [5, 7], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 14], [5, 17], [5, 18], [5, 19], [6, 8], [6, 18], [7, 8], [7, 9], [7, 11], [7, 13], [7, 15], [7, 17], [7, 18], [8, 9], [8, 11], [8, 12], [8, 13], [8, 18], [8, 19], [9, 11], [9, 12], [9, 13], [9, 14], [9, 18], [9, 19], [10, 11], [10, 12], [10, 13], [10, 16], [10, 17], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [12, 13], [12, 14], [12, 18], [12, 19], [13, 16], [13, 17], [13, 18], [13, 19], [14, 16], [15, 16], [16, 18], [18, 19]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l3-s6/instruction.md b/tasks/construct-nppc-clique-l3-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..463540ba0378369847dfb32ebc49791ca08761ed
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 20 vertices labelled 0..19 and 107 edges:
+[[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 19], [1, 3], [1, 5], [1, 7], [1, 8], [1, 11], [1, 18], [2, 3], [2, 9], [2, 10], [2, 11], [2, 13], [2, 15], [2, 16], [2, 17], [2, 18], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 18], [3, 19], [4, 5], [4, 6], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [5, 7], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 14], [5, 17], [5, 18], [5, 19], [6, 8], [6, 18], [7, 8], [7, 9], [7, 11], [7, 13], [7, 15], [7, 17], [7, 18], [8, 9], [8, 11], [8, 12], [8, 13], [8, 18], [8, 19], [9, 11], [9, 12], [9, 13], [9, 14], [9, 18], [9, 19], [10, 11], [10, 12], [10, 13], [10, 16], [10, 17], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [12, 13], [12, 14], [12, 18], [12, 19], [13, 16], [13, 17], [13, 18], [13, 19], [14, 16], [15, 16], [16, 18], [18, 19]]
+
+Find a clique of size at least 10: a set of distinct vertices every two of which are joined by an edge.
+
+Answer format: {"clique": [v_1, v_2, ...]} (at least 10 distinct integers in 0..19).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-clique-l3-s6/solution/solve.sh b/tasks/construct-nppc-clique-l3-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d89a472741132d9f9e7022a9f8d748fa4e394273
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [3, 4, 5, 8, 9, 11, 12, 13, 18, 19]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l3-s6/task.toml b/tasks/construct-nppc-clique-l3-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..8d3425f0a134f66aef98dfc6ec7408b963945e78
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-clique-l3-s6"
+version = "0.2.0"
+description = "construct/nppc_clique"
+authors = []
+keywords = ["rlmath", "construct", "nppc_clique"]
+
+[metadata]
+subset = "construct"
+family = "nppc_clique"
+problem_key = "graph_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/clique"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-clique-l3-s6/tests/check.py b/tasks/construct-nppc-clique-l3-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/tests/check.py
@@ -0,0 +1,19 @@
+"""Clique of size >= k. Accepts any valid clique."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    # upstream NPPC verifier checks len(list) >= k but only tests pairs u < v, so [v, v, ..., v] passed
+    if len(set(c)) != len(c):
+        raise Invalid("clique contains duplicates")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(c), 2):
+        if (u, v) not in es:
+            raise Invalid(f"no edge between {u} and {v}")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-clique-l3-s6/tests/instance.json b/tasks/construct-nppc-clique-l3-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..958040d3b6791cb741ac6a7c3d774ff4b24767b5
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "k": 10, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 19], [1, 3], [1, 5], [1, 7], [1, 8], [1, 11], [1, 18], [2, 3], [2, 9], [2, 10], [2, 11], [2, 13], [2, 15], [2, 16], [2, 17], [2, 18], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 18], [3, 19], [4, 5], [4, 6], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [5, 7], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 14], [5, 17], [5, 18], [5, 19], [6, 8], [6, 18], [7, 8], [7, 9], [7, 11], [7, 13], [7, 15], [7, 17], [7, 18], [8, 9], [8, 11], [8, 12], [8, 13], [8, 18], [8, 19], [9, 11], [9, 12], [9, 13], [9, 14], [9, 18], [9, 19], [10, 11], [10, 12], [10, 13], [10, 16], [10, 17], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [12, 13], [12, 14], [12, 18], [12, 19], [13, 16], [13, 17], [13, 18], [13, 19], [14, 16], [15, 16], [16, 18], [18, 19]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l3-s6/tests/run.py b/tasks/construct-nppc-clique-l3-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-clique-l3-s6/tests/test.sh b/tasks/construct-nppc-clique-l3-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-clique-l3-s8/environment/Dockerfile b/tasks/construct-nppc-clique-l3-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-clique-l3-s8/environment/instance.json b/tasks/construct-nppc-clique-l3-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..eb4f881f497c5bc1a680e94d15b497fdbd85e146
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "k": 10, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 16], [0, 17], [0, 18], [0, 19], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 10], [1, 11], [1, 13], [1, 14], [1, 16], [1, 17], [2, 3], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [3, 4], [3, 6], [3, 7], [3, 9], [3, 10], [3, 11], [3, 12], [3, 14], [3, 16], [3, 17], [3, 18], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 16], [4, 17], [4, 19], [5, 8], [5, 9], [5, 11], [5, 15], [5, 16], [5, 17], [6, 7], [6, 9], [6, 10], [6, 11], [6, 15], [6, 16], [6, 17], [6, 19], [7, 8], [7, 13], [7, 14], [7, 16], [7, 17], [7, 19], [8, 9], [8, 11], [8, 13], [8, 15], [8, 16], [9, 10], [9, 11], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [10, 11], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [11, 12], [11, 14], [11, 16], [11, 17], [11, 19], [12, 13], [12, 14], [12, 16], [12, 18], [13, 16], [13, 19], [14, 18], [14, 19], [15, 18], [15, 19], [16, 17], [17, 18], [17, 19]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l3-s8/instruction.md b/tasks/construct-nppc-clique-l3-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4e69302e74730cc3db3c6011c5bea47a562a3fd6
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 20 vertices labelled 0..19 and 120 edges:
+[[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 16], [0, 17], [0, 18], [0, 19], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 10], [1, 11], [1, 13], [1, 14], [1, 16], [1, 17], [2, 3], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [3, 4], [3, 6], [3, 7], [3, 9], [3, 10], [3, 11], [3, 12], [3, 14], [3, 16], [3, 17], [3, 18], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 16], [4, 17], [4, 19], [5, 8], [5, 9], [5, 11], [5, 15], [5, 16], [5, 17], [6, 7], [6, 9], [6, 10], [6, 11], [6, 15], [6, 16], [6, 17], [6, 19], [7, 8], [7, 13], [7, 14], [7, 16], [7, 17], [7, 19], [8, 9], [8, 11], [8, 13], [8, 15], [8, 16], [9, 10], [9, 11], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [10, 11], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [11, 12], [11, 14], [11, 16], [11, 17], [11, 19], [12, 13], [12, 14], [12, 16], [12, 18], [13, 16], [13, 19], [14, 18], [14, 19], [15, 18], [15, 19], [16, 17], [17, 18], [17, 19]]
+
+Find a clique of size at least 10: a set of distinct vertices every two of which are joined by an edge.
+
+Answer format: {"clique": [v_1, v_2, ...]} (at least 10 distinct integers in 0..19).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-clique-l3-s8/solution/solve.sh b/tasks/construct-nppc-clique-l3-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f74ceb219e38c6e2ef66bf27becde93ff5a0acef
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 1, 3, 4, 6, 9, 10, 11, 16, 17]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-clique-l3-s8/task.toml b/tasks/construct-nppc-clique-l3-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5db722e33dcef8470e2ddf21e1dd8135375f02f4
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-clique-l3-s8"
+version = "0.2.0"
+description = "construct/nppc_clique"
+authors = []
+keywords = ["rlmath", "construct", "nppc_clique"]
+
+[metadata]
+subset = "construct"
+family = "nppc_clique"
+problem_key = "graph_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/clique"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-clique-l3-s8/tests/check.py b/tasks/construct-nppc-clique-l3-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..98eb4fc9097fcfa31988cf0a8b79280cec2b7980
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/tests/check.py
@@ -0,0 +1,19 @@
+"""Clique of size >= k. Accepts any valid clique."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    # upstream NPPC verifier checks len(list) >= k but only tests pairs u < v, so [v, v, ..., v] passed
+    if len(set(c)) != len(c):
+        raise Invalid("clique contains duplicates")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(c), 2):
+        if (u, v) not in es:
+            raise Invalid(f"no edge between {u} and {v}")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-clique-l3-s8/tests/instance.json b/tasks/construct-nppc-clique-l3-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..eb4f881f497c5bc1a680e94d15b497fdbd85e146
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 20, "k": 10, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 16], [0, 17], [0, 18], [0, 19], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 8], [1, 9], [1, 10], [1, 11], [1, 13], [1, 14], [1, 16], [1, 17], [2, 3], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [3, 4], [3, 6], [3, 7], [3, 9], [3, 10], [3, 11], [3, 12], [3, 14], [3, 16], [3, 17], [3, 18], [4, 5], [4, 6], [4, 7], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 16], [4, 17], [4, 19], [5, 8], [5, 9], [5, 11], [5, 15], [5, 16], [5, 17], [6, 7], [6, 9], [6, 10], [6, 11], [6, 15], [6, 16], [6, 17], [6, 19], [7, 8], [7, 13], [7, 14], [7, 16], [7, 17], [7, 19], [8, 9], [8, 11], [8, 13], [8, 15], [8, 16], [9, 10], [9, 11], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [10, 11], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [11, 12], [11, 14], [11, 16], [11, 17], [11, 19], [12, 13], [12, 14], [12, 16], [12, 18], [13, 16], [13, 19], [14, 18], [14, 19], [15, 18], [15, 19], [16, 17], [17, 18], [17, 19]], "family": "nppc_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-clique-l3-s8/tests/run.py b/tasks/construct-nppc-clique-l3-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-clique-l3-s8/tests/test.sh b/tasks/construct-nppc-clique-l3-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-clique-l3-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-dominating-set-l3-s8/instruction.md b/tasks/construct-nppc-dominating-set-l3-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..999410e49344c64b0692c71b164e9ad2b4cb210c
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s8/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 50 vertices labelled 0..49 and 371 edges:
+[[0, 2], [0, 5], [0, 6], [0, 13], [0, 15], [0, 18], [0, 19], [0, 27], [0, 28], [0, 30], [0, 34], [0, 37], [0, 38], [0, 41], [0, 42], [0, 46], [0, 47], [0, 48], [0, 49], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 15], [1, 18], [1, 19], [1, 23], [1, 28], [1, 29], [1, 35], [1, 40], [1, 41], [1, 45], [1, 47], [2, 4], [2, 7], [2, 8], [2, 12], [2, 13], [2, 17], [2, 18], [2, 20], [2, 22], [2, 26], [2, 27], [2, 28], [2, 35], [2, 36], [2, 37], [2, 41], [2, 45], [2, 49], [3, 7], [3, 8], [3, 10], [3, 12], [3, 14], [3, 17], [3, 18], [3, 29], [3, 30], [3, 32], [3, 39], [3, 43], [3, 45], [3, 46], [3, 48], [3, 49], [4, 9], [4, 18], [4, 22], [4, 27], [4, 34], [4, 38], [4, 40], [4, 43], [4, 44], [4, 47], [4, 49], [5, 9], [5, 12], [5, 15], [5, 24], [5, 25], [5, 31], [5, 32], [5, 33], [5, 40], [5, 42], [5, 44], [5, 46], [5, 47], [6, 11], [6, 13], [6, 16], [6, 23], [6, 27], [6, 28], [6, 31], [6, 35], [6, 37], [6, 38], [6, 44], [6, 46], [6, 49], [7, 12], [7, 19], [7, 24], [7, 25], [7, 35], [7, 36], [7, 40], [7, 47], [7, 49], [8, 13], [8, 22], [8, 24], [8, 28], [8, 34], [8, 36], [8, 37], [8, 42], [8, 48], [8, 49], [9, 10], [9, 15], [9, 17], [9, 20], [9, 22], [9, 24], [9, 26], [9, 27], [9, 30], [9, 36], [9, 38], [9, 40], [9, 46], [9, 47], [10, 16], [10, 18], [10, 19], [10, 21], [10, 24], [10, 27], [10, 29], [10, 32], [10, 34], [10, 35], [10, 39], [10, 44], [11, 12], [11, 16], [11, 31], [11, 38], [11, 44], [11, 47], [11, 48], [11, 49], [12, 13], [12, 14], [12, 15], [12, 19], [12, 22], [12, 24], [12, 29], [12, 31], [12, 32], [12, 34], [12, 35], [12, 43], [12, 45], [13, 16], [13, 19], [13, 29], [13, 30], [13, 34], [13, 39], [13, 42], [13, 49], [14, 21], [14, 24], [14, 27], [14, 31], [14, 35], [14, 39], [14, 41], [14, 42], [14, 44], [14, 45], [14, 49], [15, 16], [15, 18], [15, 21], [15, 24], [15, 29], [15, 32], [15, 34], [15, 41], [15, 44], [16, 19], [16, 21], [16, 22], [16, 23], [16, 25], [16, 26], [16, 28], [16, 37], [16, 41], [17, 19], [17, 21], [17, 25], [17, 35], [17, 41], [17, 47], [17, 48], [18, 23], [18, 24], [18, 29], [18, 30], [18, 32], [18, 35], [18, 37], [18, 45], [18, 47], [19, 23], [19, 25], [19, 26], [19, 31], [19, 32], [19, 36], [19, 38], [19, 39], [20, 23], [20, 26], [20, 28], [20, 30], [20, 32], [20, 41], [20, 46], [21, 24], [21, 28], [21, 30], [21, 34], [21, 36], [21, 37], [21, 38], [21, 42], [21, 43], [21, 44], [21, 46], [22, 29], [22, 30], [22, 37], [22, 39], [22, 40], [22, 43], [22, 46], [22, 47], [22, 49], [23, 35], [23, 38], [23, 41], [23, 44], [23, 45], [23, 46], [23, 49], [24, 27], [24, 35], [24, 36], [24, 38], [24, 45], [24, 47], [24, 48], [25, 29], [25, 30], [25, 32], [25, 33], [25, 37], [25, 40], [25, 42], [25, 44], [25, 47], [25, 49], [26, 28], [26, 31], [26, 34], [26, 35], [26, 36], [26, 40], [26, 43], [26, 46], [26, 47], [27, 30], [27, 35], [27, 37], [27, 42], [27, 47], [28, 31], [28, 32], [28, 34], [28, 35], [28, 40], [28, 46], [28, 47], [29, 30], [29, 34], [29, 37], [29, 43], [29, 49], [30, 31], [30, 32], [30, 38], [31, 32], [31, 33], [31, 35], [31, 44], [31, 49], [32, 36], [32, 37], [32, 38], [32, 44], [32, 48], [32, 49], [33, 35], [33, 39], [33, 40], [33, 43], [33, 44], [33, 45], [33, 49], [34, 36], [34, 39], [34, 41], [34, 42], [34, 43], [34, 44], [34, 47], [35, 39], [35, 41], [35, 45], [35, 47], [35, 48], [36, 37], [36, 38], [36, 42], [36, 44], [36, 46], [37, 38], [37, 39], [37, 40], [37, 42], [37, 43], [38, 43], [38, 44], [38, 46], [38, 47], [39, 40], [39, 42], [39, 48], [40, 42], [41, 44], [41, 46], [42, 44], [43, 48], [44, 46], [44, 48], [44, 49], [45, 46], [46, 47], [48, 49]]
+
+Find a dominating set of size at most 20: a set D of distinct vertices such that every vertex is in D or adjacent to a vertex of D.
+
+Answer format: {"dominating_set": [v_1, v_2, ...]} (distinct integers in 0..49, at most 20 of them).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-dominating-set-l3-s8/task.toml b/tasks/construct-nppc-dominating-set-l3-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..68c5340b73c087c8f97591f1bfd2d31c67f336ee
--- /dev/null
+++ b/tasks/construct-nppc-dominating-set-l3-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-dominating-set-l3-s8"
+version = "0.2.0"
+description = "construct/nppc_dominating_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_dominating_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_dominating_set"
+problem_key = "graph_dominating_set"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/dominating_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-independent-set-l2-s1/environment/Dockerfile b/tasks/construct-nppc-independent-set-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-independent-set-l2-s1/environment/instance.json b/tasks/construct-nppc-independent-set-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..765e65881f7a524dca57415dd4d6b4bf39d88961
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 2], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 14], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 14], [1, 15], [2, 8], [3, 5], [3, 10], [3, 11], [3, 14], [3, 15], [4, 5], [4, 7], [4, 8], [4, 9], [4, 11], [4, 13], [4, 14], [4, 15], [5, 14], [6, 8], [7, 12], [7, 14], [7, 15], [8, 9], [8, 10], [8, 14], [8, 15], [9, 12], [10, 12], [10, 14], [11, 12], [11, 15], [12, 14], [13, 14], [13, 15]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l2-s1/instruction.md b/tasks/construct-nppc-independent-set-l2-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..6a1c9fa099a44bd35773c4cbe19416f75eb87aac
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 16 vertices labelled 0..15 and 47 edges:
+[[0, 1], [0, 2], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 14], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 14], [1, 15], [2, 8], [3, 5], [3, 10], [3, 11], [3, 14], [3, 15], [4, 5], [4, 7], [4, 8], [4, 9], [4, 11], [4, 13], [4, 14], [4, 15], [5, 14], [6, 8], [7, 12], [7, 14], [7, 15], [8, 9], [8, 10], [8, 14], [8, 15], [9, 12], [10, 12], [10, 14], [11, 12], [11, 15], [12, 14], [13, 14], [13, 15]]
+
+Find an independent set of size at least 8: a set of distinct vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (at least 8 distinct integers in 0..15).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-independent-set-l2-s1/solution/solve.sh b/tasks/construct-nppc-independent-set-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..4aef9aa38d2fc51d5a18f9026f5cf6beb56e5a6b
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [2, 5, 6, 7, 9, 10, 11, 13]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l2-s1/task.toml b/tasks/construct-nppc-independent-set-l2-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..9b4ac061a14c760ac17d5e7284bd78c5a6c1cd3d
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-independent-set-l2-s1"
+version = "0.2.0"
+description = "construct/nppc_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "NPPC/independent_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-independent-set-l2-s1/tests/check.py b/tasks/construct-nppc-independent-set-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/tests/check.py
@@ -0,0 +1,19 @@
+"""Independent set of size >= k. Accepts any valid independent set."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    s = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    # upstream NPPC verifier checks len(list) >= size but only tests pairs u < v, so [v]*k passed
+    if len(set(s)) != len(s):
+        raise Invalid("independent_set contains duplicates")
+    if len(s) < k:
+        raise Invalid(f"independent_set has {len(s)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(s), 2):
+        if (u, v) in es:
+            raise Invalid(f"edge between {u} and {v}")
+    return None, {"size": len(s)}
diff --git a/tasks/construct-nppc-independent-set-l2-s1/tests/instance.json b/tasks/construct-nppc-independent-set-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..765e65881f7a524dca57415dd4d6b4bf39d88961
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 2], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 14], [1, 3], [1, 4], [1, 5], [1, 9], [1, 13], [1, 14], [1, 15], [2, 8], [3, 5], [3, 10], [3, 11], [3, 14], [3, 15], [4, 5], [4, 7], [4, 8], [4, 9], [4, 11], [4, 13], [4, 14], [4, 15], [5, 14], [6, 8], [7, 12], [7, 14], [7, 15], [8, 9], [8, 10], [8, 14], [8, 15], [9, 12], [10, 12], [10, 14], [11, 12], [11, 15], [12, 14], [13, 14], [13, 15]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l2-s1/tests/run.py b/tasks/construct-nppc-independent-set-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-independent-set-l2-s1/tests/test.sh b/tasks/construct-nppc-independent-set-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-independent-set-l2-s6/environment/Dockerfile b/tasks/construct-nppc-independent-set-l2-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-independent-set-l2-s6/environment/instance.json b/tasks/construct-nppc-independent-set-l2-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e1da9e1ecf473d1f0362268f9426b597923f6cc0
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 16, "k": 8, "edges": [[0, 3], [0, 4], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [1, 2], [1, 3], [1, 6], [1, 9], [1, 11], [1, 15], [2, 3], [2, 4], [2, 7], [2, 8], [2, 10], [2, 13], [2, 14], [3, 4], [3, 5], [3, 6], [3, 8], [3, 9], [3, 11], [3, 12], [3, 15], [4, 6], [4, 11], [4, 14], [4, 15], [5, 6], [5, 14], [5, 15], [6, 9], [6, 10], [6, 13], [7, 11], [8, 14], [8, 15], [9, 11], [9, 12], [9, 13], [10, 14], [11, 12], [11, 13], [11, 14], [12, 14], [13, 15], [14, 15]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l2-s6/instruction.md b/tasks/construct-nppc-independent-set-l2-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..6a7cb8b338073e48f006105b9db1318e0e70c90b
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 16 vertices labelled 0..15 and 54 edges:
+[[0, 3], [0, 4], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [1, 2], [1, 3], [1, 6], [1, 9], [1, 11], [1, 15], [2, 3], [2, 4], [2, 7], [2, 8], [2, 10], [2, 13], [2, 14], [3, 4], [3, 5], [3, 6], [3, 8], [3, 9], [3, 11], [3, 12], [3, 15], [4, 6], [4, 11], [4, 14], [4, 15], [5, 6], [5, 14], [5, 15], [6, 9], [6, 10], [6, 13], [7, 11], [8, 14], [8, 15], [9, 11], [9, 12], [9, 13], [10, 14], [11, 12], [11, 13], [11, 14], [12, 14], [13, 15], [14, 15]]
+
+Find an independent set of size at least 8: a set of distinct vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (at least 8 distinct integers in 0..15).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-independent-set-l2-s6/solution/solve.sh b/tasks/construct-nppc-independent-set-l2-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d2d2a8595124d5583aa671a9af0ae46f55db75d5
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [1, 4, 5, 7, 8, 10, 12, 13]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l2-s6/task.toml b/tasks/construct-nppc-independent-set-l2-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ce1119f114ad0ea65cfce364517a836cc1e5f5e2
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-independent-set-l2-s6"
+version = "0.2.0"
+description = "construct/nppc_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "NPPC/independent_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-independent-set-l2-s6/tests/check.py b/tasks/construct-nppc-independent-set-l2-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/tests/check.py
@@ -0,0 +1,19 @@
+"""Independent set of size >= k. Accepts any valid independent set."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    s = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    # upstream NPPC verifier checks len(list) >= size but only tests pairs u < v, so [v]*k passed
+    if len(set(s)) != len(s):
+        raise Invalid("independent_set contains duplicates")
+    if len(s) < k:
+        raise Invalid(f"independent_set has {len(s)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(s), 2):
+        if (u, v) in es:
+            raise Invalid(f"edge between {u} and {v}")
+    return None, {"size": len(s)}
diff --git a/tasks/construct-nppc-independent-set-l2-s6/tests/instance.json b/tasks/construct-nppc-independent-set-l2-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e1da9e1ecf473d1f0362268f9426b597923f6cc0
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 16, "k": 8, "edges": [[0, 3], [0, 4], [0, 6], [0, 7], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [1, 2], [1, 3], [1, 6], [1, 9], [1, 11], [1, 15], [2, 3], [2, 4], [2, 7], [2, 8], [2, 10], [2, 13], [2, 14], [3, 4], [3, 5], [3, 6], [3, 8], [3, 9], [3, 11], [3, 12], [3, 15], [4, 6], [4, 11], [4, 14], [4, 15], [5, 6], [5, 14], [5, 15], [6, 9], [6, 10], [6, 13], [7, 11], [8, 14], [8, 15], [9, 11], [9, 12], [9, 13], [10, 14], [11, 12], [11, 13], [11, 14], [12, 14], [13, 15], [14, 15]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l2-s6/tests/run.py b/tasks/construct-nppc-independent-set-l2-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-independent-set-l2-s6/tests/test.sh b/tasks/construct-nppc-independent-set-l2-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-independent-set-l2-s8/environment/Dockerfile b/tasks/construct-nppc-independent-set-l2-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-independent-set-l2-s8/environment/instance.json b/tasks/construct-nppc-independent-set-l2-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a7f2783ad66867c5f0c50b1c8d12f813368a9a89
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 8], [0, 9], [0, 10], [0, 13], [1, 5], [1, 8], [1, 9], [1, 10], [1, 12], [1, 14], [2, 4], [2, 5], [2, 6], [2, 7], [2, 9], [2, 10], [2, 12], [2, 13], [3, 9], [3, 10], [3, 12], [3, 13], [4, 12], [4, 15], [5, 8], [5, 9], [5, 15], [6, 8], [6, 10], [6, 12], [7, 8], [7, 12], [7, 15], [8, 10], [8, 11], [8, 13], [8, 14], [9, 11], [9, 12], [9, 13], [10, 12], [10, 14], [11, 13], [12, 13], [12, 14], [12, 15]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l2-s8/instruction.md b/tasks/construct-nppc-independent-set-l2-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..64a279e1e3ff2f20ff05a5c954633ffb08f0230b
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 16 vertices labelled 0..15 and 47 edges:
+[[0, 1], [0, 8], [0, 9], [0, 10], [0, 13], [1, 5], [1, 8], [1, 9], [1, 10], [1, 12], [1, 14], [2, 4], [2, 5], [2, 6], [2, 7], [2, 9], [2, 10], [2, 12], [2, 13], [3, 9], [3, 10], [3, 12], [3, 13], [4, 12], [4, 15], [5, 8], [5, 9], [5, 15], [6, 8], [6, 10], [6, 12], [7, 8], [7, 12], [7, 15], [8, 10], [8, 11], [8, 13], [8, 14], [9, 11], [9, 12], [9, 13], [10, 12], [10, 14], [11, 13], [12, 13], [12, 14], [12, 15]]
+
+Find an independent set of size at least 8: a set of distinct vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (at least 8 distinct integers in 0..15).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-independent-set-l2-s8/solution/solve.sh b/tasks/construct-nppc-independent-set-l2-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..464b1b00325a87aa00519e34d72223747c39c7f7
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [0, 3, 4, 5, 6, 7, 11, 14]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l2-s8/task.toml b/tasks/construct-nppc-independent-set-l2-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..d70869b2a6a60bbe327bb3753b58ed6a136dd852
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-independent-set-l2-s8"
+version = "0.2.0"
+description = "construct/nppc_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "NPPC/independent_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-independent-set-l2-s8/tests/check.py b/tasks/construct-nppc-independent-set-l2-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/tests/check.py
@@ -0,0 +1,19 @@
+"""Independent set of size >= k. Accepts any valid independent set."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    s = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    # upstream NPPC verifier checks len(list) >= size but only tests pairs u < v, so [v]*k passed
+    if len(set(s)) != len(s):
+        raise Invalid("independent_set contains duplicates")
+    if len(s) < k:
+        raise Invalid(f"independent_set has {len(s)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(s), 2):
+        if (u, v) in es:
+            raise Invalid(f"edge between {u} and {v}")
+    return None, {"size": len(s)}
diff --git a/tasks/construct-nppc-independent-set-l2-s8/tests/instance.json b/tasks/construct-nppc-independent-set-l2-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a7f2783ad66867c5f0c50b1c8d12f813368a9a89
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 16, "k": 8, "edges": [[0, 1], [0, 8], [0, 9], [0, 10], [0, 13], [1, 5], [1, 8], [1, 9], [1, 10], [1, 12], [1, 14], [2, 4], [2, 5], [2, 6], [2, 7], [2, 9], [2, 10], [2, 12], [2, 13], [3, 9], [3, 10], [3, 12], [3, 13], [4, 12], [4, 15], [5, 8], [5, 9], [5, 15], [6, 8], [6, 10], [6, 12], [7, 8], [7, 12], [7, 15], [8, 10], [8, 11], [8, 13], [8, 14], [9, 11], [9, 12], [9, 13], [10, 12], [10, 14], [11, 13], [12, 13], [12, 14], [12, 15]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l2-s8/tests/run.py b/tasks/construct-nppc-independent-set-l2-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-independent-set-l2-s8/tests/test.sh b/tasks/construct-nppc-independent-set-l2-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l2-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-independent-set-l6-s0/environment/Dockerfile b/tasks/construct-nppc-independent-set-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-independent-set-l6-s0/environment/instance.json b/tasks/construct-nppc-independent-set-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e32e84d3aab3dcfb8f8c58b707937dd892a72a70
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 100, "k": 30, "edges": [[0, 1], [0, 4], [0, 7], [0, 10], [0, 12], [0, 13], [0, 22], [0, 26], [0, 36], [0, 37], [0, 38], [0, 40], [0, 41], [0, 50], [0, 52], [0, 53], [0, 54], [0, 56], [0, 64], [0, 70], [0, 80], [0, 85], [0, 92], [0, 99], [1, 6], [1, 13], [1, 15], [1, 19], [1, 26], [1, 39], [1, 41], [1, 47], [1, 48], [1, 50], [1, 53], [1, 57], [1, 68], [1, 70], [1, 71], [1, 73], [1, 74], [1, 81], [1, 91], [2, 3], [2, 5], [2, 8], [2, 13], [2, 15], [2, 20], [2, 23], [2, 24], [2, 25], [2, 33], [2, 47], [2, 48], [2, 56], [2, 58], [2, 60], [2, 63], [2, 66], [2, 71], [2, 78], [2, 85], [2, 93], [2, 97], [2, 98], [3, 7], [3, 10], [3, 12], [3, 15], [3, 27], [3, 29], [3, 30], [3, 31], [3, 35], [3, 41], [3, 44], [3, 45], [3, 52], [3, 57], [3, 62], [3, 63], [3, 67], [3, 68], [3, 69], [3, 70], [3, 75], [3, 76], [3, 81], [3, 90], [3, 91], [3, 93], [3, 95], [3, 96], [3, 99], [4, 8], [4, 14], [4, 17], [4, 18], [4, 26], [4, 37], [4, 40], [4, 48], [4, 51], [4, 56], [4, 57], [4, 58], [4, 63], [4, 66], [4, 68], [4, 71], [4, 81], [4, 85], [4, 91], [4, 97], [5, 8], [5, 9], [5, 13], [5, 14], [5, 15], [5, 16], [5, 22], [5, 23], [5, 25], [5, 26], [5, 27], [5, 29], [5, 30], [5, 32], [5, 35], [5, 36], [5, 37], [5, 39], [5, 40], [5, 41], [5, 51], [5, 54], [5, 58], [5, 60], [5, 64], [5, 68], [5, 69], [5, 70], [5, 71], [5, 73], [5, 77], [5, 78], [5, 79], [5, 80], [5, 84], [5, 85], [5, 91], [5, 94], [6, 8], [6, 9], [6, 14], [6, 16], [6, 19], [6, 20], [6, 24], [6, 27], [6, 28], [6, 29], [6, 35], [6, 36], [6, 40], [6, 45], [6, 50], [6, 61], [6, 63], [6, 64], [6, 73], [6, 80], [6, 84], [6, 88], [6, 89], [6, 94], [6, 95], [6, 97], [6, 99], [7, 9], [7, 15], [7, 16], [7, 17], [7, 18], [7, 20], [7, 21], [7, 25], [7, 31], [7, 33], [7, 35], [7, 47], [7, 54], [7, 57], [7, 61], [7, 66], [7, 67], [7, 70], [7, 77], [7, 81], [7, 82], [7, 85], [7, 87], [7, 88], [7, 89], [7, 93], [7, 95], [7, 99], [8, 9], [8, 18], [8, 22], [8, 24], [8, 29], [8, 30], [8, 35], [8, 45], [8, 50], [8, 53], [8, 60], [8, 61], [8, 65], [8, 68], [8, 70], [8, 71], [8, 74], [8, 75], [8, 78], [8, 79], [8, 82], [8, 83], [8, 93], [8, 97], [9, 10], [9, 11], [9, 15], [9, 16], [9, 18], [9, 22], [9, 33], [9, 36], [9, 38], [9, 39], [9, 41], [9, 43], [9, 49], [9, 58], [9, 60], [9, 62], [9, 63], [9, 65], [9, 66], [9, 67], [9, 69], [9, 71], [9, 75], [9, 76], [9, 78], [9, 81], [9, 87], [9, 94], [10, 11], [10, 12], [10, 13], [10, 14], [10, 21], [10, 23], [10, 29], [10, 30], [10, 38], [10, 46], [10, 56], [10, 59], [10, 60], [10, 65], [10, 67], [10, 73], [10, 75], [10, 79], [10, 81], [10, 84], [10, 85], [10, 89], [10, 92], [10, 97], [10, 99], [11, 12], [11, 16], [11, 17], [11, 19], [11, 22], [11, 24], [11, 25], [11, 34], [11, 41], [11, 45], [11, 46], [11, 50], [11, 55], [11, 60], [11, 62], [11, 63], [11, 64], [11, 65], [11, 66], [11, 67], [11, 68], [11, 70], [11, 73], [11, 76], [11, 82], [11, 83], [11, 90], [11, 98], [12, 18], [12, 20], [12, 32], [12, 34], [12, 36], [12, 38], [12, 44], [12, 54], [12, 61], [12, 71], 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new file mode 100644
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+
+Find an independent set of size at least 30: a set of distinct vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (at least 30 distinct integers in 0..99).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-independent-set-l6-s0/solution/solve.sh b/tasks/construct-nppc-independent-set-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..127093d95503cf647e1658f60a9b6fb5414308fa
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [1, 2, 4, 16, 21, 22, 27, 31, 32, 34, 36, 42, 43, 44, 46, 49, 52, 55, 65, 67, 69, 79, 80, 82, 83, 86, 88, 90, 94, 96]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l6-s0/task.toml b/tasks/construct-nppc-independent-set-l6-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..eaedabd690a7a1683f22f959d48a6d62f06e34d1
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-independent-set-l6-s0"
+version = "0.2.0"
+description = "construct/nppc_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "NPPC/independent_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-independent-set-l6-s0/tests/check.py b/tasks/construct-nppc-independent-set-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/tests/check.py
@@ -0,0 +1,19 @@
+"""Independent set of size >= k. Accepts any valid independent set."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    s = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    # upstream NPPC verifier checks len(list) >= size but only tests pairs u < v, so [v]*k passed
+    if len(set(s)) != len(s):
+        raise Invalid("independent_set contains duplicates")
+    if len(s) < k:
+        raise Invalid(f"independent_set has {len(s)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(s), 2):
+        if (u, v) in es:
+            raise Invalid(f"edge between {u} and {v}")
+    return None, {"size": len(s)}
diff --git a/tasks/construct-nppc-independent-set-l6-s0/tests/instance.json b/tasks/construct-nppc-independent-set-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e32e84d3aab3dcfb8f8c58b707937dd892a72a70
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 100, "k": 30, "edges": [[0, 1], [0, 4], [0, 7], [0, 10], [0, 12], [0, 13], [0, 22], [0, 26], [0, 36], [0, 37], [0, 38], [0, 40], [0, 41], [0, 50], [0, 52], [0, 53], [0, 54], [0, 56], [0, 64], [0, 70], [0, 80], [0, 85], [0, 92], [0, 99], [1, 6], [1, 13], [1, 15], [1, 19], [1, 26], [1, 39], [1, 41], [1, 47], [1, 48], [1, 50], [1, 53], [1, 57], [1, 68], [1, 70], [1, 71], [1, 73], [1, 74], [1, 81], [1, 91], [2, 3], [2, 5], [2, 8], [2, 13], [2, 15], [2, 20], [2, 23], [2, 24], [2, 25], [2, 33], [2, 47], [2, 48], [2, 56], [2, 58], [2, 60], [2, 63], [2, 66], [2, 71], [2, 78], [2, 85], [2, 93], [2, 97], [2, 98], [3, 7], [3, 10], [3, 12], [3, 15], [3, 27], [3, 29], [3, 30], [3, 31], [3, 35], [3, 41], [3, 44], [3, 45], [3, 52], [3, 57], [3, 62], [3, 63], [3, 67], [3, 68], [3, 69], [3, 70], [3, 75], [3, 76], [3, 81], [3, 90], [3, 91], [3, 93], [3, 95], [3, 96], [3, 99], [4, 8], [4, 14], [4, 17], [4, 18], [4, 26], [4, 37], [4, 40], [4, 48], [4, 51], [4, 56], [4, 57], [4, 58], [4, 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\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l6-s0/tests/run.py b/tasks/construct-nppc-independent-set-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-independent-set-l6-s0/tests/test.sh b/tasks/construct-nppc-independent-set-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-independent-set-l6-s7/environment/Dockerfile b/tasks/construct-nppc-independent-set-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-independent-set-l6-s7/environment/instance.json b/tasks/construct-nppc-independent-set-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4e2b19e5710968a2bcac78e588d8fba74b4637a2
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 100, "k": 30, "edges": [[0, 2], [0, 5], [0, 9], [0, 10], [0, 11], [0, 12], [0, 16], [0, 18], [0, 24], [0, 26], [0, 28], [0, 29], [0, 31], [0, 32], [0, 33], [0, 34], [0, 41], [0, 42], [0, 43], [0, 47], [0, 50], [0, 52], [0, 56], [0, 61], [0, 69], [0, 72], [0, 74], [0, 76], [0, 77], [0, 85], [0, 89], [0, 90], [0, 95], [0, 99], [1, 10], [1, 14], [1, 17], [1, 23], [1, 24], [1, 28], [1, 36], [1, 42], [1, 43], [1, 47], [1, 50], [1, 55], [1, 59], [1, 60], [1, 62], [1, 85], [1, 91], [2, 3], [2, 5], [2, 7], [2, 8], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 26], [2, 27], [2, 28], [2, 29], [2, 31], [2, 32], [2, 34], [2, 35], [2, 37], [2, 40], [2, 42], [2, 44], [2, 46], [2, 49], [2, 50], [2, 53], [2, 58], [2, 59], [2, 67], [2, 71], [2, 72], [2, 73], [2, 75], [2, 76], [2, 93], [2, 94], [2, 95], [3, 4], [3, 5], [3, 8], [3, 14], [3, 15], [3, 19], [3, 20], [3, 21], [3, 26], [3, 28], [3, 32], [3, 34], [3, 37], [3, 39], [3, 49], [3, 50], [3, 51], [3, 54], [3, 56], [3, 57], [3, 62], 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\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l6-s7/instruction.md b/tasks/construct-nppc-independent-set-l6-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..50854f34533aaa4f928175d119ab86eca2f60d51
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 100 vertices labelled 0..99 and 1347 edges:
+[[0, 2], [0, 5], [0, 9], [0, 10], [0, 11], [0, 12], [0, 16], [0, 18], [0, 24], [0, 26], [0, 28], [0, 29], [0, 31], [0, 32], [0, 33], [0, 34], [0, 41], [0, 42], [0, 43], [0, 47], [0, 50], [0, 52], [0, 56], [0, 61], [0, 69], [0, 72], [0, 74], [0, 76], [0, 77], [0, 85], [0, 89], [0, 90], [0, 95], [0, 99], [1, 10], [1, 14], [1, 17], [1, 23], [1, 24], [1, 28], [1, 36], [1, 42], [1, 43], [1, 47], [1, 50], [1, 55], [1, 59], [1, 60], [1, 62], [1, 85], [1, 91], [2, 3], [2, 5], [2, 7], [2, 8], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 26], [2, 27], [2, 28], [2, 29], [2, 31], [2, 32], [2, 34], [2, 35], [2, 37], [2, 40], [2, 42], [2, 44], [2, 46], [2, 49], [2, 50], [2, 53], [2, 58], [2, 59], [2, 67], [2, 71], [2, 72], [2, 73], [2, 75], [2, 76], [2, 93], [2, 94], [2, 95], [3, 4], [3, 5], [3, 8], [3, 14], [3, 15], [3, 19], [3, 20], [3, 21], [3, 26], [3, 28], [3, 32], [3, 34], [3, 37], [3, 39], [3, 49], [3, 50], [3, 51], [3, 54], [3, 56], [3, 57], [3, 62], [3, 63], [3, 64], [3, 66], [3, 67], 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+
+Find an independent set of size at least 30: a set of distinct vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (at least 30 distinct integers in 0..99).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-independent-set-l6-s7/solution/solve.sh b/tasks/construct-nppc-independent-set-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..41f4e84658838af3abf6d3c92085830dfc53b728
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"independent_set": [1, 5, 9, 16, 22, 25, 26, 27, 30, 31, 35, 37, 56, 57, 58, 61, 63, 68, 71, 72, 74, 80, 83, 84, 86, 88, 89, 93, 94, 98]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-independent-set-l6-s7/task.toml b/tasks/construct-nppc-independent-set-l6-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ba23a8d8421ff3fe8173f1c13165e0c0542f5b19
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-independent-set-l6-s7"
+version = "0.2.0"
+description = "construct/nppc_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "NPPC/independent_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-independent-set-l6-s7/tests/check.py b/tasks/construct-nppc-independent-set-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..92279a931488c7f39c08a3b11162b3f54a9c662a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/tests/check.py
@@ -0,0 +1,19 @@
+"""Independent set of size >= k. Accepts any valid independent set."""
+import itertools
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    s = int_list(ans.get("independent_set"), None, 0, n - 1, "independent_set")
+    # upstream NPPC verifier checks len(list) >= size but only tests pairs u < v, so [v]*k passed
+    if len(set(s)) != len(s):
+        raise Invalid("independent_set contains duplicates")
+    if len(s) < k:
+        raise Invalid(f"independent_set has {len(s)} < {k} vertices")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for u, v in itertools.combinations(sorted(s), 2):
+        if (u, v) in es:
+            raise Invalid(f"edge between {u} and {v}")
+    return None, {"size": len(s)}
diff --git a/tasks/construct-nppc-independent-set-l6-s7/tests/instance.json b/tasks/construct-nppc-independent-set-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4e2b19e5710968a2bcac78e588d8fba74b4637a2
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 100, "k": 30, "edges": [[0, 2], [0, 5], [0, 9], [0, 10], [0, 11], [0, 12], [0, 16], [0, 18], [0, 24], [0, 26], [0, 28], [0, 29], [0, 31], [0, 32], [0, 33], [0, 34], [0, 41], [0, 42], [0, 43], [0, 47], [0, 50], [0, 52], [0, 56], [0, 61], [0, 69], [0, 72], [0, 74], [0, 76], [0, 77], [0, 85], [0, 89], [0, 90], [0, 95], [0, 99], [1, 10], [1, 14], [1, 17], [1, 23], [1, 24], [1, 28], [1, 36], [1, 42], [1, 43], [1, 47], [1, 50], [1, 55], [1, 59], [1, 60], [1, 62], [1, 85], [1, 91], [2, 3], [2, 5], [2, 7], [2, 8], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 26], [2, 27], [2, 28], [2, 29], [2, 31], [2, 32], [2, 34], [2, 35], [2, 37], [2, 40], [2, 42], [2, 44], [2, 46], [2, 49], [2, 50], [2, 53], [2, 58], [2, 59], [2, 67], [2, 71], [2, 72], [2, 73], [2, 75], [2, 76], [2, 93], [2, 94], [2, 95], [3, 4], [3, 5], [3, 8], [3, 14], [3, 15], [3, 19], [3, 20], [3, 21], [3, 26], [3, 28], [3, 32], [3, 34], [3, 37], [3, 39], [3, 49], [3, 50], [3, 51], [3, 54], [3, 56], [3, 57], [3, 62], 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98], [86, 99], [87, 88], [87, 95], [88, 90], [88, 95], [88, 96], [88, 97], [88, 99], [89, 99], [90, 91], [90, 92], [90, 93], [90, 94], [90, 99], [91, 94], [91, 96], [91, 99], [92, 93], [92, 95], [92, 97], [93, 96], [95, 98], [96, 98], [97, 99]], "family": "nppc_independent_set", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-independent-set-l6-s7/tests/run.py b/tasks/construct-nppc-independent-set-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-independent-set-l6-s7/tests/test.sh b/tasks/construct-nppc-independent-set-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-independent-set-l6-s9/instruction.md b/tasks/construct-nppc-independent-set-l6-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..03ed89856a9e2b1d43bb5809b509a33c502a1d7f
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s9/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 100 vertices labelled 0..99 and 1322 edges:
+[[0, 3], [0, 5], [0, 8], [0, 9], [0, 11], [0, 17], [0, 18], [0, 20], [0, 24], [0, 26], [0, 40], [0, 45], [0, 46], [0, 48], [0, 53], [0, 56], [0, 59], [0, 60], [0, 61], [0, 64], [0, 67], [0, 72], [0, 75], [0, 76], [0, 78], [0, 79], [0, 80], [0, 82], [0, 84], [0, 92], [0, 98], [1, 5], [1, 7], [1, 12], [1, 15], [1, 16], [1, 18], [1, 21], [1, 23], [1, 33], [1, 40], [1, 41], [1, 43], [1, 46], [1, 48], [1, 51], [1, 65], [1, 66], [1, 70], [1, 71], [1, 72], [1, 73], [1, 81], [1, 84], [1, 86], [1, 89], [2, 4], [2, 10], [2, 14], [2, 15], [2, 20], [2, 22], [2, 26], [2, 28], [2, 30], [2, 31], [2, 41], [2, 42], [2, 44], [2, 50], [2, 52], [2, 60], [2, 61], [2, 62], [2, 64], [2, 65], [2, 71], [2, 86], [2, 91], [2, 94], [2, 97], [2, 98], [3, 6], [3, 7], [3, 10], [3, 13], [3, 14], [3, 17], [3, 18], [3, 19], [3, 24], [3, 31], [3, 32], [3, 35], [3, 36], [3, 38], [3, 43], [3, 49], [3, 50], [3, 53], [3, 56], [3, 59], [3, 62], [3, 65], [3, 66], [3, 70], [3, 71], [3, 73], [3, 79], [3, 80], [3, 81], [3, 82], 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47], [32, 51], [32, 52], [32, 60], [32, 62], [32, 63], [32, 64], [32, 69], [32, 70], [32, 71], [32, 73], [32, 80], [32, 81], [32, 89], [32, 94], [32, 95], [33, 34], [33, 36], [33, 42], [33, 44], [33, 49], [33, 51], [33, 56], [33, 60], [33, 67], [33, 71], [33, 73], [33, 76], [33, 79], [33, 81], [33, 83], [33, 84], [33, 95], [33, 96], [33, 98], [34, 35], [34, 39], [34, 60], [34, 62], [34, 67], [34, 74], [34, 82], [34, 85], [34, 90], [34, 92], [34, 94], [35, 36], [35, 39], [35, 44], [35, 51], [35, 54], [35, 55], [35, 60], [35, 63], [35, 66], [35, 72], [35, 73], [35, 75], [35, 79], [35, 84], [35, 85], [35, 91], [36, 39], [36, 55], [36, 57], [36, 62], [36, 65], [36, 66], [36, 67], [36, 72], [36, 73], [36, 75], [36, 76], [36, 78], [36, 79], [36, 81], [36, 84], [36, 88], [36, 92], [36, 93], [37, 39], [37, 40], [37, 44], [37, 45], [37, 48], [37, 53], [37, 56], [37, 58], [37, 59], [37, 60], [37, 62], [37, 68], [37, 77], [37, 86], [37, 95], [38, 51], [38, 63], [38, 76], [38, 85], [38, 94], [39, 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71], [46, 72], [46, 78], [46, 80], [46, 85], [46, 91], [46, 92], [46, 94], [46, 99], [47, 48], [47, 49], [47, 56], [47, 58], [47, 60], [47, 63], [47, 65], [47, 72], [47, 73], [47, 76], [47, 79], [47, 80], [47, 82], [47, 86], [47, 88], [47, 94], [47, 97], [47, 98], [47, 99], [48, 51], [48, 59], [48, 66], [48, 72], [48, 74], [48, 76], [48, 77], [48, 78], [48, 80], [48, 81], [48, 83], [48, 85], [48, 88], [48, 91], [48, 93], [48, 96], [48, 97], [49, 50], [49, 53], [49, 54], [49, 57], [49, 58], [49, 62], [49, 64], [49, 84], [49, 85], [49, 92], [50, 53], [50, 56], [50, 58], [50, 60], [50, 63], [50, 65], [50, 74], [50, 75], [50, 76], [50, 77], [50, 79], [50, 80], [50, 81], [50, 82], [50, 91], [50, 95], [50, 98], [50, 99], [51, 53], [51, 55], [51, 56], [51, 58], [51, 64], [51, 76], [51, 77], [51, 81], [51, 88], [51, 89], [51, 98], [52, 55], [52, 56], [52, 60], [52, 61], [52, 62], [52, 65], [52, 68], [52, 70], [52, 74], [52, 76], [52, 77], [52, 83], [52, 87], [52, 88], [52, 90], [52, 91], [52, 93], [52, 96], [52, 97], [53, 59], [53, 66], [53, 68], [53, 69], [53, 73], [53, 74], [53, 84], [53, 87], [53, 88], [53, 91], [53, 94], [53, 95], [53, 96], [53, 99], [54, 58], [54, 63], [54, 64], [54, 66], [54, 69], [54, 70], [54, 71], [54, 74], [54, 79], [54, 85], [54, 86], [54, 91], [54, 98], [55, 63], [55, 78], [55, 80], [55, 83], [55, 87], [55, 91], [55, 92], [55, 95], [55, 96], [55, 98], [56, 57], [56, 63], [56, 64], [56, 68], [56, 74], [56, 82], [56, 85], [56, 94], [56, 95], [56, 96], [56, 98], [57, 60], [57, 61], [57, 64], [57, 73], [57, 75], [57, 78], [57, 83], [57, 89], [57, 93], [58, 67], [58, 69], [58, 71], [58, 76], [58, 81], [58, 82], [58, 84], [58, 85], [58, 88], [58, 89], [58, 90], [58, 91], [58, 93], [58, 96], [58, 98], [58, 99], [59, 64], [59, 67], [59, 73], [59, 74], [59, 76], [59, 85], [59, 87], [59, 91], [60, 61], [60, 63], [60, 73], [60, 77], [60, 81], [60, 82], [60, 87], [60, 92], [60, 93], [60, 95], [61, 64], [61, 68], [61, 74], [61, 76], [61, 89], [61, 90], [61, 94], [62, 66], [62, 67], [62, 71], [62, 72], [62, 73], [62, 74], [62, 75], [62, 78], [62, 83], [62, 89], [62, 91], [62, 94], [62, 95], [62, 99], [63, 64], [63, 65], [63, 67], [63, 70], [63, 77], [63, 78], [63, 95], [63, 96], [63, 97], [64, 65], [64, 68], [64, 71], [64, 76], [64, 77], [64, 80], [64, 82], [64, 90], [64, 97], [64, 99], [65, 74], [65, 80], [65, 83], [65, 85], [65, 89], [65, 91], [65, 96], [66, 85], [66, 99], [67, 70], [67, 72], [67, 74], [67, 78], [67, 82], [67, 88], [67, 90], [67, 94], [67, 98], [68, 69], [68, 70], [68, 73], [68, 78], [68, 79], [68, 80], [68, 81], [68, 83], [68, 84], [68, 87], [68, 90], [68, 92], [68, 97], [68, 98], [69, 72], [69, 74], [69, 78], [69, 82], [69, 85], [69, 87], [69, 91], [69, 96], [69, 99], [70, 72], [70, 73], [70, 74], [70, 83], [70, 87], [70, 89], [70, 91], [70, 92], [70, 99], [71, 78], [71, 80], [71, 82], [71, 83], [71, 88], [72, 74], [72, 76], [72, 78], [72, 82], [72, 83], [72, 84], [72, 88], [72, 90], [72, 95], [72, 97], [72, 98], [73, 78], [73, 80], [73, 81], [73, 84], [73, 85], [73, 92], [73, 93], [73, 97], [73, 99], [74, 82], [74, 83], [74, 84], [74, 91], [74, 93], [74, 94], [74, 98], [75, 84], [75, 85], [75, 91], [75, 94], [75, 99], [76, 84], [76, 85], [76, 87], [76, 91], [76, 94], [77, 78], [77, 83], [77, 84], [77, 86], [77, 88], [77, 90], [77, 97], [77, 98], [77, 99], [78, 82], [78, 87], [78, 91], [78, 95], [79, 82], [79, 83], [79, 84], [79, 96], [80, 97], [80, 98], [81, 83], [81, 89], [81, 90], [82, 83], [82, 84], [82, 87], [82, 88], [82, 97], [82, 99], [83, 96], [84, 85], [84, 86], [84, 87], [84, 89], [84, 90], [84, 93], [84, 99], [85, 90], [85, 94], [85, 95], [86, 94], [87, 88], [87, 93], [87, 95], [87, 98], [88, 91], [88, 92], [88, 96], [89, 90], [89, 92], [89, 95], [89, 96], [89, 98], [89, 99], [90, 92], [90, 95], [90, 98], [91, 95], [91, 97], [92, 94], [92, 96], [92, 99], [93, 94], [93, 95], [93, 96], [93, 98], [94, 95], [94, 97], [94, 99], [95, 96]]
+
+Find an independent set of size at least 30: a set of distinct vertices no two of which are joined by an edge.
+
+Answer format: {"independent_set": [v_1, v_2, ...]} (at least 30 distinct integers in 0..99).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-independent-set-l6-s9/task.toml b/tasks/construct-nppc-independent-set-l6-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ca9b39a0e01cd68a70011a6c8e52f2ae1e18b8fd
--- /dev/null
+++ b/tasks/construct-nppc-independent-set-l6-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-independent-set-l6-s9"
+version = "0.2.0"
+description = "construct/nppc_independent_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_independent_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_independent_set"
+problem_key = "graph_independent_set"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "NPPC/independent_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1fad5b95682a0b9753962a56a4838670932e7bbd
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"a": 5643, "b": 2326, "c": 363873785268, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/instruction.md b/tasks/construct-nppc-quad-diophantine-l3-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..312d2c938eb7688d4901fd89c7188dc8aaa65b4e
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/instruction.md
@@ -0,0 +1,7 @@
+Find positive integers x and y (x >= 1, y >= 1) such that
+
+    5643 * x^2 + 2326 * y = 363873785268
+
+Answer format: {"x": <integer>, "y": <integer>} (JSON integers, exact).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..79e9b936dc29a0b844d6f37c0cdb3ec2cf702f0e
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 8030, "y": 3468}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/task.toml b/tasks/construct-nppc-quad-diophantine-l3-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..f53f376a2eedb914e61790222e239684c49367b6
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-quad-diophantine-l3-s0"
+version = "0.2.0"
+description = "construct/nppc_quad_diophantine"
+authors = []
+keywords = ["rlmath", "construct", "nppc_quad_diophantine"]
+
+[metadata]
+subset = "construct"
+family = "nppc_quad_diophantine"
+problem_key = "quadratic_diophantine_ax2_by_c"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/quad_diop_equ"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/tests/check.py b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/check.py
@@ -0,0 +1,11 @@
+"""a*x^2 + b*y = c in positive integers. Accepts any solution (exact integer arithmetic)."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier only checks x > 0 and y > 0, so non-integer (float) x, y were accepted
+    x = as_int(ans.get("x"), "x", lo=1)
+    y = as_int(ans.get("y"), "y", lo=1)
+    if inst["a"] * x * x + inst["b"] * y != inst["c"]:
+        raise Invalid("a*x^2 + b*y != c")
+    return None, {}
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1fad5b95682a0b9753962a56a4838670932e7bbd
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"a": 5643, "b": 2326, "c": 363873785268, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/tests/run.py b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s0/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ae5f87d75a63614d7977698b9c877a4c2a25b7f7
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"a": 4235, "b": 1017, "c": 380434568, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/instruction.md b/tasks/construct-nppc-quad-diophantine-l3-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..98c3d27c9026857a0b3df16dffb4777877cf750e
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/instruction.md
@@ -0,0 +1,7 @@
+Find positive integers x and y (x >= 1, y >= 1) such that
+
+    4235 * x^2 + 1017 * y = 380434568
+
+Answer format: {"x": <integer>, "y": <integer>} (JSON integers, exact).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..640dd7606b9265201ccc493c698a8d48fd00bf68
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 296, "y": 9224}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/task.toml b/tasks/construct-nppc-quad-diophantine-l3-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..6eabcaf39434eb8918070b3be25fcca26267646f
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-quad-diophantine-l3-s7"
+version = "0.2.0"
+description = "construct/nppc_quad_diophantine"
+authors = []
+keywords = ["rlmath", "construct", "nppc_quad_diophantine"]
+
+[metadata]
+subset = "construct"
+family = "nppc_quad_diophantine"
+problem_key = "quadratic_diophantine_ax2_by_c"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/quad_diop_equ"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/tests/check.py b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/check.py
@@ -0,0 +1,11 @@
+"""a*x^2 + b*y = c in positive integers. Accepts any solution (exact integer arithmetic)."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier only checks x > 0 and y > 0, so non-integer (float) x, y were accepted
+    x = as_int(ans.get("x"), "x", lo=1)
+    y = as_int(ans.get("y"), "y", lo=1)
+    if inst["a"] * x * x + inst["b"] * y != inst["c"]:
+        raise Invalid("a*x^2 + b*y != c")
+    return None, {}
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ae5f87d75a63614d7977698b9c877a4c2a25b7f7
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"a": 4235, "b": 1017, "c": 380434568, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/tests/run.py b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s7/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/environment/Dockerfile b/tasks/construct-nppc-quad-diophantine-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/environment/instance.json b/tasks/construct-nppc-quad-diophantine-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5b3765ab489dc4c76be8561f7571fe287b5556c6
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"a": 4277, "b": 8140, "c": 51949978765, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/instruction.md b/tasks/construct-nppc-quad-diophantine-l3-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..373d9a5a2ad21bbd78a8e88ddd2eed191b1fe0a8
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/instruction.md
@@ -0,0 +1,7 @@
+Find positive integers x and y (x >= 1, y >= 1) such that
+
+    4277 * x^2 + 8140 * y = 51949978765
+
+Answer format: {"x": <integer>, "y": <integer>} (JSON integers, exact).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/solution/solve.sh b/tasks/construct-nppc-quad-diophantine-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e53abc9370c977aa7941c4e24f7dcd2dbe2c5f5c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 3485, "y": 596}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/task.toml b/tasks/construct-nppc-quad-diophantine-l3-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..37a71d3969a740966aecd51c259cbd8d0a3c312a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-quad-diophantine-l3-s9"
+version = "0.2.0"
+description = "construct/nppc_quad_diophantine"
+authors = []
+keywords = ["rlmath", "construct", "nppc_quad_diophantine"]
+
+[metadata]
+subset = "construct"
+family = "nppc_quad_diophantine"
+problem_key = "quadratic_diophantine_ax2_by_c"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/quad_diop_equ"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/tests/check.py b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..88989d2a8839b089c9b07dd2d3c26c21bfdca58c
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/check.py
@@ -0,0 +1,11 @@
+"""a*x^2 + b*y = c in positive integers. Accepts any solution (exact integer arithmetic)."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier only checks x > 0 and y > 0, so non-integer (float) x, y were accepted
+    x = as_int(ans.get("x"), "x", lo=1)
+    y = as_int(ans.get("y"), "y", lo=1)
+    if inst["a"] * x * x + inst["b"] * y != inst["c"]:
+        raise Invalid("a*x^2 + b*y != c")
+    return None, {}
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/tests/instance.json b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5b3765ab489dc4c76be8561f7571fe287b5556c6
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"a": 4277, "b": 8140, "c": 51949978765, "family": "nppc_quad_diophantine", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/tests/run.py b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quad-diophantine-l3-s9/tests/test.sh b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quad-diophantine-l3-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2518ede94c69ce54e728ad62622399bbc5a04bad
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"a": 33461, "b": 72460, "c": 72117, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/instruction.md b/tasks/construct-nppc-quadratic-congruence-l3-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..57d24b62b303bca3467e50b091af51bd6d238d43
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/instruction.md
@@ -0,0 +1,7 @@
+Find an integer x with 1 <= x < 72117 such that
+
+    x^2 = 33461 (mod 72460).
+
+Answer format: {"x": <integer>} (a JSON integer, exact).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a1bb9e17474f81628cee19fa43017bc99a9939b1
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 25451}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/task.toml b/tasks/construct-nppc-quadratic-congruence-l3-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..7855f0e688eeab79d9360acfce5c49cf7d8735ac
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-quadratic-congruence-l3-s0"
+version = "0.2.0"
+description = "construct/nppc_quadratic_congruence"
+authors = []
+keywords = ["rlmath", "construct", "nppc_quadratic_congruence"]
+
+[metadata]
+subset = "construct"
+family = "nppc_quadratic_congruence"
+problem_key = "quadratic_congruence_bounded"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/quadratic_congruence"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/check.py
@@ -0,0 +1,11 @@
+"""Quadratic congruence: integer x with 1 <= x < c and x^2 = a (mod b). Accepts any such x."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier did int(x) (accepting "12", 12.9 -> 12) and only checked x < c, so negative x
+    # (e.g. -r for any root r) and x = 0 passed and the bound c was meaningless
+    x = as_int(ans.get("x"), "x", lo=1, hi=inst["c"] - 1)
+    if x * x % inst["b"] != inst["a"]:
+        raise Invalid("x^2 mod b != a")
+    return None, {}
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..2518ede94c69ce54e728ad62622399bbc5a04bad
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"a": 33461, "b": 72460, "c": 72117, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s7/instruction.md b/tasks/construct-nppc-quadratic-congruence-l3-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..03d3959d8551c00d9509488ae2200c70f70ac706
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s7/instruction.md
@@ -0,0 +1,7 @@
+Find an integer x with 1 <= x < 86540 such that
+
+    x^2 = 3028 (mod 36891).
+
+Answer format: {"x": <integer>} (a JSON integer, exact).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s7/task.toml b/tasks/construct-nppc-quadratic-congruence-l3-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..24ebd0b107d0f6b218c171046e0b2aaba9d0ea47
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-quadratic-congruence-l3-s7"
+version = "0.2.0"
+description = "construct/nppc_quadratic_congruence"
+authors = []
+keywords = ["rlmath", "construct", "nppc_quadratic_congruence"]
+
+[metadata]
+subset = "construct"
+family = "nppc_quadratic_congruence"
+problem_key = "quadratic_congruence_bounded"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/quadratic_congruence"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/environment/Dockerfile b/tasks/construct-nppc-quadratic-congruence-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/environment/instance.json b/tasks/construct-nppc-quadratic-congruence-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..62cb161bbc28fe1044b60a05d565c1cd0fd25129
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"a": 19175, "b": 63670, "c": 118922, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/instruction.md b/tasks/construct-nppc-quadratic-congruence-l3-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..25a1ebe8aaeed170bde744efab87dde8ad6c76a0
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/instruction.md
@@ -0,0 +1,7 @@
+Find an integer x with 1 <= x < 118922 such that
+
+    x^2 = 19175 (mod 63670).
+
+Answer format: {"x": <integer>} (a JSON integer, exact).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/solution/solve.sh b/tasks/construct-nppc-quadratic-congruence-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..ef93ef9901f19bb81d21dd476a9f0b14079d58b1
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 76915}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/task.toml b/tasks/construct-nppc-quadratic-congruence-l3-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..25f7712c30b43bd28f76b346b55ef8bee22cf648
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-quadratic-congruence-l3-s9"
+version = "0.2.0"
+description = "construct/nppc_quadratic_congruence"
+authors = []
+keywords = ["rlmath", "construct", "nppc_quadratic_congruence"]
+
+[metadata]
+subset = "construct"
+family = "nppc_quadratic_congruence"
+problem_key = "quadratic_congruence_bounded"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "NPPC/quadratic_congruence"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/check.py b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a751c071a276ca0aae7fb05bfdcd7b6e0c6d3a6
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/check.py
@@ -0,0 +1,11 @@
+"""Quadratic congruence: integer x with 1 <= x < c and x^2 = a (mod b). Accepts any such x."""
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    # upstream NPPC verifier did int(x) (accepting "12", 12.9 -> 12) and only checked x < c, so negative x
+    # (e.g. -r for any root r) and x = 0 passed and the bound c was meaningless
+    x = as_int(ans.get("x"), "x", lo=1, hi=inst["c"] - 1)
+    if x * x % inst["b"] != inst["a"]:
+        raise Invalid("x^2 mod b != a")
+    return None, {}
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/instance.json b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..62cb161bbc28fe1044b60a05d565c1cd0fd25129
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"a": 19175, "b": 63670, "c": 118922, "family": "nppc_quadratic_congruence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/run.py b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/test.sh b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-quadratic-congruence-l3-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l1-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/environment/instance.json b/tasks/construct-nppc-vertex-cover-l1-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..424bebec92b54418d0ba772ea275f8ab98af5065
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "k": 3, "edges": [[0, 2], [0, 3], [1, 4], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/instruction.md b/tasks/construct-nppc-vertex-cover-l1-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..8167752fa6a7c99d56ec68d0438b77e8cf5beef9
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 8 vertices labelled 0..7 and 11 edges:
+[[0, 2], [0, 3], [1, 4], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]]
+
+Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
+
+Answer format: {"cover": [v_1, v_2, ...]} (distinct integers in 0..7, at most 3 of them).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l1-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3cd92f46e6f5e6a61e31950f8b15491e3764ab6d
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [2, 3, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/task.toml b/tasks/construct-nppc-vertex-cover-l1-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..aab3cac668d79a209bd1015ca40d2c596313f9fb
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-vertex-cover-l1-s2"
+version = "0.2.0"
+description = "construct/nppc_vertex_cover"
+authors = []
+keywords = ["rlmath", "construct", "nppc_vertex_cover"]
+
+[metadata]
+subset = "construct"
+family = "nppc_vertex_cover"
+problem_key = "graph_vertex_cover"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "NPPC/vertex_cover"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/tests/check.py b/tasks/construct-nppc-vertex-cover-l1-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/tests/check.py
@@ -0,0 +1,18 @@
+"""Vertex cover of size <= k. Accepts any valid cover."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier converts to a set without type checks (floats/bools slip through and
+    # duplicates are silently merged); here entries must be distinct ints in range
+    c = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(c)) != len(c):
+        raise Invalid("cover contains duplicates")
+    if len(c) > k:
+        raise Invalid(f"cover has {len(c)} > {k} vertices")
+    s = set(c)
+    for u, v in inst["edges"]:
+        if u not in s and v not in s:
+            raise Invalid(f"edge ({u},{v}) not covered")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/tests/instance.json b/tasks/construct-nppc-vertex-cover-l1-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..424bebec92b54418d0ba772ea275f8ab98af5065
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "k": 3, "edges": [[0, 2], [0, 3], [1, 4], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/tests/run.py b/tasks/construct-nppc-vertex-cover-l1-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-vertex-cover-l1-s2/tests/test.sh b/tasks/construct-nppc-vertex-cover-l1-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l1-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/environment/instance.json b/tasks/construct-nppc-vertex-cover-l1-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b776d1a084cd6106bc35a1e2aad25feb17194df1
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "k": 3, "edges": [[0, 2], [0, 4], [1, 2], [2, 3], [2, 5], [3, 4], [3, 7], [4, 5], [4, 6], [4, 7]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/instruction.md b/tasks/construct-nppc-vertex-cover-l1-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..ecb00ea10e6ea7ad7d9bd57180b77fe78d0fa2fa
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 8 vertices labelled 0..7 and 10 edges:
+[[0, 2], [0, 4], [1, 2], [2, 3], [2, 5], [3, 4], [3, 7], [4, 5], [4, 6], [4, 7]]
+
+Find a vertex cover of size at most 3: a set C of distinct vertices such that every edge has at least one endpoint in C.
+
+Answer format: {"cover": [v_1, v_2, ...]} (distinct integers in 0..7, at most 3 of them).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l1-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..3cd92f46e6f5e6a61e31950f8b15491e3764ab6d
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [2, 3, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/task.toml b/tasks/construct-nppc-vertex-cover-l1-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..74b18c7efddc13dc502c613bbbdc3303db83df22
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-vertex-cover-l1-s5"
+version = "0.2.0"
+description = "construct/nppc_vertex_cover"
+authors = []
+keywords = ["rlmath", "construct", "nppc_vertex_cover"]
+
+[metadata]
+subset = "construct"
+family = "nppc_vertex_cover"
+problem_key = "graph_vertex_cover"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "NPPC/vertex_cover"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/tests/check.py b/tasks/construct-nppc-vertex-cover-l1-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/tests/check.py
@@ -0,0 +1,18 @@
+"""Vertex cover of size <= k. Accepts any valid cover."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier converts to a set without type checks (floats/bools slip through and
+    # duplicates are silently merged); here entries must be distinct ints in range
+    c = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(c)) != len(c):
+        raise Invalid("cover contains duplicates")
+    if len(c) > k:
+        raise Invalid(f"cover has {len(c)} > {k} vertices")
+    s = set(c)
+    for u, v in inst["edges"]:
+        if u not in s and v not in s:
+            raise Invalid(f"edge ({u},{v}) not covered")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/tests/instance.json b/tasks/construct-nppc-vertex-cover-l1-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b776d1a084cd6106bc35a1e2aad25feb17194df1
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 8, "k": 3, "edges": [[0, 2], [0, 4], [1, 2], [2, 3], [2, 5], [3, 4], [3, 7], [4, 5], [4, 6], [4, 7]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/tests/run.py b/tasks/construct-nppc-vertex-cover-l1-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-vertex-cover-l1-s5/tests/test.sh b/tasks/construct-nppc-vertex-cover-l1-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l1-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l5-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/environment/instance.json b/tasks/construct-nppc-vertex-cover-l5-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9d458462e92e5a40c285d24ab921fd90e3c0d750
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/environment/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "k": 40, "edges": [[0, 14], [0, 18], [0, 24], [0, 25], [0, 28], [0, 31], [0, 32], [0, 33], [0, 40], [0, 42], [0, 44], [0, 50], [0, 63], [0, 71], [1, 2], [1, 4], [1, 5], [1, 7], [1, 11], [1, 15], [1, 21], [1, 24], [1, 28], [1, 38], [1, 40], [1, 41], [1, 42], [1, 44], [1, 46], [1, 49], [1, 50], [1, 51], [1, 56], [1, 58], [1, 63], [1, 71], [1, 79], [2, 3], [2, 4], [2, 10], [2, 11], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 21], [2, 24], [2, 25], [2, 27], [2, 29], [2, 30], [2, 31], [2, 32], [2, 34], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 41], [2, 43], [2, 45], [2, 46], [2, 48], [2, 50], [2, 51], [2, 52], [2, 58], [2, 60], [2, 62], [2, 63], [2, 64], [2, 66], [2, 67], [2, 69], [2, 70], [2, 71], [2, 72], [2, 73], [2, 75], [2, 76], [2, 79], [3, 4], [3, 5], [3, 12], [3, 21], [3, 24], [3, 25], [3, 30], [3, 31], [3, 33], [3, 34], [3, 38], [3, 40], [3, 42], [3, 44], [3, 46], [3, 48], [3, 49], [3, 50], [3, 51], [3, 54], [3, 55], [3, 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\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/instruction.md b/tasks/construct-nppc-vertex-cover-l5-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c8f6d2a99d052be4856d95c425bebbee3b3cb9f9
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 80 vertices labelled 0..79 and 1373 edges:
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+
+Find a vertex cover of size at most 40: a set C of distinct vertices such that every edge has at least one endpoint in C.
+
+Answer format: {"cover": [v_1, v_2, ...]} (distinct integers in 0..79, at most 40 of them).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l5-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..43f58fcb3559a9f4c43a260557cc2e965c618d07
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [2, 4, 5, 7, 11, 12, 14, 15, 18, 21, 24, 25, 28, 30, 31, 32, 33, 34, 38, 40, 41, 42, 44, 46, 48, 49, 50, 51, 54, 55, 56, 58, 60, 61, 63, 64, 66, 71, 72, 79]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/task.toml b/tasks/construct-nppc-vertex-cover-l5-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5c25b431250e8094af70c399a63a0238335f70b7
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-vertex-cover-l5-s3"
+version = "0.2.0"
+description = "construct/nppc_vertex_cover"
+authors = []
+keywords = ["rlmath", "construct", "nppc_vertex_cover"]
+
+[metadata]
+subset = "construct"
+family = "nppc_vertex_cover"
+problem_key = "graph_vertex_cover"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "NPPC/vertex_cover"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/tests/check.py b/tasks/construct-nppc-vertex-cover-l5-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/tests/check.py
@@ -0,0 +1,18 @@
+"""Vertex cover of size <= k. Accepts any valid cover."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier converts to a set without type checks (floats/bools slip through and
+    # duplicates are silently merged); here entries must be distinct ints in range
+    c = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(c)) != len(c):
+        raise Invalid("cover contains duplicates")
+    if len(c) > k:
+        raise Invalid(f"cover has {len(c)} > {k} vertices")
+    s = set(c)
+    for u, v in inst["edges"]:
+        if u not in s and v not in s:
+            raise Invalid(f"edge ({u},{v}) not covered")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/tests/instance.json b/tasks/construct-nppc-vertex-cover-l5-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9d458462e92e5a40c285d24ab921fd90e3c0d750
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "k": 40, "edges": [[0, 14], [0, 18], [0, 24], [0, 25], [0, 28], [0, 31], [0, 32], [0, 33], [0, 40], [0, 42], [0, 44], [0, 50], [0, 63], [0, 71], [1, 2], [1, 4], [1, 5], [1, 7], [1, 11], [1, 15], [1, 21], [1, 24], [1, 28], [1, 38], [1, 40], [1, 41], [1, 42], [1, 44], [1, 46], [1, 49], [1, 50], [1, 51], [1, 56], [1, 58], [1, 63], [1, 71], [1, 79], [2, 3], [2, 4], [2, 10], [2, 11], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 21], [2, 24], [2, 25], [2, 27], [2, 29], [2, 30], [2, 31], [2, 32], [2, 34], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 41], [2, 43], [2, 45], [2, 46], [2, 48], [2, 50], [2, 51], [2, 52], [2, 58], [2, 60], [2, 62], [2, 63], [2, 64], [2, 66], [2, 67], [2, 69], [2, 70], [2, 71], [2, 72], [2, 73], [2, 75], [2, 76], [2, 79], [3, 4], [3, 5], [3, 12], [3, 21], [3, 24], [3, 25], [3, 30], [3, 31], [3, 33], [3, 34], [3, 38], [3, 40], [3, 42], [3, 44], [3, 46], [3, 48], [3, 49], [3, 50], [3, 51], [3, 54], [3, 55], [3, 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[62, 64], [62, 71], [63, 64], [63, 65], [63, 66], [63, 70], [63, 71], [63, 72], [63, 73], [63, 75], [63, 78], [64, 65], [64, 66], [64, 69], [64, 71], [64, 72], [64, 73], [64, 75], [64, 77], [64, 78], [65, 71], [66, 68], [66, 69], [66, 70], [66, 74], [66, 75], [66, 76], [66, 79], [67, 71], [67, 79], [70, 71], [70, 72], [70, 79], [71, 72], [71, 76], [71, 77], [72, 73], [72, 74], [72, 77], [72, 78], [72, 79], [73, 79], [76, 79], [78, 79]], "family": "nppc_vertex_cover", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/tests/run.py b/tasks/construct-nppc-vertex-cover-l5-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-vertex-cover-l5-s3/tests/test.sh b/tasks/construct-nppc-vertex-cover-l5-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/environment/Dockerfile b/tasks/construct-nppc-vertex-cover-l5-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/environment/instance.json b/tasks/construct-nppc-vertex-cover-l5-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e57d671f66f71897ec667b5e33dc9ee17eaaec36
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/environment/instance.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/instruction.md b/tasks/construct-nppc-vertex-cover-l5-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..746f113702fd77c8e940e90695797141cd63654e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/instruction.md
@@ -0,0 +1,8 @@
+Undirected graph with 80 vertices labelled 0..79 and 1409 edges:
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+
+Find a vertex cover of size at most 40: a set C of distinct vertices such that every edge has at least one endpoint in C.
+
+Answer format: {"cover": [v_1, v_2, ...]} (distinct integers in 0..79, at most 40 of them).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/solution/solve.sh b/tasks/construct-nppc-vertex-cover-l5-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c8f8b8f930ed4940f9a6ab96fb44ede7120fe641
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"cover": [0, 1, 4, 5, 13, 14, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 30, 35, 36, 37, 39, 40, 43, 46, 47, 51, 52, 53, 54, 60, 61, 62, 63, 65, 68, 72, 74, 76, 77, 78]}
+RLMATH_EOF
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/task.toml b/tasks/construct-nppc-vertex-cover-l5-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..bb9d2a744971e1c37620611be84843c91a843ba2
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-vertex-cover-l5-s4"
+version = "0.2.0"
+description = "construct/nppc_vertex_cover"
+authors = []
+keywords = ["rlmath", "construct", "nppc_vertex_cover"]
+
+[metadata]
+subset = "construct"
+family = "nppc_vertex_cover"
+problem_key = "graph_vertex_cover"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "NPPC/vertex_cover"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/tests/check.py b/tasks/construct-nppc-vertex-cover-l5-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..d8ed740cc660c4837d941a8d70ea394c3bc9f69e
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/tests/check.py
@@ -0,0 +1,18 @@
+"""Vertex cover of size <= k. Accepts any valid cover."""
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["num_nodes"], inst["k"]
+    # upstream NPPC verifier converts to a set without type checks (floats/bools slip through and
+    # duplicates are silently merged); here entries must be distinct ints in range
+    c = int_list(ans.get("cover"), None, 0, n - 1, "cover")
+    if len(set(c)) != len(c):
+        raise Invalid("cover contains duplicates")
+    if len(c) > k:
+        raise Invalid(f"cover has {len(c)} > {k} vertices")
+    s = set(c)
+    for u, v in inst["edges"]:
+        if u not in s and v not in s:
+            raise Invalid(f"edge ({u},{v}) not covered")
+    return None, {"size": len(c)}
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/tests/instance.json b/tasks/construct-nppc-vertex-cover-l5-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e57d671f66f71897ec667b5e33dc9ee17eaaec36
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/tests/instance.json
@@ -0,0 +1 @@
+{"num_nodes": 80, "k": 40, "edges": [[0, 1], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 11], [0, 12], [0, 13], [0, 14], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 24], [0, 26], [0, 28], [0, 30], [0, 33], [0, 35], [0, 37], [0, 40], [0, 42], [0, 46], [0, 48], [0, 50], [0, 51], [0, 52], [0, 53], [0, 54], [0, 56], [0, 57], [0, 58], [0, 59], [0, 60], [0, 61], [0, 62], [0, 63], [0, 64], [0, 65], [0, 68], [0, 69], [0, 70], [0, 71], [0, 72], [0, 73], [0, 74], [0, 76], [0, 77], [0, 78], [0, 79], [1, 4], [1, 5], [1, 9], [1, 12], [1, 13], [1, 14], [1, 15], [1, 18], [1, 21], [1, 22], [1, 23], [1, 24], [1, 26], [1, 30], [1, 31], [1, 32], [1, 35], [1, 37], [1, 38], [1, 39], [1, 41], [1, 43], [1, 44], [1, 45], [1, 47], [1, 51], [1, 52], [1, 53], [1, 54], [1, 57], [1, 58], [1, 59], [1, 60], [1, 62], [1, 63], [1, 64], [1, 66], [1, 67], [1, 68], [1, 72], [1, 73], [1, 74], [1, 75], [1, 76], [1, 77], [1, 79], [2, 4], [2, 13], [2, 14], [2, 17], [2, 18], [2, 19], [2, 20], [2, 27], [2, 28], 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\ No newline at end of file
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/tests/run.py b/tasks/construct-nppc-vertex-cover-l5-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-nppc-vertex-cover-l5-s4/tests/test.sh b/tasks/construct-nppc-vertex-cover-l5-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-nppc-vertex-cover-l5-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-graph-color-l2-s0/instruction.md b/tasks/construct-rg-graph-color-l2-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..cea704c34821dabff7d6fac21e2754a7a5794746
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l2-s0/instruction.md
@@ -0,0 +1,9 @@
+Colour the vertices of this graph so that no two adjacent vertices have the same colour.
+
+Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+Edges: [[0, 2], [0, 4], [0, 9], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [2, 4], [2, 5], [2, 6], [4, 5], [5, 9]]
+Possible colours: [1, 2, 3, 4]
+
+Answer format: {"coloring": [c_0, c_1, ..., c_9]} where c_i in 1..4 is the colour of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-graph-color-l2-s0/task.toml b/tasks/construct-rg-graph-color-l2-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..c3b6fe254336e05e35a8016ec8d9c37fd0f48b5a
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l2-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-graph-color-l2-s0"
+version = "0.2.0"
+description = "construct/rg_graph_color"
+authors = []
+keywords = ["rlmath", "construct", "rg_graph_color"]
+
+[metadata]
+subset = "construct"
+family = "rg_graph_color"
+problem_key = "graph_k_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "ReasoningGym/graph_color"
+source_license = "Apache-2.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-graph-color-l2-s9/instruction.md b/tasks/construct-rg-graph-color-l2-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..154ae288d7e12981eca1eeabf9ea6b559c2a22b9
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l2-s9/instruction.md
@@ -0,0 +1,9 @@
+Colour the vertices of this graph so that no two adjacent vertices have the same colour.
+
+Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+Edges: [[0, 9], [1, 3], [1, 4], [1, 5], [1, 6], [2, 4], [2, 7], [2, 8], [2, 9], [3, 4], [4, 9], [5, 8], [6, 9]]
+Possible colours: [1, 2, 3, 4]
+
+Answer format: {"coloring": [c_0, c_1, ..., c_9]} where c_i in 1..4 is the colour of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-graph-color-l2-s9/task.toml b/tasks/construct-rg-graph-color-l2-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..7b3ca996e3426855476e310cbd7ad322b1c8e2ef
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l2-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-graph-color-l2-s9"
+version = "0.2.0"
+description = "construct/rg_graph_color"
+authors = []
+keywords = ["rlmath", "construct", "rg_graph_color"]
+
+[metadata]
+subset = "construct"
+family = "rg_graph_color"
+problem_key = "graph_k_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "ReasoningGym/graph_color"
+source_license = "Apache-2.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-graph-color-l6-s1/instruction.md b/tasks/construct-rg-graph-color-l6-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..81c4589e77f0d87573a01a32d55849fcabd25a36
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-s1/instruction.md
@@ -0,0 +1,9 @@
+Colour the vertices of this graph so that no two adjacent vertices have the same colour.
+
+Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
+Edges: [[0, 3], [0, 4], [0, 11], [0, 31], [1, 18], [1, 26], [2, 16], [2, 25], [3, 7], [3, 13], [3, 14], [3, 19], [3, 37], [4, 16], [4, 31], [4, 33], [4, 38], [5, 6], [5, 9], [5, 13], [5, 29], [5, 32], [5, 35], [6, 12], [6, 13], [6, 33], [6, 36], [7, 13], [7, 31], [7, 32], [7, 35], [8, 22], [8, 23], [8, 29], [8, 30], [8, 32], [9, 17], [9, 28], [9, 31], [9, 33], [9, 35], [10, 28], [11, 14], [11, 25], [11, 28], [13, 19], [14, 18], [14, 23], [15, 20], [15, 28], [16, 27], [17, 18], [17, 22], [18, 21], [18, 31], [18, 32], [18, 37], [19, 32], [21, 25], [22, 23], [22, 25], [22, 27], [22, 36], [26, 35], [27, 28], [28, 29], [29, 31], [29, 34], [29, 35], [31, 36], [35, 37], [36, 38], [36, 39], [38, 39]]
+Possible colours: [1, 2, 3]
+
+Answer format: {"coloring": [c_0, c_1, ..., c_39]} where c_i in 1..3 is the colour of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-graph-color-l6-s1/task.toml b/tasks/construct-rg-graph-color-l6-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..814ed416f969912e665824631c810060e15e94f0
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-graph-color-l6-s1"
+version = "0.2.0"
+description = "construct/rg_graph_color"
+authors = []
+keywords = ["rlmath", "construct", "rg_graph_color"]
+
+[metadata]
+subset = "construct"
+family = "rg_graph_color"
+problem_key = "graph_k_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "ReasoningGym/graph_color"
+source_license = "Apache-2.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-graph-color-l6-s6/instruction.md b/tasks/construct-rg-graph-color-l6-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..5faf20c422e2be2c018ec7b75a8745389cd3d003
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-s6/instruction.md
@@ -0,0 +1,9 @@
+Colour the vertices of this graph so that no two adjacent vertices have the same colour.
+
+Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
+Edges: [[0, 6], [0, 7], [0, 10], [0, 15], [0, 33], [0, 34], [0, 38], [1, 11], [1, 17], [1, 31], [2, 18], [2, 27], [2, 36], [3, 15], [3, 28], [4, 9], [4, 10], [4, 14], [4, 16], [4, 21], [4, 38], [5, 6], [5, 11], [5, 13], [5, 15], [5, 16], [5, 27], [5, 28], [5, 38], [6, 29], [6, 30], [6, 32], [7, 9], [7, 22], [7, 24], [7, 27], [8, 13], [8, 15], [8, 36], [9, 12], [9, 14], [9, 18], [9, 19], [9, 20], [9, 33], [9, 35], [9, 37], [9, 39], [10, 26], [10, 30], [11, 23], [11, 25], [12, 15], [12, 22], [12, 29], [12, 33], [14, 31], [15, 37], [15, 38], [16, 25], [17, 28], [18, 25], [18, 30], [18, 34], [18, 35], [18, 38], [19, 30], [19, 36], [20, 27], [20, 28], [21, 22], [22, 23], [22, 32], [22, 35], [22, 36], [22, 37], [23, 31], [24, 27], [24, 29], [24, 38], [25, 27], [26, 27], [26, 29], [26, 31], [28, 36], [31, 36], [35, 38]]
+Possible colours: [1, 2, 3]
+
+Answer format: {"coloring": [c_0, c_1, ..., c_39]} where c_i in 1..3 is the colour of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-graph-color-l6-s6/task.toml b/tasks/construct-rg-graph-color-l6-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..12d6ec19824f3dc8455789a8fc868621eec8f81a
--- /dev/null
+++ b/tasks/construct-rg-graph-color-l6-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-graph-color-l6-s6"
+version = "0.2.0"
+description = "construct/rg_graph_color"
+authors = []
+keywords = ["rlmath", "construct", "rg_graph_color"]
+
+[metadata]
+subset = "construct"
+family = "rg_graph_color"
+problem_key = "graph_k_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "ReasoningGym/graph_color"
+source_license = "Apache-2.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l4-s3/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/environment/instance.json b/tasks/construct-rg-intermediate-integration-l4-s3/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..835240f24aece93cc8d19591d958c5df577a18c0
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "2*atan(3*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/instruction.md b/tasks/construct-rg-intermediate-integration-l4-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..17b6dbdb2b5d5a87182631b756014c831d8db875
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(x) of
+
+    f(x) = 2*atan(3*x)
+
+i.e. any F with dF/dx = f(x).
+
+Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l4-s3/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..210b662350a6398d6c1fee09ee822be04431fe08
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "2*x*atan(3*x) - log(9*x**2 + 1)/3 + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/task.toml b/tasks/construct-rg-intermediate-integration-l4-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..df1f370b2be8afe69b2d7007729447ae3013987a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-intermediate-integration-l4-s3"
+version = "0.2.0"
+description = "construct/rg_intermediate_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_intermediate_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_intermediate_integration"
+problem_key = "symbolic_antiderivative"
+domain = "analysis"
+tier = "competition"
+level = "4"
+source = "ReasoningGym/intermediate_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/tests/check.py b/tasks/construct-rg-intermediate-integration-l4-s3/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/tests/instance.json b/tasks/construct-rg-intermediate-integration-l4-s3/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..835240f24aece93cc8d19591d958c5df577a18c0
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "2*atan(3*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/tests/run.py b/tasks/construct-rg-intermediate-integration-l4-s3/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l4-s3/tests/test.sh b/tasks/construct-rg-intermediate-integration-l4-s3/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s3/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/environment/Dockerfile b/tasks/construct-rg-intermediate-integration-l4-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/environment/instance.json b/tasks/construct-rg-intermediate-integration-l4-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fc9a877c647a303bf5abaf66265402096e7ab3cd
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/environment/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/instruction.md b/tasks/construct-rg-intermediate-integration-l4-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b76b7e320c57757833214ac7f080344e77fc0a85
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(x) of
+
+    f(x) = -2*atan(2*x)
+
+i.e. any F with dF/dx = f(x).
+
+Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/solution/solve.sh b/tasks/construct-rg-intermediate-integration-l4-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..72db3bcb17e891799fd7f3579ba3b3e164e0de2e
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"antiderivative": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C"}
+RLMATH_EOF
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/task.toml b/tasks/construct-rg-intermediate-integration-l4-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..df37d4fa22b1113f109091216981641c453cdd07
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-intermediate-integration-l4-s4"
+version = "0.2.0"
+description = "construct/rg_intermediate_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_intermediate_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_intermediate_integration"
+problem_key = "symbolic_antiderivative"
+domain = "analysis"
+tier = "competition"
+level = "4"
+source = "ReasoningGym/intermediate_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/tests/check.py b/tasks/construct-rg-intermediate-integration-l4-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..a9e364a8ede6c8215a16a04ee6b0d3529adc647d
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/tests/check.py
@@ -0,0 +1,158 @@
+"""Antiderivative check (Reasoning Gym simple_integration / intermediate_integration, Apache-2.0).
+
+The answer string is parsed with a whitelist AST walker (no eval), differentiated with SymPy and compared
+with the integrand numerically (30-digit evaluation) at fixed points inside the integrand's real domain.
+Any additive constant (e.g. "+ C") is allowed.
+
+Upstream notes: upstream scores with sympy.parse_expr, which calls eval() on the model's string (arbitrary
+code execution), and it accepts an unevaluated "Integral(f, x)" since its derivative is f. Both are
+rejected here: only arithmetic, whitelisted elementary functions, the variable, C, E and pi are allowed."""
+import ast
+import math
+import signal
+
+import sympy
+
+from run import Invalid
+
+MAX_LEN = 3000
+MAX_NODES = 600
+MAX_POW_NEST = 4  # nested powers with a variable exponent (x**x**x**...) blow up differentiation
+TIME_LIMIT = 40  # seconds; a slower answer is rejected
+FUNCS = {"sin": sympy.sin, "cos": sympy.cos, "tan": sympy.tan, "cot": sympy.cot, "sec": sympy.sec,
+         "csc": sympy.csc, "asin": sympy.asin, "acos": sympy.acos, "atan": sympy.atan, "acot": sympy.acot,
+         "arcsin": sympy.asin, "arccos": sympy.acos, "arctan": sympy.atan, "sinh": sympy.sinh,
+         "cosh": sympy.cosh, "tanh": sympy.tanh, "asinh": sympy.asinh, "acosh": sympy.acosh,
+         "atanh": sympy.atanh, "exp": sympy.exp, "log": sympy.log, "ln": sympy.log, "sqrt": sympy.sqrt,
+         "Abs": sympy.Abs, "abs": sympy.Abs}
+POINTS = [0.3137, 0.5521, 0.8093, 1.1171, 1.4519, 1.9033, 2.3471, 2.8123, 3.3319, 3.9107, 4.6231,
+          -0.3547, -0.6529, -0.9511, -1.3027, -1.7519, -2.2013, -2.7131, -3.1397, -3.8203, -4.4111,
+          0.1231, -0.1523, 0.2129, -0.2617, 0.0517, -0.0719, 5.4127, -5.3311, 6.3019, -6.2203, 7.2213,
+          -7.1117, 8.9021, -9.3107, 10.7129, -10.6337, 12.9011, -12.8231, 15.3113, -15.2719]
+MIN_POINTS = 5
+
+
+def parse(s, var):
+    if not isinstance(s, str) or not s.strip():
+        raise Invalid("antiderivative must be a non-empty string")
+    if len(s) > MAX_LEN:
+        raise Invalid("expression too long")
+    s = s.strip()
+    try:
+        tree = ast.parse(s, mode="eval")
+    except SyntaxError:
+        raise Invalid("expression does not parse (use ** for powers and * for products)")
+    if sum(1 for _ in ast.walk(tree)) > MAX_NODES:
+        raise Invalid("expression too large")
+
+    def pow_nest(nd):
+        kids = [pow_nest(c) for c in ast.iter_child_nodes(nd)]
+        own = isinstance(nd, ast.BinOp) and isinstance(nd.op, ast.Pow) and any(
+            isinstance(c, ast.Name) and c.id == var for c in ast.walk(nd.right))
+        return max(kids, default=0) + (1 if own else 0)
+    if pow_nest(tree) > MAX_POW_NEST:
+        raise Invalid("too many nested powers with a variable exponent")
+    x = sympy.Symbol(var, real=True)
+    names = {var: x, "C": sympy.Symbol("C"), "E": sympy.E, "pi": sympy.pi}
+
+    def conv(nd):
+        if isinstance(nd, ast.Expression):
+            return conv(nd.body)
+        if isinstance(nd, ast.Constant):
+            v = nd.value
+            if isinstance(v, bool) or not isinstance(v, (int, float)):
+                raise Invalid(f"constant {v!r} not allowed")
+            if isinstance(v, int):
+                if abs(v) > 10 ** 18:
+                    raise Invalid("integer constant too large")
+                return sympy.Integer(v)
+            if not math.isfinite(v):
+                raise Invalid("non-finite constant")
+            return sympy.Float(v, 30)
+        if isinstance(nd, ast.Name):
+            if nd.id not in names:
+                raise Invalid(f"unknown name {nd.id!r} (the variable is {var})")
+            return names[nd.id]
+        if isinstance(nd, ast.UnaryOp) and isinstance(nd.op, (ast.USub, ast.UAdd)):
+            a = conv(nd.operand)
+            return -a if isinstance(nd.op, ast.USub) else a
+        if isinstance(nd, ast.BinOp):
+            a, b = conv(nd.left), conv(nd.right)
+            if isinstance(nd.op, ast.Add):
+                return a + b
+            if isinstance(nd.op, ast.Sub):
+                return a - b
+            if isinstance(nd.op, ast.Mult):
+                return a * b
+            if isinstance(nd.op, ast.Div):
+                if b == 0:
+                    raise Invalid("division by zero")
+                return a / b
+            if isinstance(nd.op, ast.Pow):
+                if not b.free_symbols:
+                    bv = complex(b.evalf(20))
+                    if bv.imag != 0 or abs(bv.real) > 100:
+                        raise Invalid("exponent too large")
+                    if not a.free_symbols and abs(complex(a.evalf(20))) > 1e6:
+                        raise Invalid("numeric power too large")
+                return a ** b
+            raise Invalid("only + - * / ** are allowed (use ** for powers)")
+        if isinstance(nd, ast.Call):
+            if not isinstance(nd.func, ast.Name) or nd.func.id not in FUNCS:
+                raise Invalid(f"function {ast.unparse(nd.func)!r} not allowed")
+            if nd.keywords or len(nd.args) != 1:
+                raise Invalid(f"{nd.func.id} takes exactly one argument")
+            return FUNCS[nd.func.id](conv(nd.args[0]))
+        raise Invalid(f"syntax element {type(nd).__name__} not allowed")
+
+    return conv(tree), x
+
+
+def value(expr, x, p):
+    v = expr.evalf(30, subs={x: sympy.Float(p, 30)})
+    try:
+        z = complex(v)
+    except (TypeError, ValueError):
+        return None
+    if not (math.isfinite(z.real) and math.isfinite(z.imag)):
+        return None
+    return z
+
+
+def _timeout(signum, frame):
+    raise Invalid(f"answer took more than {TIME_LIMIT} s to check")
+
+
+def check(inst, ans):
+    if hasattr(signal, "SIGALRM"):
+        old = signal.signal(signal.SIGALRM, _timeout)
+        signal.alarm(TIME_LIMIT)
+        try:
+            return _check(inst, ans)
+        finally:
+            signal.alarm(0)
+            signal.signal(signal.SIGALRM, old)
+    return _check(inst, ans)
+
+
+def _check(inst, ans):
+    var = inst["variable"]
+    F, x = parse(ans.get("antiderivative"), var)
+    f, x2 = parse(inst["integrand"], var)
+    if not F.has(x):
+        raise Invalid("antiderivative does not depend on the variable")
+    dF = sympy.diff(F, x)
+    used = 0
+    for p in POINTS:
+        fv = value(f, x2, p)
+        if fv is None or abs(fv.imag) > 1e-20 * (1 + abs(fv.real)):
+            continue  # outside the integrand's real domain
+        gv = value(dF, x, p)
+        if gv is None:
+            raise Invalid(f"derivative of the answer cannot be evaluated at {var} = {p}")
+        if abs(gv - fv) > 1e-9 * max(1.0, abs(fv)):
+            raise Invalid(f"derivative of the answer differs from the integrand at {var} = {p}")
+        used += 1
+    if used < MIN_POINTS:
+        raise Invalid("too few evaluation points in the integrand's domain")
+    return None, {"points": used}
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/tests/instance.json b/tasks/construct-rg-intermediate-integration-l4-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fc9a877c647a303bf5abaf66265402096e7ab3cd
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/tests/instance.json
@@ -0,0 +1 @@
+{"variable": "x", "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/tests/run.py b/tasks/construct-rg-intermediate-integration-l4-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rg-intermediate-integration-l4-s4/tests/test.sh b/tasks/construct-rg-intermediate-integration-l4-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rg-intermediate-integration-l4-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rg-simple-integration-l2-s6/instruction.md b/tasks/construct-rg-simple-integration-l2-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..fb43c84ef367d9979bbc24db32aa486de87057d4
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s6/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(x) of
+
+    f(x) = 20*x**3/7 + 21*x**2 - 14*x
+
+i.e. any F with dF/dx = f(x).
+
+Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-simple-integration-l2-s6/task.toml b/tasks/construct-rg-simple-integration-l2-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..175515a082ee9008167e65d0b2a24eebb53b2c21
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-simple-integration-l2-s6"
+version = "0.2.0"
+description = "construct/rg_simple_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_simple_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_simple_integration"
+problem_key = "symbolic_antiderivative_polynomial"
+domain = "analysis"
+tier = "competition"
+level = "2"
+source = "ReasoningGym/simple_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-simple-integration-l2-s8/instruction.md b/tasks/construct-rg-simple-integration-l2-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..7a8b480f7a36c54fc14a4654d5212d3ab0d8a402
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s8/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(X) of
+
+    f(X) = -81*X**4/2 + 4*X
+
+i.e. any F with dF/dX = f(X).
+
+Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-simple-integration-l2-s8/task.toml b/tasks/construct-rg-simple-integration-l2-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..fc40b562c033c3dfbeaab5b1fbbd0509a4ccf197
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l2-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-simple-integration-l2-s8"
+version = "0.2.0"
+description = "construct/rg_simple_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_simple_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_simple_integration"
+problem_key = "symbolic_antiderivative_polynomial"
+domain = "analysis"
+tier = "competition"
+level = "2"
+source = "ReasoningGym/simple_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-simple-integration-l6-s0/instruction.md b/tasks/construct-rg-simple-integration-l6-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..cf8d3f6638078aa18c1f2038cddf6be3fe672a40
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s0/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(x) of
+
+    f(x) = -45*x**8/7 - 12*x**3/7 + 7/x**2 + 4/x**3 + 20/(3*x**6)
+
+i.e. any F with dF/dx = f(x).
+
+Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-simple-integration-l6-s0/task.toml b/tasks/construct-rg-simple-integration-l6-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..1620f9cc2c2f7c64ef9fd7a08454ae4afa7ade08
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-simple-integration-l6-s0"
+version = "0.2.0"
+description = "construct/rg_simple_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_simple_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_simple_integration"
+problem_key = "symbolic_antiderivative_polynomial"
+domain = "analysis"
+tier = "competition"
+level = "6"
+source = "ReasoningGym/simple_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-simple-integration-l6-s7/instruction.md b/tasks/construct-rg-simple-integration-l6-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..628a043a3cb1218031092759927d6e3f470aed1b
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s7/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(X) of
+
+    f(X) = 18*X**5 + 5*X**2 - 2 - 10/X**2 + 4/X**9 - 27/X**10 + 25/(4*X**11)
+
+i.e. any F with dF/dX = f(X).
+
+Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-simple-integration-l6-s7/task.toml b/tasks/construct-rg-simple-integration-l6-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..e3f4f34170b33528bd37ec56becb6879bc42cc70
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-simple-integration-l6-s7"
+version = "0.2.0"
+description = "construct/rg_simple_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_simple_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_simple_integration"
+problem_key = "symbolic_antiderivative_polynomial"
+domain = "analysis"
+tier = "competition"
+level = "6"
+source = "ReasoningGym/simple_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rg-simple-integration-l6-s9/instruction.md b/tasks/construct-rg-simple-integration-l6-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a734ae8598a06e6b414676a24019556ff728508b
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s9/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(x) of
+
+    f(x) = 108*x**11 + 60*x**9 - 27*x**8/10 + 8*x**7 + 28*x**6/5 + 30/x**6 + 81/(7*x**10)
+
+i.e. any F with dF/dx = f(x).
+
+Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rg-simple-integration-l6-s9/task.toml b/tasks/construct-rg-simple-integration-l6-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ca9fb95366eaae3ce4b55572809d1bed3f186417
--- /dev/null
+++ b/tasks/construct-rg-simple-integration-l6-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-simple-integration-l6-s9"
+version = "0.2.0"
+description = "construct/rg_simple_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_simple_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_simple_integration"
+problem_key = "symbolic_antiderivative_polynomial"
+domain = "analysis"
+tier = "competition"
+level = "6"
+source = "ReasoningGym/simple_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-antiderivative-l3-s6/instruction.md b/tasks/construct-rlve-antiderivative-l3-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a64178778de32f447c3e67116f1830735b8b779b
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s6/instruction.md
@@ -0,0 +1,11 @@
+Find an antiderivative F(x) of
+
+f(x) = -sin(x - 3)
+
+(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
+
+Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the functions sin cos tan asin acos atan sinh cosh tanh exp log sqrt and constants E, pi (no decimals, no other names; always write * explicitly).
+
+Answer format: {"F": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-antiderivative-l3-s6/task.toml b/tasks/construct-rlve-antiderivative-l3-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5447271467fcc0b06d2f7a53b319753e079d4c68
--- /dev/null
+++ b/tasks/construct-rlve-antiderivative-l3-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-antiderivative-l3-s6"
+version = "0.2.0"
+description = "construct/rlve_antiderivative"
+authors = []
+keywords = ["rlmath", "construct", "rlve_antiderivative"]
+
+[metadata]
+subset = "construct"
+family = "rlve_antiderivative"
+problem_key = "symbolic_antiderivative"
+domain = "analysis"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/integral"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-bezout-identity-l2-s5/instruction.md b/tasks/construct-rlve-bezout-identity-l2-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a40e00d27e1cf23b97146de6d454ad24f7cd2d05
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l2-s5/instruction.md
@@ -0,0 +1,10 @@
+You are given 4 nonzero integers A = [-25, -120, -65, -100] (A[0], ..., A[3]).
+
+Find integers X[0], ..., X[3] (any sign, any size) such that
+S = A[0]*X[0] + ... + A[3]*X[3] = 5.
+
+(5 is the smallest positive value S can take.)
+
+Answer format: {"X": [X_0, ..., X_3]}  (a JSON list of 4 integers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-bezout-identity-l2-s5/task.toml b/tasks/construct-rlve-bezout-identity-l2-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..9eacac38effe4674310690546a8dd97079cce07a
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l2-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-bezout-identity-l2-s5"
+version = "0.2.0"
+description = "construct/rlve_bezout_identity"
+authors = []
+keywords = ["rlmath", "construct", "rlve_bezout_identity"]
+
+[metadata]
+subset = "construct"
+family = "rlve_bezout_identity"
+problem_key = "bezout_coefficients"
+domain = "number_theory"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/bezout_identity"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-bezout-identity-l6-s3/instruction.md b/tasks/construct-rlve-bezout-identity-l6-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..8d55097afd7c5021af7289d2912a79ef63f1b4d3
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l6-s3/instruction.md
@@ -0,0 +1,10 @@
+You are given 12 nonzero integers A = [25112, 18022, -25110, 21082, 11580, -25860, -13642, -924, 10358, 11718, 17014, 21086] (A[0], ..., A[11]).
+
+Find integers X[0], ..., X[11] (any sign, any size) such that
+S = A[0]*X[0] + ... + A[11]*X[11] = 2.
+
+(2 is the smallest positive value S can take.)
+
+Answer format: {"X": [X_0, ..., X_11]}  (a JSON list of 12 integers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-bezout-identity-l6-s3/task.toml b/tasks/construct-rlve-bezout-identity-l6-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..dc039a61b5b9fb16bc2821617313e48fd79ac364
--- /dev/null
+++ b/tasks/construct-rlve-bezout-identity-l6-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-bezout-identity-l6-s3"
+version = "0.2.0"
+description = "construct/rlve_bezout_identity"
+authors = []
+keywords = ["rlmath", "construct", "rlve_bezout_identity"]
+
+[metadata]
+subset = "construct"
+family = "rlve_bezout_identity"
+problem_key = "bezout_coefficients"
+domain = "number_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/bezout_identity"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0046d16e224a1cd6b7b51f9dc90d89e3047f681
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 248959893, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/instruction.md b/tasks/construct-rlve-construct-hack-interval-l4-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..215fdde708699f3aee94b0944ae3158923bdb89c
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/instruction.md
@@ -0,0 +1,6 @@
+Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 2489598930 (that is, 10 * 248959893) such that
+f(L) + f(L+1) + ... + f(R) is divisible by 248959893.
+
+Answer format: {"L": <integer>, "R": <integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c9e7887c0550bce284db3d7e3be7a5a7ceb8f164
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"L": 134398395, "R": 234398394}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/task.toml b/tasks/construct-rlve-construct-hack-interval-l4-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..bed1bc5932c9cf3958ca1af50249a5b42de31d59
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-construct-hack-interval-l4-s0"
+version = "0.2.0"
+description = "construct/rlve_construct_hack_interval"
+authors = []
+keywords = ["rlmath", "construct", "rlve_construct_hack_interval"]
+
+[metadata]
+subset = "construct"
+family = "rlve_construct_hack_interval"
+problem_key = "cf468c_hack_interval"
+domain = "number_theory"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/construct_hack_interval"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/check.py
@@ -0,0 +1,30 @@
+from run import Invalid, as_int
+
+
+def digit_sum_prefix(n):
+    """sum of digit sums of all integers in [0, n] (exact, digit DP)."""
+    if n <= 0:
+        return 0
+    s = str(n)
+    total, prefix_sum = 0, 0
+    k = len(s)
+    for i, ch in enumerate(s):
+        d = int(ch)
+        rest = k - i - 1
+        p = 10 ** rest
+        # numbers with this digit < d, free suffix of `rest` digits
+        total += d * prefix_sum * p + (d * (d - 1) // 2) * p + d * (45 * rest * p // 10 if rest else 0)
+        prefix_sum += d
+    return total + prefix_sum  # include n itself
+
+
+def check(inst, ans):
+    mod = inst["mod"]
+    L = as_int(ans.get("L"), "L", lo=1)
+    R = as_int(ans.get("R"), "R", lo=1, hi=10 * mod)
+    if L > R:
+        raise Invalid("need L <= R")
+    total = digit_sum_prefix(R) - digit_sum_prefix(L - 1)
+    if total % mod:
+        raise Invalid(f"sum of digit sums over [L, R] is {total}, not divisible by {mod}")
+    return None, {}
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0046d16e224a1cd6b7b51f9dc90d89e3047f681
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 248959893, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4743e9d30da414db008aa62409eacd93e8b65130
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 6110377305, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/instruction.md b/tasks/construct-rlve-construct-hack-interval-l4-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..f4414c477622baa4d45c9cd2f3156d9884bcbead
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/instruction.md
@@ -0,0 +1,6 @@
+Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 61103773050 (that is, 10 * 6110377305) such that
+f(L) + f(L+1) + ... + f(R) is divisible by 6110377305.
+
+Answer format: {"L": <integer>, "R": <integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c2fac9231015e20c7631892fa971c7c119c9ec96
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"L": 2272641135, "R": 3272641134}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/task.toml b/tasks/construct-rlve-construct-hack-interval-l4-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..cb9c67d51d266f04cf5708cd15a10e6f465e0f8e
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-construct-hack-interval-l4-s7"
+version = "0.2.0"
+description = "construct/rlve_construct_hack_interval"
+authors = []
+keywords = ["rlmath", "construct", "rlve_construct_hack_interval"]
+
+[metadata]
+subset = "construct"
+family = "rlve_construct_hack_interval"
+problem_key = "cf468c_hack_interval"
+domain = "number_theory"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/construct_hack_interval"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/check.py
@@ -0,0 +1,30 @@
+from run import Invalid, as_int
+
+
+def digit_sum_prefix(n):
+    """sum of digit sums of all integers in [0, n] (exact, digit DP)."""
+    if n <= 0:
+        return 0
+    s = str(n)
+    total, prefix_sum = 0, 0
+    k = len(s)
+    for i, ch in enumerate(s):
+        d = int(ch)
+        rest = k - i - 1
+        p = 10 ** rest
+        # numbers with this digit < d, free suffix of `rest` digits
+        total += d * prefix_sum * p + (d * (d - 1) // 2) * p + d * (45 * rest * p // 10 if rest else 0)
+        prefix_sum += d
+    return total + prefix_sum  # include n itself
+
+
+def check(inst, ans):
+    mod = inst["mod"]
+    L = as_int(ans.get("L"), "L", lo=1)
+    R = as_int(ans.get("R"), "R", lo=1, hi=10 * mod)
+    if L > R:
+        raise Invalid("need L <= R")
+    total = digit_sum_prefix(R) - digit_sum_prefix(L - 1)
+    if total % mod:
+        raise Invalid(f"sum of digit sums over [L, R] is {total}, not divisible by {mod}")
+    return None, {}
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4743e9d30da414db008aa62409eacd93e8b65130
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 6110377305, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/environment/Dockerfile b/tasks/construct-rlve-construct-hack-interval-l4-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/environment/instance.json b/tasks/construct-rlve-construct-hack-interval-l4-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aea4a400d7c9160e912e7c2301699370524be33b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/environment/instance.json
@@ -0,0 +1 @@
+{"mod": 5085864627, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/instruction.md b/tasks/construct-rlve-construct-hack-interval-l4-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..31761bed5f5da210be4691d250903851edbb0d49
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/instruction.md
@@ -0,0 +1,6 @@
+Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 50858646270 (that is, 10 * 5085864627) such that
+f(L) + f(L+1) + ... + f(R) is divisible by 5085864627.
+
+Answer format: {"L": <integer>, "R": <integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/solution/solve.sh b/tasks/construct-rlve-construct-hack-interval-l4-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..bc09e1a5ddaa408ce459d911b43d95e32d9d5538
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"L": 186917016, "R": 1186917015}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/task.toml b/tasks/construct-rlve-construct-hack-interval-l4-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..a8a47b36b506ba7f4b7f1de0b35a5dc3ad571c0c
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-construct-hack-interval-l4-s9"
+version = "0.2.0"
+description = "construct/rlve_construct_hack_interval"
+authors = []
+keywords = ["rlmath", "construct", "rlve_construct_hack_interval"]
+
+[metadata]
+subset = "construct"
+family = "rlve_construct_hack_interval"
+problem_key = "cf468c_hack_interval"
+domain = "number_theory"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/construct_hack_interval"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/check.py b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..34b46e9758e3a50ed16c9c2a29cfc0abe663926b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/check.py
@@ -0,0 +1,30 @@
+from run import Invalid, as_int
+
+
+def digit_sum_prefix(n):
+    """sum of digit sums of all integers in [0, n] (exact, digit DP)."""
+    if n <= 0:
+        return 0
+    s = str(n)
+    total, prefix_sum = 0, 0
+    k = len(s)
+    for i, ch in enumerate(s):
+        d = int(ch)
+        rest = k - i - 1
+        p = 10 ** rest
+        # numbers with this digit < d, free suffix of `rest` digits
+        total += d * prefix_sum * p + (d * (d - 1) // 2) * p + d * (45 * rest * p // 10 if rest else 0)
+        prefix_sum += d
+    return total + prefix_sum  # include n itself
+
+
+def check(inst, ans):
+    mod = inst["mod"]
+    L = as_int(ans.get("L"), "L", lo=1)
+    R = as_int(ans.get("R"), "R", lo=1, hi=10 * mod)
+    if L > R:
+        raise Invalid("need L <= R")
+    total = digit_sum_prefix(R) - digit_sum_prefix(L - 1)
+    if total % mod:
+        raise Invalid(f"sum of digit sums over [L, R] is {total}, not divisible by {mod}")
+    return None, {}
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/instance.json b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..aea4a400d7c9160e912e7c2301699370524be33b
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/instance.json
@@ -0,0 +1 @@
+{"mod": 5085864627, "family": "rlve_construct_hack_interval", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/run.py b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/test.sh b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-construct-hack-interval-l4-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-crt-l1-s0/instruction.md b/tasks/construct-rlve-crt-l1-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..6c013a32d57a4142a3a3670be039c6b85c0347e6
--- /dev/null
+++ b/tasks/construct-rlve-crt-l1-s0/instruction.md
@@ -0,0 +1,7 @@
+Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
+x ≡ 3 (mod 6)
+x ≡ 0 (mod 5)
+
+Answer format: {"x": <non-negative integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-crt-l1-s0/task.toml b/tasks/construct-rlve-crt-l1-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..17ee50277a24b1ef681ddc6814e00ae83286653c
--- /dev/null
+++ b/tasks/construct-rlve-crt-l1-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-crt-l1-s0"
+version = "0.2.0"
+description = "construct/rlve_crt"
+authors = []
+keywords = ["rlmath", "construct", "rlve_crt"]
+
+[metadata]
+subset = "construct"
+family = "rlve_crt"
+problem_key = "generalized_crt"
+domain = "number_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/crt"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-crt-l1-s7/instruction.md b/tasks/construct-rlve-crt-l1-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..e4068f6684cb7c5fdca2e23cd3d853c998196134
--- /dev/null
+++ b/tasks/construct-rlve-crt-l1-s7/instruction.md
@@ -0,0 +1,7 @@
+Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
+x ≡ 2 (mod 4)
+x ≡ 2 (mod 3)
+
+Answer format: {"x": <non-negative integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-crt-l1-s7/task.toml b/tasks/construct-rlve-crt-l1-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..79ac66ef0bca348820a722ac1ab6a7c7fe20e8e3
--- /dev/null
+++ b/tasks/construct-rlve-crt-l1-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-crt-l1-s7"
+version = "0.2.0"
+description = "construct/rlve_crt"
+authors = []
+keywords = ["rlmath", "construct", "rlve_crt"]
+
+[metadata]
+subset = "construct"
+family = "rlve_crt"
+problem_key = "generalized_crt"
+domain = "number_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/crt"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-crt-l5-s1/instruction.md b/tasks/construct-rlve-crt-l5-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..368c4a2bb123a8d37bc3d5855a2bf70e6f84c978
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s1/instruction.md
@@ -0,0 +1,11 @@
+Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
+x ≡ 1015714744 (mod 1689557742)
+x ≡ 274208535 (mod 5810179435)
+x ≡ 2925635784 (mod 3158752186)
+x ≡ 67495816 (mod 231418929)
+x ≡ 518152197 (mod 795176539)
+x ≡ 329203893 (mod 5755184077)
+
+Answer format: {"x": <non-negative integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-crt-l5-s1/task.toml b/tasks/construct-rlve-crt-l5-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..9ee27670c4a602bb2bf47d841b86fd5c6b73e06f
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-crt-l5-s1"
+version = "0.2.0"
+description = "construct/rlve_crt"
+authors = []
+keywords = ["rlmath", "construct", "rlve_crt"]
+
+[metadata]
+subset = "construct"
+family = "rlve_crt"
+problem_key = "generalized_crt"
+domain = "number_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/crt"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-crt-l5-s8/instruction.md b/tasks/construct-rlve-crt-l5-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..475e0ed84d6da66dba79b6c918a545f8b4e5329a
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s8/instruction.md
@@ -0,0 +1,11 @@
+Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
+x ≡ 232122125 (mod 1560168774)
+x ≡ 142292393 (mod 1605083640)
+x ≡ 451836503 (mod 580124634)
+x ≡ 1081095101 (mod 2271364572)
+x ≡ 190662348 (mod 632359465)
+x ≡ 718556341 (mod 1316951666)
+
+Answer format: {"x": <non-negative integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-crt-l5-s8/task.toml b/tasks/construct-rlve-crt-l5-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5467454fcf6f625871e48603a9c4eb82deb4f32c
--- /dev/null
+++ b/tasks/construct-rlve-crt-l5-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-crt-l5-s8"
+version = "0.2.0"
+description = "construct/rlve_crt"
+authors = []
+keywords = ["rlmath", "construct", "rlve_crt"]
+
+[metadata]
+subset = "construct"
+family = "rlve_crt"
+problem_key = "generalized_crt"
+domain = "number_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/crt"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s6/instruction.md b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3a119a31037482d840750a75530523213757f751
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s6/instruction.md
@@ -0,0 +1,7 @@
+You are given an array A of 14 distinct integers: A = [15, 11, 25, 4, 0, 10, 17, 16, 19, 3, 24, 9, 21, 22] (positions 1..14).
+
+Output an array B that is a permutation of A such that for every non-empty proper subset S of positions (S a subset of {1, ..., 14}, 0 < |S| < 14) the sums of A and of B over the positions in S are different.
+
+Answer format: {"B": [B_1, ..., B_14]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s6/task.toml b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5995d7b232ca488743367e3873df86f384f75a3c
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-distinct-subset-sum-permutation-l4-s6"
+version = "0.2.0"
+description = "construct/rlve_distinct_subset_sum_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_distinct_subset_sum_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_distinct_subset_sum_permutation"
+problem_key = "cf892d_gluttony"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/distinct_array_permutation"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s8/instruction.md b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..88d032d578e22989dc0704778e541683abe0c663
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s8/instruction.md
@@ -0,0 +1,7 @@
+You are given an array A of 14 distinct integers: A = [0, 24, 6, 26, 21, 7, 2, 16, 27, 18, 4, 22, 13, 25] (positions 1..14).
+
+Output an array B that is a permutation of A such that for every non-empty proper subset S of positions (S a subset of {1, ..., 14}, 0 < |S| < 14) the sums of A and of B over the positions in S are different.
+
+Answer format: {"B": [B_1, ..., B_14]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s8/task.toml b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..11cdee237b5ff47826803051ffdb9fa6be3bbeee
--- /dev/null
+++ b/tasks/construct-rlve-distinct-subset-sum-permutation-l4-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-distinct-subset-sum-permutation-l4-s8"
+version = "0.2.0"
+description = "construct/rlve_distinct_subset_sum_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_distinct_subset_sum_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_distinct_subset_sum_permutation"
+problem_key = "cf892d_gluttony"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/distinct_array_permutation"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s7/instruction.md b/tasks/construct-rlve-even-degree-partition-l1-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..ed3c18bf0e085683bdcda21e5235df8a46f7d8d1
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s7/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 5 vertices labelled 0..4 and edge list
+[[0, 2], [0, 3], [0, 4], [2, 3]]
+
+Assign every vertex to group 1 or group 2 so that, for every vertex v, the number of neighbours of v lying in the same group as v is even (zero counts as even). One of the groups may be empty.
+
+Answer format: {"groups": [g_0, ..., g_4]}  with each g_i in {1, 2}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s7/task.toml b/tasks/construct-rlve-even-degree-partition-l1-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..bd4d77e7f33b30cbfad928e1e547d44d2666c8e4
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-even-degree-partition-l1-s7"
+version = "0.2.0"
+description = "construct/rlve_even_degree_partition"
+authors = []
+keywords = ["rlmath", "construct", "rlve_even_degree_partition"]
+
+[metadata]
+subset = "construct"
+family = "rlve_even_degree_partition"
+problem_key = "gallai_even_partition"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/even_degree_graph_partitioning"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s9/instruction.md b/tasks/construct-rlve-even-degree-partition-l1-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..11eb5c0d80ed94b29ee05e0735f4e27400dac96d
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s9/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 5 vertices labelled 0..4 and edge list
+[[0, 2], [0, 4], [1, 3], [1, 4], [2, 3]]
+
+Assign every vertex to group 1 or group 2 so that, for every vertex v, the number of neighbours of v lying in the same group as v is even (zero counts as even). One of the groups may be empty.
+
+Answer format: {"groups": [g_0, ..., g_4]}  with each g_i in {1, 2}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-even-degree-partition-l1-s9/task.toml b/tasks/construct-rlve-even-degree-partition-l1-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..b737120856ba0dbd52bb4abcd17e05e88c87151d
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l1-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-even-degree-partition-l1-s9"
+version = "0.2.0"
+description = "construct/rlve_even_degree_partition"
+authors = []
+keywords = ["rlmath", "construct", "rlve_even_degree_partition"]
+
+[metadata]
+subset = "construct"
+family = "rlve_even_degree_partition"
+problem_key = "gallai_even_partition"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/even_degree_graph_partitioning"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s1/instruction.md b/tasks/construct-rlve-even-degree-partition-l5-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4cae29ba1dbd07ab065a4424d3c613c6049a0750
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s1/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 28 vertices labelled 0..27 and edge list
+[[0, 2], [0, 5], [0, 23], [1, 3], [1, 4], [1, 12], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 24], [1, 27], [2, 11], [2, 20], [3, 11], [3, 17], [3, 19], [3, 21], [3, 22], [3, 27], [4, 21], [4, 22], [4, 27], [5, 6], [5, 7], [5, 9], [5, 10], [5, 13], [5, 14], [5, 15], [5, 17], [5, 23], [5, 25], [5, 26], [6, 9], [6, 15], [6, 17], [6, 25], [6, 26], [7, 9], [7, 13], [7, 15], [7, 17], [7, 23], [8, 11], [8, 14], [8, 19], [9, 10], [9, 13], [9, 14], [9, 15], [9, 17], [9, 23], [9, 25], [9, 27], [10, 15], [10, 23], [10, 25], [10, 26], [11, 12], [11, 18], [11, 19], [11, 20], [11, 21], [11, 22], [11, 23], [11, 27], [12, 18], [12, 19], [12, 21], [12, 22], [12, 24], [12, 25], [12, 27], [13, 15], [13, 17], [13, 23], [14, 15], [14, 17], [14, 21], [15, 17], [15, 23], [15, 25], [17, 25], [18, 20], [18, 21], [18, 22], [18, 24], [18, 27], [19, 20], [19, 21], [19, 22], [19, 24], [19, 27], [20, 21], [21, 22], [21, 27], [22, 24], [22, 27], [23, 26], [24, 25], [24, 27]]
+
+Assign every vertex to group 1 or group 2 so that, for every vertex v, the number of neighbours of v lying in the same group as v is even (zero counts as even). One of the groups may be empty.
+
+Answer format: {"groups": [g_0, ..., g_27]}  with each g_i in {1, 2}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s1/task.toml b/tasks/construct-rlve-even-degree-partition-l5-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..22c528b8819e5740d792ffc5009720f42914c290
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-even-degree-partition-l5-s1"
+version = "0.2.0"
+description = "construct/rlve_even_degree_partition"
+authors = []
+keywords = ["rlmath", "construct", "rlve_even_degree_partition"]
+
+[metadata]
+subset = "construct"
+family = "rlve_even_degree_partition"
+problem_key = "gallai_even_partition"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/even_degree_graph_partitioning"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s6/instruction.md b/tasks/construct-rlve-even-degree-partition-l5-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..75c378213a789489387c2353e449dc892dcfb178
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s6/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 28 vertices labelled 0..27 and edge list
+[[0, 5], [0, 8], [0, 11], [0, 14], [0, 15], [0, 16], [0, 18], [0, 20], [0, 21], [0, 22], [0, 25], [1, 2], [1, 3], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 11], [1, 14], [1, 16], [1, 18], [1, 19], [1, 21], [1, 22], [1, 25], [2, 5], [2, 7], [2, 8], [2, 11], [2, 12], [2, 14], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [2, 22], [2, 24], [2, 25], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 11], [3, 14], [3, 16], [3, 19], [3, 20], [3, 22], [3, 25], [4, 5], [4, 7], [4, 9], [4, 11], [4, 13], [4, 14], [4, 16], [4, 19], [4, 20], [4, 21], [4, 25], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 15], [5, 16], [5, 18], [5, 20], [5, 21], [5, 22], [5, 23], [5, 24], [5, 26], [5, 27], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 15], [6, 17], [6, 18], [6, 19], [6, 20], [6, 21], [6, 24], [6, 25], [6, 26], [6, 27], [7, 9], [7, 10], [7, 11], [7, 13], [7, 14], [7, 16], [7, 17], [7, 19], [7, 20], [7, 24], [7, 25], [8, 11], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 22], [8, 24], [8, 26], [8, 27], [9, 10], [9, 14], [9, 15], [9, 20], [9, 23], [9, 24], [9, 25], [9, 26], [10, 11], [10, 14], [10, 17], [10, 19], [10, 20], [10, 21], [10, 25], [10, 27], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 19], [11, 20], [11, 22], [11, 23], [11, 24], [11, 26], [11, 27], [12, 21], [12, 22], [13, 14], [13, 15], [13, 16], [13, 17], [13, 19], [13, 20], [13, 21], [13, 22], [13, 24], [13, 27], [14, 15], [14, 23], [14, 24], [14, 27], [15, 16], [15, 19], [15, 20], [15, 21], [15, 22], [15, 25], [16, 18], [16, 19], [16, 20], [16, 21], [16, 23], [16, 24], [16, 25], [16, 26], [16, 27], [17, 18], [17, 19], [17, 20], [17, 21], [17, 25], [17, 26], [18, 19], [18, 20], [18, 21], [18, 24], [18, 25], [18, 26], [18, 27], [19, 20], [19, 22], [19, 23], [19, 24], [19, 25], [19, 26], [19, 27], [20, 21], [20, 23], [20, 24], [20, 26], [21, 22], [21, 23], [21, 24], [21, 25], [21, 27], [22, 23], [22, 26], [22, 27], [24, 25], [25, 26], [25, 27]]
+
+Assign every vertex to group 1 or group 2 so that, for every vertex v, the number of neighbours of v lying in the same group as v is even (zero counts as even). One of the groups may be empty.
+
+Answer format: {"groups": [g_0, ..., g_27]}  with each g_i in {1, 2}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s6/task.toml b/tasks/construct-rlve-even-degree-partition-l5-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..50e798a0a70363d29cb9c4564bb763a98200c29b
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-even-degree-partition-l5-s6"
+version = "0.2.0"
+description = "construct/rlve_even_degree_partition"
+authors = []
+keywords = ["rlmath", "construct", "rlve_even_degree_partition"]
+
+[metadata]
+subset = "construct"
+family = "rlve_even_degree_partition"
+problem_key = "gallai_even_partition"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/even_degree_graph_partitioning"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s8/instruction.md b/tasks/construct-rlve-even-degree-partition-l5-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..dad7b0950ddb2f40369f2fe63ae4f4ae934d4f48
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s8/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 28 vertices labelled 0..27 and edge list
+[[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 20], [0, 21], [0, 22], [0, 23], [0, 27], [1, 2], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [1, 17], [1, 18], [1, 19], [1, 20], [1, 23], [1, 26], [1, 27], [2, 4], [2, 6], [2, 7], [2, 8], [2, 11], [2, 14], [2, 18], [2, 19], [2, 23], [2, 24], [2, 25], [2, 26], [3, 5], [3, 6], [3, 8], [3, 9], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 17], [3, 18], [3, 19], [3, 23], [3, 25], [4, 5], [4, 6], [4, 7], [4, 11], [4, 12], [4, 13], [4, 14], [4, 17], [4, 20], [4, 21], [4, 24], [5, 8], [5, 11], [5, 12], [5, 14], [5, 15], [5, 17], [5, 18], [5, 19], [5, 20], [5, 22], [5, 24], [5, 25], [5, 26], [6, 7], [6, 9], [6, 12], [6, 13], [6, 14], [6, 18], [6, 20], [6, 23], [6, 27], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [7, 22], [7, 23], [7, 24], [7, 25], [7, 26], [8, 13], [8, 15], [8, 16], [8, 17], [8, 18], [8, 21], [8, 22], [8, 24], [9, 10], [9, 13], [9, 14], [9, 16], [9, 18], [9, 20], [9, 21], [9, 23], [9, 24], [9, 26], [10, 11], [10, 13], [10, 15], [10, 17], [10, 19], [10, 20], [10, 21], [10, 22], [10, 25], [10, 26], [10, 27], [11, 12], [11, 15], [11, 20], [11, 22], [11, 23], [11, 24], [11, 25], [11, 27], [12, 16], [12, 17], [12, 19], [12, 21], [12, 23], [12, 24], [12, 26], [12, 27], [13, 14], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 22], [13, 23], [13, 25], [13, 26], [13, 27], [14, 17], [14, 18], [14, 19], [14, 20], [14, 23], [14, 26], [14, 27], [15, 16], [15, 18], [15, 19], [15, 20], [15, 22], [15, 24], [16, 19], [16, 22], [16, 23], [16, 26], [17, 18], [17, 20], [17, 22], [17, 23], [17, 26], [18, 19], [18, 20], [18, 23], [18, 24], [18, 25], [19, 22], [19, 23], [19, 25], [20, 21], [20, 22], [20, 23], [20, 25], [20, 26], [20, 27], [21, 22], [21, 23], [21, 24], [21, 25], [22, 26], [22, 27], [23, 24], [23, 25], [23, 26], [24, 25], [25, 27], [26, 27]]
+
+Assign every vertex to group 1 or group 2 so that, for every vertex v, the number of neighbours of v lying in the same group as v is even (zero counts as even). One of the groups may be empty.
+
+Answer format: {"groups": [g_0, ..., g_27]}  with each g_i in {1, 2}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-even-degree-partition-l5-s8/task.toml b/tasks/construct-rlve-even-degree-partition-l5-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..79770a4e85509c8f7975fb52d38bbb5b8aa5df78
--- /dev/null
+++ b/tasks/construct-rlve-even-degree-partition-l5-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-even-degree-partition-l5-s8"
+version = "0.2.0"
+description = "construct/rlve_even_degree_partition"
+authors = []
+keywords = ["rlmath", "construct", "rlve_even_degree_partition"]
+
+[metadata]
+subset = "construct"
+family = "rlve_even_degree_partition"
+problem_key = "gallai_even_partition"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/even_degree_graph_partitioning"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-graph-isomorphism-l3-s5/instruction.md b/tasks/construct-rlve-graph-isomorphism-l3-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..faf46681ea1d1f2abd8fd8ffdec732d1d90e829f
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-s5/instruction.md
@@ -0,0 +1,9 @@
+Two undirected simple graphs G1 and G2 each have 12 vertices labelled 0..11 and 29 edges.
+G1 edges: [[1, 5], [1, 8], [0, 2], [4, 11], [7, 8], [5, 8], [0, 8], [6, 10], [6, 9], [8, 9], [1, 11], [2, 5], [0, 6], [0, 3], [3, 8], [8, 10], [0, 11], [0, 9], [1, 10], [6, 7], [0, 5], [7, 10], [1, 2], [3, 7], [2, 8], [4, 7], [1, 9], [9, 11], [0, 4]]
+G2 edges: [[0, 5], [0, 10], [4, 6], [1, 6], [6, 10], [5, 10], [7, 8], [6, 8], [0, 2], [3, 5], [7, 11], [4, 5], [1, 3], [6, 9], [1, 10], [8, 10], [0, 6], [0, 3], [2, 4], [5, 8], [0, 4], [2, 5], [0, 11], [0, 9], [6, 7], [9, 11], [2, 6], [1, 11], [3, 11]]
+
+Find a bijection p from the vertices of G1 to the vertices of G2 such that (u, v) is an edge of G1 if and only if (p(u), p(v)) is an edge of G2.
+
+Answer format: {"p": [p(0), ..., p(11)]}  (a permutation of 0..11)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-graph-isomorphism-l3-s5/task.toml b/tasks/construct-rlve-graph-isomorphism-l3-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..87926fd64c6d06eb4d1f19c7efe4664173ea77e3
--- /dev/null
+++ b/tasks/construct-rlve-graph-isomorphism-l3-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-graph-isomorphism-l3-s5"
+version = "0.2.0"
+description = "construct/rlve_graph_isomorphism"
+authors = []
+keywords = ["rlmath", "construct", "rlve_graph_isomorphism"]
+
+[metadata]
+subset = "construct"
+family = "rlve_graph_isomorphism"
+problem_key = "graph_isomorphism"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/graph_isomorphism"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-grid-parity-construction-l3-s2/instruction.md b/tasks/construct-rlve-grid-parity-construction-l3-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a239c726642c775d16d08be980d0b74852129a26
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-s2/instruction.md
@@ -0,0 +1,15 @@
+Construct an 8 x 4 binary matrix G (entries 0/1) whose parity matrix equals P below. The parity of cell (i, j) is the XOR of G[i][j] and its up/down/left/right neighbours inside the grid (cells outside the grid count as 0).
+
+P (one row per line):
+0110
+0010
+1011
+0110
+0010
+1000
+0100
+0100
+
+Answer format: {"grid": [row_0, ..., row_7]}  where each row is a string of 4 characters '0'/'1'
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-grid-parity-construction-l3-s2/task.toml b/tasks/construct-rlve-grid-parity-construction-l3-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..44ecc1b817b7c51200447a602844d1c9c60a94f3
--- /dev/null
+++ b/tasks/construct-rlve-grid-parity-construction-l3-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-grid-parity-construction-l3-s2"
+version = "0.2.0"
+description = "construct/rlve_grid_parity_construction"
+authors = []
+keywords = ["rlmath", "construct", "rlve_grid_parity_construction"]
+
+[metadata]
+subset = "construct"
+family = "rlve_grid_parity_construction"
+problem_key = "lights_out_gf2"
+domain = "algebra"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/grid_parity_construction"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-imp-party-l1-s3/instruction.md b/tasks/construct-rlve-imp-party-l1-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..bbca7029d49638bff20c29b8f674c78ec68de455
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s3/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 9 vertices labelled 0..8 and edge list
+[[0, 5], [0, 7], [1, 2], [1, 3], [1, 5], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]
+
+It is guaranteed that the graph contains a clique of size 6. Find any clique of size 3: 3 distinct vertices every two of which are adjacent.
+
+Answer format: {"clique": [v_1, ..., v_3]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-imp-party-l1-s3/task.toml b/tasks/construct-rlve-imp-party-l1-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..96c7bd60359b8edf027136dc8fe2a2b6f2318997
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-imp-party-l1-s3"
+version = "0.2.0"
+description = "construct/rlve_imp_party"
+authors = []
+keywords = ["rlmath", "construct", "rlve_imp_party"]
+
+[metadata]
+subset = "construct"
+family = "rlve_imp_party"
+problem_key = "poi_party_clique_3n"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/imp_party"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-imp-party-l1-s4/environment/Dockerfile b/tasks/construct-rlve-imp-party-l1-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-imp-party-l1-s4/environment/instance.json b/tasks/construct-rlve-imp-party-l1-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe712c0a9bae910a47054e127c6977ca25760221
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/environment/instance.json
@@ -0,0 +1 @@
+{"n": 3, "edges": [[0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l1-s4/instruction.md b/tasks/construct-rlve-imp-party-l1-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..790ccaa06334d176e673399cc0a0150002e5149e
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 9 vertices labelled 0..8 and edge list
+[[0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]
+
+It is guaranteed that the graph contains a clique of size 6. Find any clique of size 3: 3 distinct vertices every two of which are adjacent.
+
+Answer format: {"clique": [v_1, ..., v_3]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-imp-party-l1-s4/solution/solve.sh b/tasks/construct-rlve-imp-party-l1-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..da2a43c1fe05b22807800c696916113bf111109c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [5, 6, 7]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-imp-party-l1-s4/task.toml b/tasks/construct-rlve-imp-party-l1-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..39d2124ace55927a9e658f30b7ecdb66a4a7bd64
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-imp-party-l1-s4"
+version = "0.2.0"
+description = "construct/rlve_imp_party"
+authors = []
+keywords = ["rlmath", "construct", "rlve_imp_party"]
+
+[metadata]
+subset = "construct"
+family = "rlve_imp_party"
+problem_key = "poi_party_clique_3n"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/imp_party"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-imp-party-l1-s4/tests/check.py b/tasks/construct-rlve-imp-party-l1-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..97b5a037a2ba8bf4495cf87cc074d1c60b11311c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/tests/check.py
@@ -0,0 +1,14 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    c = int_list(ans.get("clique"), n, 0, 3 * n - 1, "clique")
+    if len(set(c)) != n:
+        raise Invalid("vertices must be distinct")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(n):
+        for j in range(i + 1, n):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-imp-party-l1-s4/tests/instance.json b/tasks/construct-rlve-imp-party-l1-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe712c0a9bae910a47054e127c6977ca25760221
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/tests/instance.json
@@ -0,0 +1 @@
+{"n": 3, "edges": [[0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l1-s4/tests/run.py b/tasks/construct-rlve-imp-party-l1-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-imp-party-l1-s4/tests/test.sh b/tasks/construct-rlve-imp-party-l1-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l1-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-imp-party-l5-s2/environment/Dockerfile b/tasks/construct-rlve-imp-party-l5-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-imp-party-l5-s2/environment/instance.json b/tasks/construct-rlve-imp-party-l5-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..489a64ed1f7ff0afc1c22efdd32d21feb8cfa688
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/environment/instance.json
@@ -0,0 +1 @@
+{"n": 18, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 29], [0, 30], [0, 31], [0, 32], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [0, 40], [0, 43], [0, 44], [0, 45], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [0, 53], [1, 2], [1, 8], [1, 9], [1, 10], [1, 11], [1, 13], [1, 15], [1, 17], [1, 24], [1, 25], [1, 30], [1, 32], [1, 38], [1, 39], [1, 43], [1, 45], [1, 46], [1, 48], [1, 50], [1, 52], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 17], [2, 20], [2, 21], [2, 22], [2, 23], [2, 24], [2, 25], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [2, 34], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 41], [2, 43], [2, 44], [2, 45], [2, 46], [2, 47], [2, 48], [2, 50], [2, 51], [2, 52], [2, 53], [3, 4], [3, 5], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 15], [3, 16], [3, 17], [3, 19], [3, 21], [3, 23], [3, 24], [3, 25], [3, 26], [3, 30], [3, 31], [3, 32], [3, 33], [3, 34], [3, 35], [3, 36], [3, 37], [3, 38], [3, 39], [3, 40], [3, 41], [3, 42], [3, 43], [3, 44], [3, 45], [3, 46], [3, 47], [3, 48], [3, 49], [3, 50], [3, 51], [3, 52], [3, 53], [4, 5], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 15], [4, 16], [4, 17], [4, 18], [4, 21], [4, 23], [4, 24], [4, 25], [4, 27], [4, 28], [4, 30], [4, 31], [4, 32], [4, 33], [4, 34], [4, 35], [4, 36], [4, 37], [4, 38], [4, 39], [4, 40], [4, 43], [4, 44], [4, 45], [4, 46], [4, 47], [4, 48], [4, 50], [4, 51], [4, 52], [4, 53], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 15], [5, 16], [5, 17], [5, 18], [5, 21], [5, 23], [5, 24], [5, 25], [5, 28], [5, 29], [5, 30], [5, 31], [5, 32], [5, 33], [5, 34], [5, 35], [5, 37], [5, 38], [5, 39], [5, 40], [5, 43], [5, 44], [5, 45], [5, 46], [5, 47], [5, 48], [5, 50], [5, 51], [5, 52], [5, 53], [6, 9], [6, 11], [6, 13], [6, 16], [6, 23], [6, 25], [6, 38], [6, 40], [6, 44], [6, 46], [6, 48], [6, 51], [7, 9], [7, 12], [7, 15], [7, 23], [7, 30], [7, 32], [7, 34], [7, 37], [7, 38], [7, 39], [7, 40], [7, 45], [7, 46], [7, 47], [7, 48], [7, 50], [7, 53], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 15], [8, 16], [8, 17], [8, 20], [8, 21], [8, 23], [8, 24], [8, 25], [8, 27], [8, 28], [8, 30], [8, 31], [8, 32], [8, 34], [8, 35], [8, 36], [8, 37], [8, 38], [8, 39], [8, 40], [8, 42], [8, 43], [8, 44], [8, 45], [8, 46], [8, 47], [8, 48], [8, 49], [8, 50], [8, 51], [8, 52], [8, 53], [9, 10], [9, 11], [9, 12], [9, 13], [9, 15], [9, 16], [9, 17], [9, 18], [9, 21], [9, 23], [9, 24], [9, 25], [9, 26], [9, 27], [9, 30], [9, 32], [9, 34], [9, 35], [9, 37], [9, 38], [9, 39], [9, 40], [9, 43], [9, 44], [9, 45], [9, 46], [9, 47], [9, 48], [9, 50], [9, 51], [9, 52], [9, 53], [10, 11], [10, 12], [10, 13], [10, 15], [10, 16], [10, 17], [10, 19], [10, 20], [10, 21], [10, 23], [10, 24], [10, 25], [10, 30], [10, 31], [10, 32], [10, 33], [10, 34], [10, 35], [10, 36], [10, 37], [10, 38], [10, 39], [10, 40], [10, 42], [10, 43], [10, 44], [10, 45], [10, 46], [10, 47], [10, 48], [10, 50], [10, 51], [10, 52], [10, 53], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 20], [11, 21], [11, 23], [11, 24], [11, 25], [11, 26], [11, 28], [11, 29], [11, 30], [11, 32], [11, 33], [11, 34], [11, 35], [11, 37], [11, 38], [11, 39], [11, 40], [11, 43], [11, 44], [11, 45], [11, 46], [11, 47], [11, 48], [11, 50], [11, 51], [11, 52], [11, 53], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 19], [12, 20], [12, 21], [12, 23], [12, 24], [12, 25], [12, 27], [12, 28], [12, 29], [12, 30], [12, 32], [12, 33], [12, 34], [12, 35], [12, 36], [12, 37], [12, 38], [12, 39], [12, 40], [12, 43], [12, 44], [12, 45], [12, 46], [12, 47], [12, 48], [12, 50], [12, 51], [12, 52], [12, 53], [13, 14], [13, 15], [13, 16], [13, 17], [13, 19], [13, 20], [13, 21], [13, 22], [13, 23], [13, 24], [13, 25], [13, 26], [13, 27], [13, 30], [13, 31], [13, 32], [13, 34], [13, 35], [13, 37], [13, 38], [13, 39], [13, 40], [13, 41], [13, 43], [13, 44], [13, 45], [13, 46], [13, 47], [13, 48], [13, 49], [13, 50], [13, 51], [13, 52], [13, 53], [14, 16], [14, 17], [14, 21], [14, 24], [14, 25], [14, 30], [14, 32], [14, 34], [14, 37], [14, 38], [14, 39], [14, 40], [14, 43], [14, 45], [14, 46], [14, 48], [14, 52], [14, 53], [15, 16], [15, 17], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 25], [15, 26], [15, 27], [15, 28], [15, 30], [15, 31], [15, 32], [15, 33], [15, 34], [15, 35], [15, 36], [15, 37], [15, 38], [15, 39], [15, 40], [15, 43], [15, 44], [15, 45], [15, 46], [15, 47], [15, 48], [15, 50], [15, 51], [15, 52], [15, 53], [16, 17], [16, 18], [16, 20], [16, 21], [16, 23], [16, 24], [16, 25], [16, 26], [16, 29], [16, 30], [16, 32], [16, 33], [16, 34], [16, 35], [16, 36], [16, 37], [16, 38], [16, 39], [16, 40], [16, 42], [16, 43], [16, 44], [16, 45], [16, 46], [16, 47], [16, 48], 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[22, 25], [22, 30], [22, 32], [22, 34], [22, 37], [22, 38], [22, 39], [22, 43], [22, 44], [22, 47], [22, 48], [22, 51], [23, 24], [23, 25], [23, 28], [23, 29], [23, 30], [23, 32], [23, 34], [23, 35], [23, 37], [23, 38], [23, 39], [23, 40], [23, 43], [23, 44], [23, 45], [23, 46], [23, 47], [23, 48], [23, 49], [23, 50], [23, 51], [23, 52], [23, 53], [24, 25], [24, 28], [24, 30], [24, 31], [24, 32], [24, 34], [24, 35], [24, 36], [24, 37], [24, 38], [24, 39], [24, 40], [24, 41], [24, 43], [24, 44], [24, 45], [24, 46], [24, 47], [24, 48], [24, 50], [24, 51], [24, 52], [24, 53], [25, 27], [25, 28], [25, 30], [25, 31], [25, 32], [25, 34], [25, 35], [25, 37], [25, 38], [25, 39], [25, 40], [25, 43], [25, 44], [25, 45], [25, 46], [25, 47], [25, 48], [25, 49], [25, 50], [25, 51], [25, 52], [25, 53], [26, 30], [26, 32], [26, 34], [26, 37], [26, 40], [26, 45], [26, 48], [26, 50], [26, 52], [26, 53], [27, 32], [27, 35], [27, 37], [27, 38], [27, 43], [27, 45], [27, 53], [28, 30], [28, 34], [28, 44], [28, 53], [29, 30], [29, 32], [29, 34], [29, 37], [29, 38], [29, 45], [29, 46], [29, 47], [29, 48], [29, 50], [29, 51], [29, 53], [30, 31], [30, 32], [30, 34], [30, 35], [30, 37], [30, 38], [30, 39], [30, 40], [30, 41], [30, 43], [30, 44], [30, 45], [30, 46], [30, 47], [30, 48], [30, 49], [30, 50], [30, 51], [30, 52], [30, 53], [31, 34], [31, 35], [31, 37], [31, 39], [31, 40], [31, 44], [31, 47], [31, 48], [31, 52], [31, 53], [32, 34], [32, 35], [32, 37], [32, 38], [32, 39], [32, 40], [32, 41], [32, 43], [32, 44], [32, 45], [32, 46], [32, 47], [32, 48], [32, 49], [32, 50], [32, 51], [32, 52], [32, 53], [33, 34], [33, 37], [33, 38], [33, 39], [33, 45], [33, 46], [33, 47], [34, 35], [34, 37], [34, 38], [34, 39], [34, 40], [34, 43], [34, 44], [34, 45], [34, 46], [34, 47], [34, 48], [34, 49], [34, 50], [34, 51], [34, 52], [34, 53], [35, 36], [35, 37], [35, 38], [35, 39], [35, 40], [35, 41], [35, 43], [35, 44], [35, 45], [35, 46], [35, 47], [35, 48], [35, 50], [35, 51], [35, 52], [35, 53], 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[46, 47], [46, 48], [46, 50], [46, 51], [46, 52], [46, 53], [47, 48], [47, 49], [47, 50], [47, 51], [47, 52], [47, 53], [48, 49], [48, 50], [48, 51], [48, 52], [48, 53], [49, 50], [49, 53], [50, 51], [50, 52], [50, 53], [51, 52], [51, 53], [52, 53]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l5-s2/instruction.md b/tasks/construct-rlve-imp-party-l5-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..40c9f70cb54f742577d880331f6441948fc49549
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 54 vertices labelled 0..53 and edge list
+[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 29], [0, 30], [0, 31], [0, 32], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [0, 40], [0, 43], [0, 44], [0, 45], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [0, 53], [1, 2], [1, 8], [1, 9], [1, 10], [1, 11], [1, 13], [1, 15], [1, 17], [1, 24], [1, 25], [1, 30], [1, 32], [1, 38], [1, 39], [1, 43], [1, 45], [1, 46], [1, 48], [1, 50], [1, 52], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 17], [2, 20], [2, 21], [2, 22], [2, 23], [2, 24], [2, 25], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [2, 34], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 41], [2, 43], [2, 44], [2, 45], [2, 46], [2, 47], [2, 48], [2, 50], [2, 51], [2, 52], [2, 53], [3, 4], [3, 5], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], 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48], [46, 50], [46, 51], [46, 52], [46, 53], [47, 48], [47, 49], [47, 50], [47, 51], [47, 52], [47, 53], [48, 49], [48, 50], [48, 51], [48, 52], [48, 53], [49, 50], [49, 53], [50, 51], [50, 52], [50, 53], [51, 52], [51, 53], [52, 53]]
+
+It is guaranteed that the graph contains a clique of size 36. Find any clique of size 18: 18 distinct vertices every two of which are adjacent.
+
+Answer format: {"clique": [v_1, ..., v_18]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-imp-party-l5-s2/solution/solve.sh b/tasks/construct-rlve-imp-party-l5-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9f464ce4aab954059c97bc2e387c1d376d9543c1
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [4, 9, 12, 16, 17, 23, 25, 35, 37, 38, 39, 40, 43, 46, 47, 48, 50, 51]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-imp-party-l5-s2/task.toml b/tasks/construct-rlve-imp-party-l5-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..9943cd06b9b7dfaa40cbf56d9f68e24549a03bac
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-imp-party-l5-s2"
+version = "0.2.0"
+description = "construct/rlve_imp_party"
+authors = []
+keywords = ["rlmath", "construct", "rlve_imp_party"]
+
+[metadata]
+subset = "construct"
+family = "rlve_imp_party"
+problem_key = "poi_party_clique_3n"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/imp_party"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-imp-party-l5-s2/tests/check.py b/tasks/construct-rlve-imp-party-l5-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..97b5a037a2ba8bf4495cf87cc074d1c60b11311c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/tests/check.py
@@ -0,0 +1,14 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    c = int_list(ans.get("clique"), n, 0, 3 * n - 1, "clique")
+    if len(set(c)) != n:
+        raise Invalid("vertices must be distinct")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(n):
+        for j in range(i + 1, n):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-imp-party-l5-s2/tests/instance.json b/tasks/construct-rlve-imp-party-l5-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..489a64ed1f7ff0afc1c22efdd32d21feb8cfa688
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/tests/instance.json
@@ -0,0 +1 @@
+{"n": 18, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [0, 19], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 29], [0, 30], [0, 31], [0, 32], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 39], [0, 40], [0, 43], [0, 44], [0, 45], [0, 46], [0, 47], [0, 48], [0, 49], [0, 50], [0, 51], [0, 52], [0, 53], [1, 2], [1, 8], [1, 9], [1, 10], [1, 11], [1, 13], [1, 15], [1, 17], [1, 24], [1, 25], [1, 30], [1, 32], [1, 38], [1, 39], [1, 43], [1, 45], [1, 46], [1, 48], [1, 50], [1, 52], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 15], [2, 16], [2, 17], [2, 20], [2, 21], [2, 22], [2, 23], [2, 24], [2, 25], [2, 29], [2, 30], [2, 31], [2, 32], [2, 33], [2, 34], [2, 35], [2, 36], [2, 37], [2, 38], [2, 39], [2, 40], [2, 41], [2, 43], [2, 44], [2, 45], [2, 46], [2, 47], [2, 48], [2, 50], [2, 51], [2, 52], [2, 53], [3, 4], [3, 5], [3, 8], [3, 9], [3, 10], 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[46, 47], [46, 48], [46, 50], [46, 51], [46, 52], [46, 53], [47, 48], [47, 49], [47, 50], [47, 51], [47, 52], [47, 53], [48, 49], [48, 50], [48, 51], [48, 52], [48, 53], [49, 50], [49, 53], [50, 51], [50, 52], [50, 53], [51, 52], [51, 53], [52, 53]], "family": "rlve_imp_party", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l5-s2/tests/run.py b/tasks/construct-rlve-imp-party-l5-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-imp-party-l5-s2/tests/test.sh b/tasks/construct-rlve-imp-party-l5-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-imp-party-l5-s5/environment/Dockerfile b/tasks/construct-rlve-imp-party-l5-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-imp-party-l5-s5/environment/instance.json b/tasks/construct-rlve-imp-party-l5-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8a965066a1ae3ab46e0ca7084cd1c73478c7a558
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/environment/instance.json
@@ -0,0 +1 @@
+{"n": 18, "edges": [[0, 1], [0, 3], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 40], [0, 41], [0, 42], [0, 45], [0, 50], [0, 51], [0, 53], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 34], [1, 35], [1, 36], [1, 37], [1, 38], [1, 39], [1, 40], [1, 41], [1, 42], [1, 43], [1, 44], [1, 45], [1, 46], [1, 47], [1, 48], [1, 49], [1, 50], [1, 51], [1, 52], [1, 53], [2, 3], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [2, 24], [2, 25], [2, 26], [2, 27], [2, 28], [2, 31], [2, 33], [2, 34], [2, 35], [2, 36], 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\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l5-s5/instruction.md b/tasks/construct-rlve-imp-party-l5-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..1fd6f8d5cd2def76a6dd45a67b430c3ad10859cd
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 54 vertices labelled 0..53 and edge list
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+
+It is guaranteed that the graph contains a clique of size 36. Find any clique of size 18: 18 distinct vertices every two of which are adjacent.
+
+Answer format: {"clique": [v_1, ..., v_18]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-imp-party-l5-s5/solution/solve.sh b/tasks/construct-rlve-imp-party-l5-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..32f46e62d506cfed6ecc064c6aa1d2b06fe72b5a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [3, 6, 8, 10, 14, 16, 18, 21, 24, 25, 26, 28, 31, 35, 38, 40, 47, 53]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-imp-party-l5-s5/task.toml b/tasks/construct-rlve-imp-party-l5-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..0afc4a3d9000dce34173d6160e78c296ff20b428
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-imp-party-l5-s5"
+version = "0.2.0"
+description = "construct/rlve_imp_party"
+authors = []
+keywords = ["rlmath", "construct", "rlve_imp_party"]
+
+[metadata]
+subset = "construct"
+family = "rlve_imp_party"
+problem_key = "poi_party_clique_3n"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/imp_party"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-imp-party-l5-s5/tests/check.py b/tasks/construct-rlve-imp-party-l5-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..97b5a037a2ba8bf4495cf87cc074d1c60b11311c
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/tests/check.py
@@ -0,0 +1,14 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    c = int_list(ans.get("clique"), n, 0, 3 * n - 1, "clique")
+    if len(set(c)) != n:
+        raise Invalid("vertices must be distinct")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(n):
+        for j in range(i + 1, n):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-imp-party-l5-s5/tests/instance.json b/tasks/construct-rlve-imp-party-l5-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8a965066a1ae3ab46e0ca7084cd1c73478c7a558
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/tests/instance.json
@@ -0,0 +1 @@
+{"n": 18, "edges": [[0, 1], [0, 3], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 38], [0, 40], [0, 41], [0, 42], [0, 45], [0, 50], [0, 51], [0, 53], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [1, 24], [1, 25], [1, 26], [1, 27], [1, 28], [1, 29], [1, 30], [1, 31], [1, 32], [1, 33], [1, 34], [1, 35], [1, 36], [1, 37], [1, 38], [1, 39], [1, 40], [1, 41], [1, 42], [1, 43], [1, 44], [1, 45], [1, 46], [1, 47], [1, 48], [1, 49], [1, 50], [1, 51], [1, 52], [1, 53], [2, 3], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 12], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [2, 24], [2, 25], [2, 26], [2, 27], [2, 28], [2, 31], [2, 33], [2, 34], [2, 35], [2, 36], 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\ No newline at end of file
diff --git a/tasks/construct-rlve-imp-party-l5-s5/tests/run.py b/tasks/construct-rlve-imp-party-l5-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-imp-party-l5-s5/tests/test.sh b/tasks/construct-rlve-imp-party-l5-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-imp-party-l5-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l2-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/environment/instance.json b/tasks/construct-rlve-integer-linear-system-l2-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dfe35b5a8f3110f15d8769f6697b7de0f8fac982
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[0, 0, 1, 1, 1], [1, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 1, 0, 1], [1, 1, 0, 1, 1], [0, 0, 1, 0, 1], [1, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, 1, 0, 0, 0], [1, 1, 1, 0, 1]], "rhs": [10, 13, 12, 10, 12, 16, 5, 3, 6, 4, 12], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/instruction.md b/tasks/construct-rlve-integer-linear-system-l2-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..89f960077750eb23360fba84e1af42c010d845ca
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/instruction.md
@@ -0,0 +1,16 @@
+Find integers x[0], ..., x[4] satisfying all of the following 11 equations:
+1*x[2] + 1*x[3] + 1*x[4] = 10
+1*x[0] + 1*x[1] + 1*x[2] + 1*x[3] = 13
+1*x[0] + 1*x[1] + 1*x[3] = 12
+1*x[1] + 1*x[2] + 1*x[3] = 10
+1*x[0] + 1*x[1] + 1*x[2] + 1*x[4] = 12
+1*x[0] + 1*x[1] + 1*x[3] + 1*x[4] = 16
+1*x[2] + 1*x[4] = 5
+1*x[0] = 3
+1*x[2] + 1*x[3] = 6
+1*x[1] = 4
+1*x[0] + 1*x[1] + 1*x[2] + 1*x[4] = 12
+
+Answer format: {"x": [x_0, ..., x_4]}  (integers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l2-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f188d94dc66f48bd3e49a2a1f546c89c5810bdd0
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [3, 4, 1, 5, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/task.toml b/tasks/construct-rlve-integer-linear-system-l2-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..8cc2d5d62ab2ff2cc5a96233e4b48e16a2e6c390
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-integer-linear-system-l2-s2"
+version = "0.2.0"
+description = "construct/rlve_integer_linear_system"
+authors = []
+keywords = ["rlmath", "construct", "rlve_integer_linear_system"]
+
+[metadata]
+subset = "construct"
+family = "rlve_integer_linear_system"
+problem_key = "integer_linear_system"
+domain = "algebra"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/gaussian_elimination"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/tests/check.py b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = len(inst["coeffs"][0])
+    x = int_list(ans.get("x"), n, name="x")
+    for k, (e, r) in enumerate(zip(inst["coeffs"], inst["rhs"])):
+        if sum(c * v for c, v in zip(e, x)) != r:
+            raise Invalid(f"equation {k} is violated")
+    return None, {}
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..dfe35b5a8f3110f15d8769f6697b7de0f8fac982
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[0, 0, 1, 1, 1], [1, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 1, 0, 1], [1, 1, 0, 1, 1], [0, 0, 1, 0, 1], [1, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, 1, 0, 0, 0], [1, 1, 1, 0, 1]], "rhs": [10, 13, 12, 10, 12, 16, 5, 3, 6, 4, 12], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/tests/run.py b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s2/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l2-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/environment/instance.json b/tasks/construct-rlve-integer-linear-system-l2-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c3b07c3d594b4c5f4a3b580b5c3b34d95e178998
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[0, 1, 1, 1, 1], [0, 0, 0, 1, 0], [0, 1, 0, 1, 1], [1, 1, 1, 1, 1], [0, 0, 0, 1, 1], [0, 1, 1, 0, 1], [1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 1, 0, 1], [0, 0, 1, 0, 1], [1, 0, 1, 0, 0]], "rhs": [12, 4, 9, 15, 6, 8, 10, 9, 5, 7, 8, 5, 6], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/instruction.md b/tasks/construct-rlve-integer-linear-system-l2-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a4a48554a6e1109953fa6aa8a76242c4ee40fd43
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/instruction.md
@@ -0,0 +1,18 @@
+Find integers x[0], ..., x[4] satisfying all of the following 13 equations:
+1*x[1] + 1*x[2] + 1*x[3] + 1*x[4] = 12
+1*x[3] = 4
+1*x[1] + 1*x[3] + 1*x[4] = 9
+1*x[0] + 1*x[1] + 1*x[2] + 1*x[3] + 1*x[4] = 15
+1*x[3] + 1*x[4] = 6
+1*x[1] + 1*x[2] + 1*x[4] = 8
+1*x[0] + 1*x[1] + 1*x[3] = 10
+1*x[0] + 1*x[1] + 1*x[2] = 9
+1*x[0] + 1*x[4] = 5
+1*x[0] + 1*x[3] = 7
+1*x[1] + 1*x[2] + 1*x[4] = 8
+1*x[2] + 1*x[4] = 5
+1*x[0] + 1*x[2] = 6
+
+Answer format: {"x": [x_0, ..., x_4]}  (integers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l2-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..192ce73b571a85e188af0ecc235a7daa4fba30de
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [3, 3, 3, 4, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/task.toml b/tasks/construct-rlve-integer-linear-system-l2-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..efff1a50ca96baa65c67e61630c48552385cbe38
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-integer-linear-system-l2-s5"
+version = "0.2.0"
+description = "construct/rlve_integer_linear_system"
+authors = []
+keywords = ["rlmath", "construct", "rlve_integer_linear_system"]
+
+[metadata]
+subset = "construct"
+family = "rlve_integer_linear_system"
+problem_key = "integer_linear_system"
+domain = "algebra"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/gaussian_elimination"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/tests/check.py b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = len(inst["coeffs"][0])
+    x = int_list(ans.get("x"), n, name="x")
+    for k, (e, r) in enumerate(zip(inst["coeffs"], inst["rhs"])):
+        if sum(c * v for c, v in zip(e, x)) != r:
+            raise Invalid(f"equation {k} is violated")
+    return None, {}
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..c3b07c3d594b4c5f4a3b580b5c3b34d95e178998
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[0, 1, 1, 1, 1], [0, 0, 0, 1, 0], [0, 1, 0, 1, 1], [1, 1, 1, 1, 1], [0, 0, 0, 1, 1], [0, 1, 1, 0, 1], [1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 1, 0, 1], [0, 0, 1, 0, 1], [1, 0, 1, 0, 0]], "rhs": [12, 4, 9, 15, 6, 8, 10, 9, 5, 7, 8, 5, 6], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/tests/run.py b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-integer-linear-system-l2-s5/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l2-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s3/instruction.md b/tasks/construct-rlve-integer-linear-system-l6-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..12444600673aa0ad1fe3e492951ad5068668d9b5
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s3/instruction.md
@@ -0,0 +1,62 @@
+Find integers x[0], ..., x[25] satisfying all of the following 57 equations:
+3*x[0] + 5*x[1] + 3*x[2] + 5*x[3] + 1*x[4] + 4*x[8] + 3*x[10] + 4*x[11] + 1*x[12] + 3*x[13] + 2*x[15] + 3*x[17] + 2*x[18] + 4*x[19] + 4*x[20] + 2*x[21] + 2*x[25] = 685
+2*x[2] + 2*x[3] + 4*x[5] + 4*x[8] + 1*x[9] + 2*x[13] + 5*x[15] + 1*x[23] + 2*x[24] + 1*x[25] = 275
+2*x[0] + 3*x[2] + 1*x[3] + 5*x[6] + 4*x[10] + 1*x[14] + 5*x[18] + 3*x[21] + 1*x[22] + 1*x[23] + 3*x[24] + 1*x[25] = 431
+3*x[1] + 1*x[2] + 5*x[6] + 1*x[7] + 1*x[9] + 4*x[20] + 2*x[21] + 4*x[22] + 1*x[25] = 296
+1*x[0] + 5*x[1] + 4*x[2] + 2*x[3] + 1*x[5] + 4*x[8] + 1*x[10] + 4*x[14] + 3*x[15] + 3*x[22] + 5*x[23] + 1*x[24] + 5*x[25] = 552
+1*x[0] + 5*x[2] + 1*x[3] + 4*x[4] + 1*x[7] + 5*x[9] + 4*x[10] + 5*x[11] + 1*x[12] + 1*x[16] + 3*x[17] + 2*x[20] + 3*x[21] + 5*x[23] + 5*x[25] = 611
+5*x[0] + 4*x[1] + 3*x[3] + 1*x[4] + 5*x[6] + 2*x[8] + 2*x[13] + 5*x[14] + 2*x[15] + 4*x[16] + 1*x[17] + 3*x[19] + 4*x[21] + 5*x[24] + 4*x[25] = 712
+5*x[1] + 2*x[3] + 3*x[4] + 2*x[5] + 5*x[6] + 5*x[10] + 5*x[11] + 3*x[12] + 5*x[14] + 1*x[16] + 3*x[17] + 4*x[18] + 5*x[21] + 2*x[23] + 4*x[24] + 4*x[25] = 877
+2*x[2] + 5*x[3] + 2*x[8] + 4*x[9] + 4*x[10] + 2*x[13] + 2*x[15] + 4*x[16] + 5*x[17] + 4*x[18] + 2*x[19] + 1*x[23] + 3*x[24] + 5*x[25] = 542
+4*x[0] + 3*x[2] + 1*x[3] + 2*x[5] + 4*x[11] + 3*x[14] + 4*x[16] + 2*x[17] + 1*x[19] + 2*x[22] + 4*x[23] = 414
+3*x[2] + 4*x[6] + 2*x[8] + 5*x[13] + 2*x[14] + 3*x[15] + 3*x[18] + 2*x[22] + 3*x[23] + 3*x[24] = 467
+1*x[0] + 2*x[2] + 4*x[6] + 1*x[7] + 5*x[9] + 4*x[10] + 4*x[13] + 3*x[16] + 4*x[17] + 2*x[18] + 4*x[19] + 1*x[21] + 3*x[24] = 497
+3*x[1] + 2*x[7] + 4*x[11] + 1*x[12] + 3*x[14] + 3*x[19] + 5*x[22] + 2*x[23] + 4*x[24] + 3*x[25] = 579
+2*x[0] + 4*x[2] + 5*x[3] + 1*x[4] + 5*x[8] + 2*x[13] + 1*x[14] + 2*x[16] + 5*x[17] + 5*x[20] + 4*x[23] + 1*x[24] + 2*x[25] = 473
+2*x[0] + 1*x[1] + 4*x[5] + 5*x[6] + 1*x[9] + 1*x[10] + 1*x[13] + 5*x[14] + 4*x[16] + 5*x[18] + 4*x[19] + 3*x[20] + 4*x[21] + 1*x[22] + 3*x[23] + 1*x[25] = 539
+4*x[0] + 5*x[1] + 5*x[7] + 1*x[9] + 5*x[12] + 5*x[13] + 2*x[14] + 3*x[15] + 1*x[17] + 3*x[18] + 4*x[21] + 1*x[24] = 578
+1*x[1] + 1*x[2] + 2*x[6] + 5*x[7] + 5*x[8] + 3*x[9] + 4*x[11] + 1*x[15] + 3*x[21] + 4*x[22] = 417
+4*x[3] + 2*x[5] + 5*x[7] + 1*x[8] + 4*x[9] + 5*x[14] + 5*x[15] + 5*x[19] + 5*x[22] + 5*x[23] + 1*x[24] + 2*x[25] = 549
+2*x[0] + 1*x[2] + 2*x[3] + 5*x[5] + 4*x[7] + 2*x[12] + 3*x[13] + 1*x[15] + 5*x[16] + 3*x[17] + 2*x[18] + 3*x[21] + 5*x[23] + 1*x[24] = 488
+5*x[0] + 3*x[3] + 5*x[5] + 5*x[6] + 3*x[7] + 4*x[9] + 1*x[13] + 3*x[14] + 2*x[15] + 4*x[16] + 2*x[17] + 2*x[19] + 2*x[23] + 3*x[24] = 498
+2*x[0] + 5*x[1] + 2*x[7] + 3*x[8] + 3*x[9] + 2*x[10] + 3*x[11] + 1*x[12] + 2*x[16] + 1*x[17] + 1*x[19] + 1*x[20] + 1*x[21] + 3*x[25] = 387
+4*x[2] + 1*x[4] + 1*x[6] + 2*x[7] + 1*x[8] + 1*x[12] + 3*x[14] + 3*x[15] + 2*x[16] + 1*x[17] + 2*x[18] + 3*x[19] + 2*x[21] = 333
+1*x[0] + 2*x[2] + 2*x[6] + 5*x[7] + 4*x[11] + 1*x[13] + 3*x[15] + 3*x[16] + 1*x[18] + 3*x[20] + 2*x[22] + 1*x[25] = 339
+5*x[0] + 4*x[1] + 1*x[2] + 1*x[3] + 2*x[7] + 4*x[8] + 3*x[10] + 1*x[11] + 5*x[14] + 3*x[15] + 5*x[18] + 1*x[20] + 3*x[21] + 5*x[23] + 5*x[24] + 2*x[25] = 688
+1*x[0] + 1*x[1] + 4*x[3] + 1*x[5] + 3*x[6] + 4*x[7] + 5*x[8] + 2*x[10] + 3*x[12] + 5*x[15] + 3*x[16] + 3*x[18] + 5*x[19] + 3*x[22] + 4*x[23] + 3*x[24] = 675
+2*x[0] + 3*x[1] + 5*x[2] + 3*x[4] + 3*x[5] + 3*x[6] + 5*x[8] + 4*x[9] + 5*x[11] + 1*x[15] + 2*x[17] + 2*x[18] + 3*x[19] + 1*x[20] + 5*x[23] + 2*x[25] = 702
+3*x[2] + 4*x[3] + 1*x[6] + 4*x[7] + 5*x[8] + 1*x[9] + 2*x[10] + 2*x[13] + 3*x[14] + 4*x[17] + 3*x[20] + 2*x[21] + 3*x[24] + 3*x[25] = 511
+2*x[3] + 5*x[4] + 4*x[5] + 2*x[7] + 3*x[9] + 4*x[10] + 4*x[12] + 4*x[15] + 5*x[16] + 3*x[18] + 4*x[19] + 2*x[24] = 498
+2*x[0] + 4*x[2] + 3*x[4] + 5*x[7] + 2*x[9] + 5*x[10] + 3*x[13] + 4*x[14] + 5*x[15] + 1*x[16] + 5*x[17] + 5*x[22] + 2*x[24] = 640
+5*x[4] + 2*x[7] + 4*x[8] + 3*x[9] + 5*x[10] + 3*x[12] + 1*x[13] + 3*x[15] + 5*x[16] + 3*x[18] + 2*x[24] + 3*x[25] = 485
+5*x[1] + 1*x[2] + 5*x[7] + 1*x[11] + 5*x[13] + 4*x[14] + 3*x[18] + 1*x[19] + 5*x[23] + 3*x[24] = 514
+2*x[0] + 3*x[1] + 1*x[5] + 1*x[9] + 2*x[14] + 2*x[15] + 5*x[16] + 4*x[18] + 4*x[19] + 2*x[21] + 2*x[22] + 1*x[24] = 369
+2*x[0] + 5*x[1] + 3*x[2] + 2*x[3] + 2*x[4] + 2*x[7] + 3*x[8] + 4*x[9] + 5*x[13] + 1*x[15] + 5*x[16] + 3*x[17] + 1*x[18] + 4*x[19] + 1*x[24] + 5*x[25] = 657
+2*x[0] + 3*x[1] + 2*x[3] + 2*x[4] + 4*x[7] + 1*x[8] + 3*x[13] + 3*x[14] + 4*x[16] + 1*x[19] + 3*x[20] + 3*x[21] + 1*x[23] + 2*x[24] + 1*x[25] = 432
+1*x[0] + 1*x[5] + 2*x[7] + 4*x[9] + 2*x[10] + 2*x[18] + 5*x[20] + 4*x[24] = 201
+4*x[0] + 4*x[1] + 5*x[8] + 5*x[12] + 1*x[16] + 3*x[20] + 4*x[24] + 1*x[25] = 429
+3*x[1] + 1*x[3] + 3*x[4] + 3*x[5] + 2*x[6] + 2*x[7] + 4*x[8] + 4*x[9] + 1*x[12] + 2*x[18] + 2*x[19] + 4*x[21] + 5*x[22] + 3*x[23] + 4*x[24] + 5*x[25] = 773
+3*x[2] + 2*x[4] + 4*x[6] + 5*x[8] + 1*x[9] + 5*x[11] + 3*x[14] + 5*x[17] + 5*x[18] + 2*x[19] + 4*x[21] + 1*x[23] + 4*x[24] = 719
+4*x[2] + 4*x[3] + 2*x[4] + 1*x[6] + 1*x[7] + 4*x[9] + 5*x[11] + 5*x[12] + 5*x[13] + 3*x[14] + 3*x[20] + 3*x[22] + 1*x[23] + 1*x[24] + 1*x[25] = 621
+5*x[2] + 2*x[6] + 4*x[8] + 2*x[9] + 1*x[10] + 3*x[12] + 5*x[13] + 3*x[14] + 5*x[16] + 2*x[19] + 1*x[20] + 2*x[21] + 5*x[22] + 2*x[23] + 2*x[24] = 638
+2*x[0] + 1*x[3] + 4*x[5] + 2*x[6] + 4*x[7] + 2*x[8] + 2*x[11] + 5*x[15] + 3*x[17] + 1*x[18] + 3*x[20] + 2*x[21] + 2*x[23] + 4*x[24] + 2*x[25] = 509
+3*x[0] + 3*x[1] + 5*x[3] + 3*x[6] + 2*x[7] + 1*x[10] + 2*x[12] + 2*x[13] + 4*x[14] + 3*x[16] + 2*x[17] + 2*x[22] + 4*x[23] + 4*x[24] = 559
+4*x[1] + 3*x[2] + 2*x[4] + 3*x[5] + 4*x[8] + 4*x[10] + 2*x[11] + 3*x[12] + 5*x[13] + 4*x[14] + 3*x[20] + 4*x[25] = 580
+2*x[0] + 2*x[2] + 3*x[10] + 1*x[12] + 2*x[15] + 5*x[16] + 1*x[21] + 5*x[22] + 5*x[23] + 4*x[25] = 411
+4*x[1] + 2*x[2] + 4*x[3] + 4*x[5] + 2*x[7] + 5*x[11] + 5*x[13] + 3*x[15] + 3*x[17] + 4*x[19] + 2*x[21] + 4*x[24] = 638
+3*x[4] + 2*x[6] + 1*x[7] + 1*x[8] + 1*x[9] + 1*x[10] + 4*x[14] + 4*x[16] + 2*x[20] + 3*x[21] + 2*x[25] = 256
+4*x[1] + 1*x[3] + 3*x[5] + 3*x[6] + 1*x[7] + 5*x[8] + 5*x[10] + 4*x[12] + 2*x[13] + 4*x[16] + 4*x[17] + 4*x[23] + 2*x[24] = 564
+3*x[0] + 1*x[1] + 4*x[4] + 1*x[5] + 5*x[6] + 5*x[8] + 1*x[9] + 5*x[11] + 1*x[14] + 5*x[16] + 2*x[18] + 1*x[19] + 5*x[20] + 5*x[21] + 4*x[22] + 1*x[23] + 1*x[24] = 685
+4*x[1] + 5*x[3] + 5*x[5] + 1*x[8] + 5*x[12] + 2*x[16] + 5*x[17] + 3*x[19] + 1*x[22] + 1*x[24] = 464
+1*x[2] + 2*x[4] + 1*x[5] + 5*x[6] + 4*x[7] + 2*x[8] + 2*x[9] + 4*x[18] + 2*x[19] + 2*x[20] + 2*x[21] + 2*x[22] + 3*x[23] + 3*x[25] = 498
+1*x[1] + 3*x[2] + 5*x[3] + 3*x[4] + 5*x[11] + 5*x[12] + 5*x[15] + 2*x[17] + 1*x[20] + 4*x[23] = 468
+4*x[1] + 4*x[3] + 4*x[4] + 2*x[6] + 1*x[8] + 5*x[10] + 3*x[11] + 5*x[13] + 2*x[14] + 4*x[16] + 4*x[17] + 5*x[18] + 1*x[23] + 2*x[25] = 624
+4*x[1] + 5*x[3] + 1*x[4] + 2*x[8] + 2*x[12] + 5*x[14] + 4*x[15] + 2*x[18] + 5*x[20] + 5*x[22] + 4*x[23] = 461
+4*x[0] + 5*x[4] + 1*x[5] + 4*x[6] + 4*x[9] + 3*x[11] + 2*x[12] + 2*x[13] + 1*x[15] + 3*x[17] + 3*x[18] + 4*x[22] + 4*x[24] = 696
+4*x[3] + 5*x[4] + 1*x[5] + 1*x[6] + 4*x[7] + 5*x[8] + 5*x[10] + 5*x[11] + 1*x[12] + 3*x[16] + 5*x[17] + 1*x[18] + 3*x[19] + 5*x[21] + 1*x[22] + 4*x[23] = 743
+1*x[0] + 3*x[3] + 4*x[4] + 4*x[9] + 1*x[11] + 1*x[13] + 4*x[14] + 3*x[15] + 1*x[18] + 1*x[19] + 1*x[24] = 271
+3*x[2] + 5*x[4] + 3*x[5] + 5*x[7] + 1*x[10] + 1*x[12] + 4*x[14] + 1*x[16] + 5*x[22] + 3*x[23] + 3*x[25] = 544
+
+Answer format: {"x": [x_0, ..., x_25]}  (integers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s3/task.toml b/tasks/construct-rlve-integer-linear-system-l6-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..a00dc7351314aa167465405dc623f5e8396aaad7
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-integer-linear-system-l6-s3"
+version = "0.2.0"
+description = "construct/rlve_integer_linear_system"
+authors = []
+keywords = ["rlmath", "construct", "rlve_integer_linear_system"]
+
+[metadata]
+subset = "construct"
+family = "rlve_integer_linear_system"
+problem_key = "integer_linear_system"
+domain = "algebra"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/gaussian_elimination"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/environment/Dockerfile b/tasks/construct-rlve-integer-linear-system-l6-s4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/environment/instance.json b/tasks/construct-rlve-integer-linear-system-l6-s4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e38dcdf9fb8786376c836100ff5bde93560514ed
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/environment/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[2, 5, 1, 3, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, 3, 5, 0, 0], [2, 5, 0, 4, 3, 0, 0, 3, 0, 3, 4, 0, 2, 0, 2, 5, 4, 0, 0, 0, 0, 3, 3, 0, 0, 0], [4, 5, 5, 0, 3, 0, 0, 0, 0, 0, 3, 4, 3, 3, 3, 0, 5, 0, 0, 4, 1, 0, 0, 0, 3, 3], [0, 0, 2, 2, 5, 0, 0, 2, 0, 4, 0, 0, 0, 2, 2, 1, 2, 0, 2, 3, 0, 0, 0, 0, 1, 0], [2, 5, 0, 1, 5, 0, 0, 0, 2, 0, 1, 4, 0, 2, 5, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 5, 1, 3, 3, 4, 5, 5, 0, 0, 2, 1, 0, 4, 0, 4, 5, 0, 0, 1, 0, 4, 0, 4, 4], [3, 0, 4, 5, 0, 0, 0, 0, 2, 3, 0, 1, 0, 0, 0, 3, 2, 0, 0, 0, 5, 0, 5, 0, 0, 3], [1, 1, 0, 0, 0, 1, 0, 3, 0, 0, 2, 3, 0, 0, 2, 0, 3, 0, 5, 0, 0, 0, 0, 0, 0, 2], [0, 3, 2, 0, 2, 5, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 3, 0], [5, 2, 0, 2, 4, 0, 4, 3, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 3, 2, 0, 0, 1, 3], [0, 4, 0, 2, 1, 4, 0, 2, 0, 1, 0, 3, 0, 0, 2, 4, 0, 5, 5, 0, 4, 2, 0, 0, 5, 0], [3, 0, 0, 5, 0, 1, 1, 2, 2, 4, 4, 0, 5, 0, 0, 0, 0, 5, 4, 4, 4, 0, 0, 0, 3, 0], [0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 5, 0, 4, 4, 0, 5, 4, 1, 3, 0, 0, 5, 0], [4, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 4, 2, 3, 2, 0, 5, 0, 1, 0, 0, 0, 0, 1, 2, 5], [2, 1, 0, 3, 0, 0, 3, 3, 2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 1, 0, 0, 0, 0, 1], [0, 0, 0, 4, 4, 0, 1, 5, 0, 5, 5, 1, 0, 4, 0, 0, 0, 0, 0, 0, 3, 3, 2, 0, 4, 0], [5, 0, 4, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 5, 3, 5, 0, 3, 0, 0, 0, 0], [4, 0, 0, 0, 4, 0, 4, 2, 2, 0, 0, 0, 2, 2, 1, 5, 0, 1, 0, 1, 0, 5, 4, 3, 0, 0], [0, 1, 3, 0, 0, 0, 3, 4, 1, 0, 0, 2, 0, 5, 0, 0, 0, 5, 0, 4, 0, 0, 0, 0, 3, 5], [1, 5, 2, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 4, 4, 0, 0, 0, 0, 4, 3, 4, 4, 0, 4, 3], [4, 0, 4, 5, 0, 1, 4, 0, 0, 0, 0, 0, 0, 1, 0, 1, 5, 0, 0, 5, 0, 3, 5, 0, 0, 3], [2, 4, 0, 0, 0, 3, 0, 5, 1, 5, 3, 0, 5, 4, 0, 0, 0, 5, 0, 0, 5, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0], [0, 4, 2, 0, 3, 5, 0, 0, 2, 0, 1, 0, 4, 3, 4, 4, 0, 0, 0, 0, 2, 2, 1, 0, 2, 1], [2, 5, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 2, 1, 3, 0, 5, 0, 2, 3, 1, 0, 0, 0, 3, 5], [2, 0, 0, 0, 0, 0, 5, 2, 0, 3, 0, 0, 3, 3, 5, 0, 3, 5, 5, 4, 1, 5, 4, 5, 0, 5], [4, 0, 5, 0, 1, 5, 2, 0, 0, 2, 5, 3, 0, 0, 3, 0, 3, 2, 0, 0, 1, 0, 5, 3, 0, 0], [0, 2, 3, 1, 0, 3, 0, 1, 1, 0, 5, 5, 0, 0, 0, 0, 0, 5, 0, 3, 4, 0, 0, 5, 4, 0], [5, 2, 0, 4, 0, 5, 0, 0, 0, 0, 2, 5, 0, 0, 2, 1, 5, 0, 0, 0, 0, 1, 0, 1, 0, 5], [0, 2, 2, 1, 0, 0, 0, 2, 3, 0, 1, 1, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 2, 0], [0, 4, 0, 0, 4, 0, 5, 4, 2, 0, 5, 0, 3, 3, 5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 5], [5, 3, 0, 0, 1, 0, 5, 2, 0, 1, 2, 0, 0, 2, 1, 1, 0, 0, 4, 0, 5, 0, 2, 0, 0, 3], [0, 2, 0, 5, 4, 2, 2, 0, 4, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 1, 5, 0, 2, 2, 3, 0], [0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 1, 0, 0, 5, 3, 0, 0, 1, 5, 0, 0, 0, 0, 0, 3, 0], [0, 3, 1, 0, 0, 0, 1, 0, 0, 0, 4, 2, 0, 1, 3, 3, 5, 1, 3, 4, 2, 2, 0, 5, 0, 5], [0, 0, 5, 0, 1, 4, 0, 4, 0, 3, 5, 0, 0, 1, 4, 3, 1, 5, 0, 3, 5, 3, 0, 5, 4, 3], [0, 1, 3, 3, 0, 5, 5, 5, 1, 1, 4, 0, 0, 5, 5, 4, 4, 0, 0, 0, 0, 4, 4, 5, 1, 2], [5, 0, 2, 2, 4, 4, 0, 0, 4, 3, 5, 5, 5, 1, 0, 4, 1, 0, 5, 0, 0, 5, 4, 4, 0, 0], [2, 0, 0, 4, 1, 0, 3, 0, 4, 0, 2, 0, 5, 0, 3, 4, 4, 5, 0, 5, 2, 3, 0, 0, 0, 0], [3, 5, 1, 5, 0, 2, 0, 0, 0, 0, 0, 4, 5, 0, 0, 2, 0, 5, 0, 3, 1, 2, 4, 0, 0, 0], [3, 3, 5, 1, 0, 3, 0, 0, 1, 0, 0, 3, 3, 2, 5, 4, 5, 3, 1, 5, 3, 0, 1, 0, 0, 0], [0, 4, 4, 0, 1, 3, 0, 4, 0, 0, 4, 0, 2, 0, 0, 1, 2, 4, 4, 0, 3, 0, 0, 0, 0, 2], [0, 3, 3, 5, 2, 0, 5, 1, 4, 3, 0, 2, 1, 0, 1, 1, 1, 2, 5, 3, 0, 4, 0, 0, 3, 0], [4, 4, 0, 0, 1, 0, 0, 3, 0, 0, 0, 5, 5, 1, 0, 5, 1, 0, 1, 0, 0, 0, 5, 1, 5, 3], [0, 0, 0, 4, 3, 3, 0, 0, 0, 3, 3, 4, 1, 0, 2, 1, 0, 0, 1, 4, 3, 4, 0, 0, 0, 2], [0, 2, 0, 0, 4, 5, 0, 1, 2, 5, 4, 3, 0, 0, 0, 0, 4, 2, 0, 4, 2, 4, 1, 3, 0, 2], [5, 0, 5, 3, 0, 4, 0, 0, 5, 3, 5, 3, 3, 0, 0, 0, 0, 2, 5, 2, 0, 5, 1, 1, 0, 3], [4, 2, 3, 0, 5, 0, 1, 4, 3, 2, 2, 0, 3, 0, 0, 1, 2, 3, 0, 2, 0, 5, 3, 0, 0, 0], [1, 0, 2, 4, 2, 4, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 5, 5, 0], [0, 0, 0, 5, 4, 5, 0, 2, 4, 3, 0, 4, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 0, 2, 5, 0, 1, 0, 0, 4, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 5, 2, 0, 0, 2], [3, 0, 0, 0, 0, 0, 5, 3, 0, 0, 0, 2, 0, 0, 4, 0, 3, 0, 4, 4, 2, 4, 1, 0, 3, 0], [4, 0, 5, 4, 0, 0, 4, 4, 1, 3, 2, 5, 0, 2, 5, 5, 0, 3, 4, 5, 0, 0, 5, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1, 0, 1, 1, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0], [3, 4, 0, 4, 2, 0, 3, 3, 5, 1, 0, 1, 0, 0, 4, 0, 1, 0, 5, 0, 0, 0, 2, 4, 0, 2], [5, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 0, 0, 3, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 4], [4, 3, 0, 1, 2, 0, 0, 0, 0, 0, 5, 2, 5, 0, 0, 3, 0, 2, 5, 5, 0, 4, 4, 0, 4, 0]], "rhs": [358, 556, 571, 406, 251, 691, 468, 203, 242, 380, 422, 605, 418, 346, 343, 620, 456, 493, 429, 574, 699, 419, 155, 385, 421, 740, 565, 474, 420, 300, 446, 335, 477, 253, 456, 698, 813, 728, 628, 537, 573, 348, 725, 444, 559, 622, 680, 601, 430, 497, 356, 554, 837, 74, 433, 249, 605], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/instruction.md b/tasks/construct-rlve-integer-linear-system-l6-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..d8d3a9bc27154169036d6f03fcd45efaabc907d5
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/instruction.md
@@ -0,0 +1,62 @@
+Find integers x[0], ..., x[25] satisfying all of the following 57 equations:
+2*x[0] + 5*x[1] + 1*x[2] + 3*x[3] + 4*x[4] + 4*x[10] + 1*x[15] + 3*x[17] + 2*x[21] + 3*x[22] + 5*x[23] = 358
+2*x[0] + 5*x[1] + 4*x[3] + 3*x[4] + 3*x[7] + 3*x[9] + 4*x[10] + 2*x[12] + 2*x[14] + 5*x[15] + 4*x[16] + 3*x[21] + 3*x[22] = 556
+4*x[0] + 5*x[1] + 5*x[2] + 3*x[4] + 3*x[10] + 4*x[11] + 3*x[12] + 3*x[13] + 3*x[14] + 5*x[16] + 4*x[19] + 1*x[20] + 3*x[24] + 3*x[25] = 571
+2*x[2] + 2*x[3] + 5*x[4] + 2*x[7] + 4*x[9] + 2*x[13] + 2*x[14] + 1*x[15] + 2*x[16] + 2*x[18] + 3*x[19] + 1*x[24] = 406
+2*x[0] + 5*x[1] + 1*x[3] + 5*x[4] + 2*x[8] + 1*x[10] + 4*x[11] + 2*x[13] + 5*x[14] + 1*x[19] + 1*x[25] = 251
+5*x[2] + 1*x[3] + 3*x[4] + 3*x[5] + 4*x[6] + 5*x[7] + 5*x[8] + 2*x[11] + 1*x[12] + 4*x[14] + 4*x[16] + 5*x[17] + 1*x[20] + 4*x[22] + 4*x[24] + 4*x[25] = 691
+3*x[0] + 4*x[2] + 5*x[3] + 2*x[8] + 3*x[9] + 1*x[11] + 3*x[15] + 2*x[16] + 5*x[20] + 5*x[22] + 3*x[25] = 468
+1*x[0] + 1*x[1] + 1*x[5] + 3*x[7] + 2*x[10] + 3*x[11] + 2*x[14] + 3*x[16] + 5*x[18] + 2*x[25] = 203
+3*x[1] + 2*x[2] + 2*x[4] + 5*x[5] + 1*x[8] + 1*x[11] + 2*x[14] + 2*x[17] + 2*x[20] + 1*x[22] + 3*x[24] = 242
+5*x[0] + 2*x[1] + 2*x[3] + 4*x[4] + 4*x[6] + 3*x[7] + 1*x[8] + 1*x[11] + 2*x[13] + 2*x[18] + 3*x[20] + 2*x[21] + 1*x[24] + 3*x[25] = 380
+4*x[1] + 2*x[3] + 1*x[4] + 4*x[5] + 2*x[7] + 1*x[9] + 3*x[11] + 2*x[14] + 4*x[15] + 5*x[17] + 5*x[18] + 4*x[20] + 2*x[21] + 5*x[24] = 422
+3*x[0] + 5*x[3] + 1*x[5] + 1*x[6] + 2*x[7] + 2*x[8] + 4*x[9] + 4*x[10] + 5*x[12] + 5*x[17] + 4*x[18] + 4*x[19] + 4*x[20] + 3*x[24] = 605
+1*x[1] + 5*x[8] + 3*x[10] + 5*x[13] + 4*x[15] + 4*x[16] + 5*x[18] + 4*x[19] + 1*x[20] + 3*x[21] + 5*x[24] = 418
+4*x[0] + 2*x[2] + 1*x[5] + 1*x[9] + 4*x[11] + 2*x[12] + 3*x[13] + 2*x[14] + 5*x[16] + 1*x[18] + 1*x[23] + 2*x[24] + 5*x[25] = 346
+2*x[0] + 1*x[1] + 3*x[3] + 3*x[6] + 3*x[7] + 2*x[8] + 5*x[15] + 5*x[19] + 1*x[20] + 1*x[25] = 343
+4*x[3] + 4*x[4] + 1*x[6] + 5*x[7] + 5*x[9] + 5*x[10] + 1*x[11] + 4*x[13] + 3*x[20] + 3*x[21] + 2*x[22] + 4*x[24] = 620
+5*x[0] + 4*x[2] + 3*x[4] + 2*x[5] + 4*x[15] + 4*x[16] + 5*x[17] + 3*x[18] + 5*x[19] + 3*x[21] = 456
+4*x[0] + 4*x[4] + 4*x[6] + 2*x[7] + 2*x[8] + 2*x[12] + 2*x[13] + 1*x[14] + 5*x[15] + 1*x[17] + 1*x[19] + 5*x[21] + 4*x[22] + 3*x[23] = 493
+1*x[1] + 3*x[2] + 3*x[6] + 4*x[7] + 1*x[8] + 2*x[11] + 5*x[13] + 5*x[17] + 4*x[19] + 3*x[24] + 5*x[25] = 429
+1*x[0] + 5*x[1] + 2*x[2] + 1*x[4] + 2*x[7] + 2*x[9] + 2*x[10] + 1*x[11] + 4*x[13] + 4*x[14] + 4*x[19] + 3*x[20] + 4*x[21] + 4*x[22] + 4*x[24] + 3*x[25] = 574
+4*x[0] + 4*x[2] + 5*x[3] + 1*x[5] + 4*x[6] + 1*x[13] + 1*x[15] + 5*x[16] + 5*x[19] + 3*x[21] + 5*x[22] + 3*x[25] = 699
+2*x[0] + 4*x[1] + 3*x[5] + 5*x[7] + 1*x[8] + 5*x[9] + 3*x[10] + 5*x[12] + 4*x[13] + 5*x[17] + 5*x[20] + 1*x[22] = 419
+1*x[6] + 1*x[9] + 5*x[20] + 5*x[24] = 155
+4*x[1] + 2*x[2] + 3*x[4] + 5*x[5] + 2*x[8] + 1*x[10] + 4*x[12] + 3*x[13] + 4*x[14] + 4*x[15] + 2*x[20] + 2*x[21] + 1*x[22] + 2*x[24] + 1*x[25] = 385
+2*x[0] + 5*x[1] + 4*x[7] + 3*x[9] + 2*x[12] + 1*x[13] + 3*x[14] + 5*x[16] + 2*x[18] + 3*x[19] + 1*x[20] + 3*x[24] + 5*x[25] = 421
+2*x[0] + 5*x[6] + 2*x[7] + 3*x[9] + 3*x[12] + 3*x[13] + 5*x[14] + 3*x[16] + 5*x[17] + 5*x[18] + 4*x[19] + 1*x[20] + 5*x[21] + 4*x[22] + 5*x[23] + 5*x[25] = 740
+4*x[0] + 5*x[2] + 1*x[4] + 5*x[5] + 2*x[6] + 2*x[9] + 5*x[10] + 3*x[11] + 3*x[14] + 3*x[16] + 2*x[17] + 1*x[20] + 5*x[22] + 3*x[23] = 565
+2*x[1] + 3*x[2] + 1*x[3] + 3*x[5] + 1*x[7] + 1*x[8] + 5*x[10] + 5*x[11] + 5*x[17] + 3*x[19] + 4*x[20] + 5*x[23] + 4*x[24] = 474
+5*x[0] + 2*x[1] + 4*x[3] + 5*x[5] + 2*x[10] + 5*x[11] + 2*x[14] + 1*x[15] + 5*x[16] + 1*x[21] + 1*x[23] + 5*x[25] = 420
+2*x[1] + 2*x[2] + 1*x[3] + 2*x[7] + 3*x[8] + 1*x[10] + 1*x[11] + 3*x[12] + 1*x[13] + 1*x[20] + 5*x[22] + 2*x[24] = 300
+4*x[1] + 4*x[4] + 5*x[6] + 4*x[7] + 2*x[8] + 5*x[10] + 3*x[12] + 3*x[13] + 5*x[14] + 1*x[22] + 1*x[24] + 5*x[25] = 446
+5*x[0] + 3*x[1] + 1*x[4] + 5*x[6] + 2*x[7] + 1*x[9] + 2*x[10] + 2*x[13] + 1*x[14] + 1*x[15] + 4*x[18] + 5*x[20] + 2*x[22] + 3*x[25] = 335
+2*x[1] + 5*x[3] + 4*x[4] + 2*x[5] + 2*x[6] + 4*x[8] + 5*x[12] + 5*x[18] + 1*x[19] + 5*x[20] + 2*x[22] + 2*x[23] + 3*x[24] = 477
+4*x[6] + 2*x[7] + 1*x[10] + 5*x[13] + 3*x[14] + 1*x[17] + 5*x[18] + 3*x[24] = 253
+3*x[1] + 1*x[2] + 1*x[6] + 4*x[10] + 2*x[11] + 1*x[13] + 3*x[14] + 3*x[15] + 5*x[16] + 1*x[17] + 3*x[18] + 4*x[19] + 2*x[20] + 2*x[21] + 5*x[23] + 5*x[25] = 456
+5*x[2] + 1*x[4] + 4*x[5] + 4*x[7] + 3*x[9] + 5*x[10] + 1*x[13] + 4*x[14] + 3*x[15] + 1*x[16] + 5*x[17] + 3*x[19] + 5*x[20] + 3*x[21] + 5*x[23] + 4*x[24] + 3*x[25] = 698
+1*x[1] + 3*x[2] + 3*x[3] + 5*x[5] + 5*x[6] + 5*x[7] + 1*x[8] + 1*x[9] + 4*x[10] + 5*x[13] + 5*x[14] + 4*x[15] + 4*x[16] + 4*x[21] + 4*x[22] + 5*x[23] + 1*x[24] + 2*x[25] = 813
+5*x[0] + 2*x[2] + 2*x[3] + 4*x[4] + 4*x[5] + 4*x[8] + 3*x[9] + 5*x[10] + 5*x[11] + 5*x[12] + 1*x[13] + 4*x[15] + 1*x[16] + 5*x[18] + 5*x[21] + 4*x[22] + 4*x[23] = 728
+2*x[0] + 4*x[3] + 1*x[4] + 3*x[6] + 4*x[8] + 2*x[10] + 5*x[12] + 3*x[14] + 4*x[15] + 4*x[16] + 5*x[17] + 5*x[19] + 2*x[20] + 3*x[21] = 628
+3*x[0] + 5*x[1] + 1*x[2] + 5*x[3] + 2*x[5] + 4*x[11] + 5*x[12] + 2*x[15] + 5*x[17] + 3*x[19] + 1*x[20] + 2*x[21] + 4*x[22] = 537
+3*x[0] + 3*x[1] + 5*x[2] + 1*x[3] + 3*x[5] + 1*x[8] + 3*x[11] + 3*x[12] + 2*x[13] + 5*x[14] + 4*x[15] + 5*x[16] + 3*x[17] + 1*x[18] + 5*x[19] + 3*x[20] + 1*x[22] = 573
+4*x[1] + 4*x[2] + 1*x[4] + 3*x[5] + 4*x[7] + 4*x[10] + 2*x[12] + 1*x[15] + 2*x[16] + 4*x[17] + 4*x[18] + 3*x[20] + 2*x[25] = 348
+3*x[1] + 3*x[2] + 5*x[3] + 2*x[4] + 5*x[6] + 1*x[7] + 4*x[8] + 3*x[9] + 2*x[11] + 1*x[12] + 1*x[14] + 1*x[15] + 1*x[16] + 2*x[17] + 5*x[18] + 3*x[19] + 4*x[21] + 3*x[24] = 725
+4*x[0] + 4*x[1] + 1*x[4] + 3*x[7] + 5*x[11] + 5*x[12] + 1*x[13] + 5*x[15] + 1*x[16] + 1*x[18] + 5*x[22] + 1*x[23] + 5*x[24] + 3*x[25] = 444
+4*x[3] + 3*x[4] + 3*x[5] + 3*x[9] + 3*x[10] + 4*x[11] + 1*x[12] + 2*x[14] + 1*x[15] + 1*x[18] + 4*x[19] + 3*x[20] + 4*x[21] + 2*x[25] = 559
+2*x[1] + 4*x[4] + 5*x[5] + 1*x[7] + 2*x[8] + 5*x[9] + 4*x[10] + 3*x[11] + 4*x[16] + 2*x[17] + 4*x[19] + 2*x[20] + 4*x[21] + 1*x[22] + 3*x[23] + 2*x[25] = 622
+5*x[0] + 5*x[2] + 3*x[3] + 4*x[5] + 5*x[8] + 3*x[9] + 5*x[10] + 3*x[11] + 3*x[12] + 2*x[17] + 5*x[18] + 2*x[19] + 5*x[21] + 1*x[22] + 1*x[23] + 3*x[25] = 680
+4*x[0] + 2*x[1] + 3*x[2] + 5*x[4] + 1*x[6] + 4*x[7] + 3*x[8] + 2*x[9] + 2*x[10] + 3*x[12] + 1*x[15] + 2*x[16] + 3*x[17] + 2*x[19] + 5*x[21] + 3*x[22] = 601
+1*x[0] + 2*x[2] + 4*x[3] + 2*x[4] + 4*x[5] + 1*x[8] + 3*x[11] + 2*x[16] + 5*x[17] + 2*x[18] + 5*x[23] + 5*x[24] = 430
+5*x[3] + 4*x[4] + 5*x[5] + 2*x[7] + 4*x[8] + 3*x[9] + 4*x[11] + 5*x[17] + 5*x[18] + 5*x[24] = 497
+2*x[4] + 5*x[5] + 1*x[7] + 4*x[10] + 5*x[14] + 1*x[16] + 5*x[21] + 2*x[22] + 2*x[25] = 356
+3*x[0] + 5*x[6] + 3*x[7] + 2*x[11] + 4*x[14] + 3*x[16] + 4*x[18] + 4*x[19] + 2*x[20] + 4*x[21] + 1*x[22] + 3*x[24] = 554
+4*x[0] + 5*x[2] + 4*x[3] + 4*x[6] + 4*x[7] + 1*x[8] + 3*x[9] + 2*x[10] + 5*x[11] + 2*x[13] + 5*x[14] + 5*x[15] + 3*x[17] + 4*x[18] + 5*x[19] + 5*x[22] + 3*x[23] = 837
+4*x[8] + 1*x[11] + 1*x[13] + 1*x[14] + 5*x[18] + 5*x[20] = 74
+3*x[0] + 4*x[1] + 4*x[3] + 2*x[4] + 3*x[6] + 3*x[7] + 5*x[8] + 1*x[9] + 1*x[11] + 4*x[14] + 1*x[16] + 5*x[18] + 2*x[22] + 4*x[23] + 2*x[25] = 433
+5*x[0] + 3*x[7] + 3*x[8] + 3*x[9] + 1*x[10] + 1*x[11] + 3*x[14] + 5*x[15] + 5*x[20] + 4*x[25] = 249
+4*x[0] + 3*x[1] + 1*x[3] + 2*x[4] + 5*x[10] + 2*x[11] + 5*x[12] + 3*x[15] + 2*x[17] + 5*x[18] + 5*x[19] + 4*x[21] + 4*x[22] + 4*x[24] = 605
+
+Answer format: {"x": [x_0, ..., x_25]}  (integers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/solution/solve.sh b/tasks/construct-rlve-integer-linear-system-l6-s4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..db7a3aa6455a7c1e2f1fa5a26fc3a1154ee54ca5
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [5, 2, 20, 25, 11, 10, 24, 13, 3, 21, 12, 13, 14, 5, 9, 4, 16, 6, 2, 22, 5, 24, 17, 6, 17, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/task.toml b/tasks/construct-rlve-integer-linear-system-l6-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..43543726693d30d7ab6add52e17aa16257134345
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-integer-linear-system-l6-s4"
+version = "0.2.0"
+description = "construct/rlve_integer_linear_system"
+authors = []
+keywords = ["rlmath", "construct", "rlve_integer_linear_system"]
+
+[metadata]
+subset = "construct"
+family = "rlve_integer_linear_system"
+problem_key = "integer_linear_system"
+domain = "algebra"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/gaussian_elimination"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/tests/check.py b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..ff19002b3fddc9597f84ee31ef5ffbee5d3fac32
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/check.py
@@ -0,0 +1,10 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = len(inst["coeffs"][0])
+    x = int_list(ans.get("x"), n, name="x")
+    for k, (e, r) in enumerate(zip(inst["coeffs"], inst["rhs"])):
+        if sum(c * v for c, v in zip(e, x)) != r:
+            raise Invalid(f"equation {k} is violated")
+    return None, {}
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/tests/instance.json b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e38dcdf9fb8786376c836100ff5bde93560514ed
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/instance.json
@@ -0,0 +1 @@
+{"coeffs": [[2, 5, 1, 3, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, 3, 5, 0, 0], [2, 5, 0, 4, 3, 0, 0, 3, 0, 3, 4, 0, 2, 0, 2, 5, 4, 0, 0, 0, 0, 3, 3, 0, 0, 0], [4, 5, 5, 0, 3, 0, 0, 0, 0, 0, 3, 4, 3, 3, 3, 0, 5, 0, 0, 4, 1, 0, 0, 0, 3, 3], [0, 0, 2, 2, 5, 0, 0, 2, 0, 4, 0, 0, 0, 2, 2, 1, 2, 0, 2, 3, 0, 0, 0, 0, 1, 0], [2, 5, 0, 1, 5, 0, 0, 0, 2, 0, 1, 4, 0, 2, 5, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 5, 1, 3, 3, 4, 5, 5, 0, 0, 2, 1, 0, 4, 0, 4, 5, 0, 0, 1, 0, 4, 0, 4, 4], [3, 0, 4, 5, 0, 0, 0, 0, 2, 3, 0, 1, 0, 0, 0, 3, 2, 0, 0, 0, 5, 0, 5, 0, 0, 3], [1, 1, 0, 0, 0, 1, 0, 3, 0, 0, 2, 3, 0, 0, 2, 0, 3, 0, 5, 0, 0, 0, 0, 0, 0, 2], [0, 3, 2, 0, 2, 5, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 3, 0], [5, 2, 0, 2, 4, 0, 4, 3, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 3, 2, 0, 0, 1, 3], [0, 4, 0, 2, 1, 4, 0, 2, 0, 1, 0, 3, 0, 0, 2, 4, 0, 5, 5, 0, 4, 2, 0, 0, 5, 0], [3, 0, 0, 5, 0, 1, 1, 2, 2, 4, 4, 0, 5, 0, 0, 0, 0, 5, 4, 4, 4, 0, 0, 0, 3, 0], [0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 5, 0, 4, 4, 0, 5, 4, 1, 3, 0, 0, 5, 0], [4, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 4, 2, 3, 2, 0, 5, 0, 1, 0, 0, 0, 0, 1, 2, 5], [2, 1, 0, 3, 0, 0, 3, 3, 2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 1, 0, 0, 0, 0, 1], [0, 0, 0, 4, 4, 0, 1, 5, 0, 5, 5, 1, 0, 4, 0, 0, 0, 0, 0, 0, 3, 3, 2, 0, 4, 0], [5, 0, 4, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 5, 3, 5, 0, 3, 0, 0, 0, 0], [4, 0, 0, 0, 4, 0, 4, 2, 2, 0, 0, 0, 2, 2, 1, 5, 0, 1, 0, 1, 0, 5, 4, 3, 0, 0], [0, 1, 3, 0, 0, 0, 3, 4, 1, 0, 0, 2, 0, 5, 0, 0, 0, 5, 0, 4, 0, 0, 0, 0, 3, 5], [1, 5, 2, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 4, 4, 0, 0, 0, 0, 4, 3, 4, 4, 0, 4, 3], [4, 0, 4, 5, 0, 1, 4, 0, 0, 0, 0, 0, 0, 1, 0, 1, 5, 0, 0, 5, 0, 3, 5, 0, 0, 3], [2, 4, 0, 0, 0, 3, 0, 5, 1, 5, 3, 0, 5, 4, 0, 0, 0, 5, 0, 0, 5, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0], [0, 4, 2, 0, 3, 5, 0, 0, 2, 0, 1, 0, 4, 3, 4, 4, 0, 0, 0, 0, 2, 2, 1, 0, 2, 1], [2, 5, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 2, 1, 3, 0, 5, 0, 2, 3, 1, 0, 0, 0, 3, 5], [2, 0, 0, 0, 0, 0, 5, 2, 0, 3, 0, 0, 3, 3, 5, 0, 3, 5, 5, 4, 1, 5, 4, 5, 0, 5], [4, 0, 5, 0, 1, 5, 2, 0, 0, 2, 5, 3, 0, 0, 3, 0, 3, 2, 0, 0, 1, 0, 5, 3, 0, 0], [0, 2, 3, 1, 0, 3, 0, 1, 1, 0, 5, 5, 0, 0, 0, 0, 0, 5, 0, 3, 4, 0, 0, 5, 4, 0], [5, 2, 0, 4, 0, 5, 0, 0, 0, 0, 2, 5, 0, 0, 2, 1, 5, 0, 0, 0, 0, 1, 0, 1, 0, 5], [0, 2, 2, 1, 0, 0, 0, 2, 3, 0, 1, 1, 3, 1, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 2, 0], [0, 4, 0, 0, 4, 0, 5, 4, 2, 0, 5, 0, 3, 3, 5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 5], [5, 3, 0, 0, 1, 0, 5, 2, 0, 1, 2, 0, 0, 2, 1, 1, 0, 0, 4, 0, 5, 0, 2, 0, 0, 3], [0, 2, 0, 5, 4, 2, 2, 0, 4, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 1, 5, 0, 2, 2, 3, 0], [0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 1, 0, 0, 5, 3, 0, 0, 1, 5, 0, 0, 0, 0, 0, 3, 0], [0, 3, 1, 0, 0, 0, 1, 0, 0, 0, 4, 2, 0, 1, 3, 3, 5, 1, 3, 4, 2, 2, 0, 5, 0, 5], [0, 0, 5, 0, 1, 4, 0, 4, 0, 3, 5, 0, 0, 1, 4, 3, 1, 5, 0, 3, 5, 3, 0, 5, 4, 3], [0, 1, 3, 3, 0, 5, 5, 5, 1, 1, 4, 0, 0, 5, 5, 4, 4, 0, 0, 0, 0, 4, 4, 5, 1, 2], [5, 0, 2, 2, 4, 4, 0, 0, 4, 3, 5, 5, 5, 1, 0, 4, 1, 0, 5, 0, 0, 5, 4, 4, 0, 0], [2, 0, 0, 4, 1, 0, 3, 0, 4, 0, 2, 0, 5, 0, 3, 4, 4, 5, 0, 5, 2, 3, 0, 0, 0, 0], [3, 5, 1, 5, 0, 2, 0, 0, 0, 0, 0, 4, 5, 0, 0, 2, 0, 5, 0, 3, 1, 2, 4, 0, 0, 0], [3, 3, 5, 1, 0, 3, 0, 0, 1, 0, 0, 3, 3, 2, 5, 4, 5, 3, 1, 5, 3, 0, 1, 0, 0, 0], [0, 4, 4, 0, 1, 3, 0, 4, 0, 0, 4, 0, 2, 0, 0, 1, 2, 4, 4, 0, 3, 0, 0, 0, 0, 2], [0, 3, 3, 5, 2, 0, 5, 1, 4, 3, 0, 2, 1, 0, 1, 1, 1, 2, 5, 3, 0, 4, 0, 0, 3, 0], [4, 4, 0, 0, 1, 0, 0, 3, 0, 0, 0, 5, 5, 1, 0, 5, 1, 0, 1, 0, 0, 0, 5, 1, 5, 3], [0, 0, 0, 4, 3, 3, 0, 0, 0, 3, 3, 4, 1, 0, 2, 1, 0, 0, 1, 4, 3, 4, 0, 0, 0, 2], [0, 2, 0, 0, 4, 5, 0, 1, 2, 5, 4, 3, 0, 0, 0, 0, 4, 2, 0, 4, 2, 4, 1, 3, 0, 2], [5, 0, 5, 3, 0, 4, 0, 0, 5, 3, 5, 3, 3, 0, 0, 0, 0, 2, 5, 2, 0, 5, 1, 1, 0, 3], [4, 2, 3, 0, 5, 0, 1, 4, 3, 2, 2, 0, 3, 0, 0, 1, 2, 3, 0, 2, 0, 5, 3, 0, 0, 0], [1, 0, 2, 4, 2, 4, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 5, 5, 0], [0, 0, 0, 5, 4, 5, 0, 2, 4, 3, 0, 4, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 0, 2, 5, 0, 1, 0, 0, 4, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 5, 2, 0, 0, 2], [3, 0, 0, 0, 0, 0, 5, 3, 0, 0, 0, 2, 0, 0, 4, 0, 3, 0, 4, 4, 2, 4, 1, 0, 3, 0], [4, 0, 5, 4, 0, 0, 4, 4, 1, 3, 2, 5, 0, 2, 5, 5, 0, 3, 4, 5, 0, 0, 5, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1, 0, 1, 1, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0], [3, 4, 0, 4, 2, 0, 3, 3, 5, 1, 0, 1, 0, 0, 4, 0, 1, 0, 5, 0, 0, 0, 2, 4, 0, 2], [5, 0, 0, 0, 0, 0, 0, 3, 3, 3, 1, 1, 0, 0, 3, 5, 0, 0, 0, 0, 5, 0, 0, 0, 0, 4], [4, 3, 0, 1, 2, 0, 0, 0, 0, 0, 5, 2, 5, 0, 0, 3, 0, 2, 5, 5, 0, 4, 4, 0, 4, 0]], "rhs": [358, 556, 571, 406, 251, 691, 468, 203, 242, 380, 422, 605, 418, 346, 343, 620, 456, 493, 429, 574, 699, 419, 155, 385, 421, 740, 565, 474, 420, 300, 446, 335, 477, 253, 456, 698, 813, 728, 628, 537, 573, 348, 725, 444, 559, 622, 680, 601, 430, 497, 356, 554, 837, 74, 433, 249, 605], "family": "rlve_integer_linear_system", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/tests/run.py b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-integer-linear-system-l6-s4/tests/test.sh b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-integer-linear-system-l6-s4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-largest-convex-polygon-l5-s3/instruction.md b/tasks/construct-rlve-largest-convex-polygon-l5-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..17f71720a346bab6afe78a0a6bd9637a0136ec26
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l5-s3/instruction.md
@@ -0,0 +1,32 @@
+You are given 25 points in the plane, indexed 0..24 (distinct, no three collinear):
+0: (20, 17)
+1: (8, 0)
+2: (9, 5)
+3: (16, 4)
+4: (1, 9)
+5: (25, 19)
+6: (7, 16)
+7: (21, 21)
+8: (20, 19)
+9: (21, 18)
+10: (5, 3)
+11: (14, 18)
+12: (25, 0)
+13: (10, 8)
+14: (2, 10)
+15: (16, 9)
+16: (9, 25)
+17: (11, 22)
+18: (6, 16)
+19: (23, 11)
+20: (19, 1)
+21: (0, 3)
+22: (8, 25)
+23: (2, 21)
+24: (13, 24)
+
+The largest subset of these points in convex position has exactly 11 points. Find 11 distinct points that are the vertices of a convex polygon (every chosen point is a vertex of the convex hull of the chosen points).
+
+Answer format: {"indices": [i_1, ..., i_11]}  (any order)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-largest-convex-polygon-l5-s3/task.toml b/tasks/construct-rlve-largest-convex-polygon-l5-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5d99ebee00fc73ea9669b26ce7afe2911c3ee3d9
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l5-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-largest-convex-polygon-l5-s3"
+version = "0.2.0"
+description = "construct/rlve_largest_convex_polygon"
+authors = []
+keywords = ["rlmath", "construct", "rlve_largest_convex_polygon"]
+
+[metadata]
+subset = "construct"
+family = "rlve_largest_convex_polygon"
+problem_key = "largest_convex_subset"
+domain = "discrete_geometry"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/largest_convex_polygon"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-largest-convex-polygon-l5-s4/instruction.md b/tasks/construct-rlve-largest-convex-polygon-l5-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b2c1c316ab0bf869e468f1a96f7c3cedb9f8529f
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l5-s4/instruction.md
@@ -0,0 +1,32 @@
+You are given 25 points in the plane, indexed 0..24 (distinct, no three collinear):
+0: (22, 14)
+1: (22, 23)
+2: (14, 19)
+3: (12, 25)
+4: (25, 1)
+5: (17, 18)
+6: (16, 4)
+7: (25, 16)
+8: (0, 23)
+9: (2, 20)
+10: (15, 17)
+11: (23, 3)
+12: (14, 0)
+13: (20, 16)
+14: (17, 20)
+15: (5, 24)
+16: (6, 1)
+17: (16, 9)
+18: (18, 12)
+19: (3, 2)
+20: (11, 6)
+21: (1, 13)
+22: (13, 12)
+23: (1, 19)
+24: (18, 14)
+
+The largest subset of these points in convex position has exactly 11 points. Find 11 distinct points that are the vertices of a convex polygon (every chosen point is a vertex of the convex hull of the chosen points).
+
+Answer format: {"indices": [i_1, ..., i_11]}  (any order)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-largest-convex-polygon-l5-s4/task.toml b/tasks/construct-rlve-largest-convex-polygon-l5-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..47ed0803e2408222cd240631fca76e57dea2c8e5
--- /dev/null
+++ b/tasks/construct-rlve-largest-convex-polygon-l5-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-largest-convex-polygon-l5-s4"
+version = "0.2.0"
+description = "construct/rlve_largest_convex_polygon"
+authors = []
+keywords = ["rlmath", "construct", "rlve_largest_convex_polygon"]
+
+[metadata]
+subset = "construct"
+family = "rlve_largest_convex_polygon"
+problem_key = "largest_convex_subset"
+domain = "discrete_geometry"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/largest_convex_polygon"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1e3ef6d4b6913ab03cac29c1a50c059e58b8b9bf
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["00110101000", "01100000000", "00000000000", "00001110000", "00000010000", "00101000011"], "B": ["00100100011", "00011000110", "00000000000", "10000000010", "00010101000", "00000001000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/instruction.md b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..7cf3a0cebeee63b077a7a1b6c61e40afd3f55e74
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/instruction.md
@@ -0,0 +1,21 @@
+A and B are 6 x 11 binary matrices (0-indexed, one row per line).
+A:
+00110101000
+01100000000
+00000000000
+00001110000
+00000010000
+00101000011
+B:
+00100100011
+00011000110
+00000000000
+10000000010
+00010101000
+00000001000
+
+Find a permutation a of 0..5 and a permutation b of 0..10 such that A[a[i]][b[j]] = B[i][j] for all 0 <= i < 6, 0 <= j < 11.
+
+Answer format: {"a": [a_0, ...], "b": [b_0, ...]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..23cd27daa2a4ef394c06f82504954c8b1704ce3a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"a": [5, 0, 2, 1, 3, 4], "b": [1, 8, 9, 5, 3, 4, 0, 6, 7, 2, 10]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/task.toml b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..72ce9b3819968be50078ac6bd2146ab27464614d
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-matrix-permutation-equivalence-l4-s0"
+version = "0.2.0"
+description = "construct/rlve_matrix_permutation_equivalence"
+authors = []
+keywords = ["rlmath", "construct", "rlve_matrix_permutation_equivalence"]
+
+[metadata]
+subset = "construct"
+family = "rlve_matrix_permutation_equivalence"
+problem_key = "binary_matrix_permutation_equivalence"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/matrix_permutation_equivalence"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A, B = inst["A"], inst["B"]
+    N, M = len(A), len(A[0])
+    a = int_list(ans.get("a"), N, 0, N - 1, "a")
+    b = int_list(ans.get("b"), M, 0, M - 1, "b")
+    if len(set(a)) != N or len(set(b)) != M:
+        raise Invalid("a and b must be permutations")
+    for i in range(N):
+        for j in range(M):
+            if A[a[i]][b[j]] != B[i][j]:
+                raise Invalid(f"mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1e3ef6d4b6913ab03cac29c1a50c059e58b8b9bf
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["00110101000", "01100000000", "00000000000", "00001110000", "00000010000", "00101000011"], "B": ["00100100011", "00011000110", "00000000000", "10000000010", "00010101000", "00000001000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9776b41ce154cd761b35526997388097b4de9ce6
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["0111010", "1100001"], "B": ["1100110", "1011000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/instruction.md b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3bc8ab2b36cca7c9c9a590a251e7d868fd2d77da
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/instruction.md
@@ -0,0 +1,13 @@
+A and B are 2 x 7 binary matrices (0-indexed, one row per line).
+A:
+0111010
+1100001
+B:
+1100110
+1011000
+
+Find a permutation a of 0..1 and a permutation b of 0..6 such that A[a[i]][b[j]] = B[i][j] for all 0 <= i < 2, 0 <= j < 7.
+
+Answer format: {"a": [a_0, ...], "b": [b_0, ...]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..67efb2257bc5c38ea7150d45115efe725cb3bebc
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"a": [0, 1], "b": [1, 3, 0, 6, 5, 2, 4]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/task.toml b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..363b8ee4f46e1309370da026a7c9a2bab3746b2b
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-matrix-permutation-equivalence-l4-s7"
+version = "0.2.0"
+description = "construct/rlve_matrix_permutation_equivalence"
+authors = []
+keywords = ["rlmath", "construct", "rlve_matrix_permutation_equivalence"]
+
+[metadata]
+subset = "construct"
+family = "rlve_matrix_permutation_equivalence"
+problem_key = "binary_matrix_permutation_equivalence"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/matrix_permutation_equivalence"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A, B = inst["A"], inst["B"]
+    N, M = len(A), len(A[0])
+    a = int_list(ans.get("a"), N, 0, N - 1, "a")
+    b = int_list(ans.get("b"), M, 0, M - 1, "b")
+    if len(set(a)) != N or len(set(b)) != M:
+        raise Invalid("a and b must be permutations")
+    for i in range(N):
+        for j in range(M):
+            if A[a[i]][b[j]] != B[i][j]:
+                raise Invalid(f"mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9776b41ce154cd761b35526997388097b4de9ce6
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["0111010", "1100001"], "B": ["1100110", "1011000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/environment/Dockerfile b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/environment/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9979072e5f2cc629063aff8f55cbd0ac40cb4296
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/environment/instance.json
@@ -0,0 +1 @@
+{"A": ["100000000000", "000000000000", "000000000000", "000001000000", "000000000000", "001000000000", "000000000000", "100000000000"], "B": ["000001000000", "000000000000", "000000000000", "000001000000", "000000100000", "000000000000", "000000000100", "000000000000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/instruction.md b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b06f0a6bcfb1f938b5feadc46cc46eea7b7bdebd
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/instruction.md
@@ -0,0 +1,25 @@
+A and B are 8 x 12 binary matrices (0-indexed, one row per line).
+A:
+100000000000
+000000000000
+000000000000
+000001000000
+000000000000
+001000000000
+000000000000
+100000000000
+B:
+000001000000
+000000000000
+000000000000
+000001000000
+000000100000
+000000000000
+000000000100
+000000000000
+
+Find a permutation a of 0..7 and a permutation b of 0..11 such that A[a[i]][b[j]] = B[i][j] for all 0 <= i < 8, 0 <= j < 12.
+
+Answer format: {"a": [a_0, ...], "b": [b_0, ...]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/solution/solve.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a57b4470c23ef6c527a94b62760e275f8cec16de
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"a": [7, 1, 4, 0, 3, 2, 5, 6], "b": [7, 11, 6, 3, 4, 0, 5, 8, 1, 2, 9, 10]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/task.toml b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5d7d38f4c2cef4b644874528c4a2645b32f638e9
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-matrix-permutation-equivalence-l4-s9"
+version = "0.2.0"
+description = "construct/rlve_matrix_permutation_equivalence"
+authors = []
+keywords = ["rlmath", "construct", "rlve_matrix_permutation_equivalence"]
+
+[metadata]
+subset = "construct"
+family = "rlve_matrix_permutation_equivalence"
+problem_key = "binary_matrix_permutation_equivalence"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/matrix_permutation_equivalence"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/check.py b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..310a1d2c8b6afd7a82a35ba2a4c802c1ce289d03
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    A, B = inst["A"], inst["B"]
+    N, M = len(A), len(A[0])
+    a = int_list(ans.get("a"), N, 0, N - 1, "a")
+    b = int_list(ans.get("b"), M, 0, M - 1, "b")
+    if len(set(a)) != N or len(set(b)) != M:
+        raise Invalid("a and b must be permutations")
+    for i in range(N):
+        for j in range(M):
+            if A[a[i]][b[j]] != B[i][j]:
+                raise Invalid(f"mismatch at ({i}, {j})")
+    return None, {}
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/instance.json b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9979072e5f2cc629063aff8f55cbd0ac40cb4296
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/instance.json
@@ -0,0 +1 @@
+{"A": ["100000000000", "000000000000", "000000000000", "000001000000", "000000000000", "001000000000", "000000000000", "100000000000"], "B": ["000001000000", "000000000000", "000000000000", "000001000000", "000000100000", "000000000000", "000000000100", "000000000000"], "family": "rlve_matrix_permutation_equivalence", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/run.py b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/test.sh b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-matrix-permutation-equivalence-l4-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l1-s3/task.toml b/tasks/construct-rlve-max-achromatic-coloring-l1-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..0a06007a27b0707ad49280d2b2c23c629e7341e4
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l1-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-max-achromatic-coloring-l1-s3"
+version = "0.2.0"
+description = "construct/rlve_max_achromatic_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_max_achromatic_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_max_achromatic_coloring"
+problem_key = "achromatic_number"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/maximum_achromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l5-s2/instruction.md b/tasks/construct-rlve-max-achromatic-coloring-l5-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a110965c43d74276bc3dcc9d2960570f28669012
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l5-s2/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 13 vertices labelled 0..12 and edge list
+[[0, 1], [0, 2], [0, 4], [0, 5], [0, 9], [0, 10], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 9], [1, 10], [1, 11], [2, 3], [2, 4], [2, 7], [2, 9], [2, 10], [2, 11], [2, 12], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [4, 6], [4, 8], [4, 12], [5, 6], [5, 7], [5, 8], [5, 9], [5, 11], [6, 7], [6, 9], [6, 10], [6, 11], [6, 12], [7, 8], [7, 9], [7, 10], [7, 11], [8, 9], [8, 11], [9, 10], [9, 11], [10, 11], [10, 12], [11, 12]]
+
+A complete colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every pair of distinct colours x, y that are used, some edge has one endpoint coloured x and the other coloured y. The largest number of colours in a complete colouring of this graph (its achromatic number) is 9. Give a complete colouring that uses all 9 colours 0..8.
+
+Answer format: {"colors": [c_0, ..., c_12]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l5-s2/task.toml b/tasks/construct-rlve-max-achromatic-coloring-l5-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..4a50cb59d130934f4157d906cde9b9807c8ac4c8
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l5-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-max-achromatic-coloring-l5-s2"
+version = "0.2.0"
+description = "construct/rlve_max_achromatic_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_max_achromatic_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_max_achromatic_coloring"
+problem_key = "achromatic_number"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/maximum_achromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l5-s5/instruction.md b/tasks/construct-rlve-max-achromatic-coloring-l5-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..0af6f3fb7f360474ce0d6b095110d962be2ed6e8
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l5-s5/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 13 vertices labelled 0..12 and edge list
+[[0, 1], [0, 2], [0, 3], [0, 4], [0, 7], [0, 8], [0, 9], [1, 2], [1, 3], [1, 4], [1, 5], [1, 8], [1, 10], [1, 11], [1, 12], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 10], [2, 11], [3, 4], [3, 6], [3, 8], [3, 10], [3, 11], [4, 9], [4, 10], [4, 11], [4, 12], [5, 6], [5, 7], [5, 8], [5, 10], [5, 12], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [7, 8], [7, 9], [7, 10], [7, 11], [8, 11], [8, 12], [9, 10], [9, 11], [9, 12], [10, 11], [10, 12], [11, 12]]
+
+A complete colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every pair of distinct colours x, y that are used, some edge has one endpoint coloured x and the other coloured y. The largest number of colours in a complete colouring of this graph (its achromatic number) is 9. Give a complete colouring that uses all 9 colours 0..8.
+
+Answer format: {"colors": [c_0, ..., c_12]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-max-achromatic-coloring-l5-s5/task.toml b/tasks/construct-rlve-max-achromatic-coloring-l5-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..17a662fecbb024f41434b0087f6c3226a2870df5
--- /dev/null
+++ b/tasks/construct-rlve-max-achromatic-coloring-l5-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-max-achromatic-coloring-l5-s5"
+version = "0.2.0"
+description = "construct/rlve_max_achromatic_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_max_achromatic_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_max_achromatic_coloring"
+problem_key = "achromatic_number"
+domain = "graph_theory"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/maximum_achromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/environment/instance.json b/tasks/construct-rlve-maximum-clique-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8799bc37bebe5042e49f1af3d4d4e313f654bc1e
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 22, "k": 11, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [0, 20], [0, 21], [1, 2], [1, 3], [1, 4], [1, 6], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [2, 3], [2, 4], [2, 6], [2, 8], [2, 9], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 19], [3, 21], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [5, 6], [5, 7], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [5, 21], [6, 7], [6, 8], [6, 9], [6, 10], [6, 12], [6, 13], [6, 14], [6, 16], [6, 18], [6, 19], [6, 20], [6, 21], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 14], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 11], [8, 12], [8, 13], [8, 15], [8, 16], [8, 17], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [9, 20], [9, 21], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 19], [10, 20], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [14, 15], [14, 16], [14, 17], [14, 18], [14, 19], [14, 21], [15, 16], [15, 18], [15, 19], [15, 20], [15, 21], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [17, 18], [17, 19], [17, 20], [17, 21], [18, 19], [18, 20], [19, 20], [19, 21], [20, 21]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/instruction.md b/tasks/construct-rlve-maximum-clique-l3-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3b424262070833fbf9562f5137320e73944a7758
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 22 vertices labelled 0..21 and edge list
+[[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [0, 20], [0, 21], [1, 2], [1, 3], [1, 4], [1, 6], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [2, 3], [2, 4], [2, 6], [2, 8], [2, 9], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 19], [3, 21], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [5, 6], [5, 7], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [5, 21], [6, 7], [6, 8], [6, 9], [6, 10], [6, 12], [6, 13], [6, 14], [6, 16], [6, 18], [6, 19], [6, 20], [6, 21], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 14], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 11], [8, 12], [8, 13], [8, 15], [8, 16], [8, 17], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [9, 20], [9, 21], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 19], [10, 20], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [14, 15], [14, 16], [14, 17], [14, 18], [14, 19], [14, 21], [15, 16], [15, 18], [15, 19], [15, 20], [15, 21], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [17, 18], [17, 19], [17, 20], [17, 21], [18, 19], [18, 20], [19, 20], [19, 21], [20, 21]]
+
+The largest clique in this graph has exactly 11 vertices. Find a clique of size 11: 11 distinct vertices every two of which are adjacent.
+
+Answer format: {"clique": [v_1, ..., v_11]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1a312a4fe7520406625ad25ec4f463096fbde71a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 1, 2, 3, 4, 8, 9, 11, 13, 16, 17]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/task.toml b/tasks/construct-rlve-maximum-clique-l3-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..dccbcdfd5c43b62d36da09d78bbf59eab74916f2
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-maximum-clique-l3-s0"
+version = "0.2.0"
+description = "construct/rlve_maximum_clique"
+authors = []
+keywords = ["rlmath", "construct", "rlve_maximum_clique"]
+
+[metadata]
+subset = "construct"
+family = "rlve_maximum_clique"
+problem_key = "maximum_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/maximum_clique"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/tests/check.py b/tasks/construct-rlve-maximum-clique-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(c)) != len(c):
+        raise Invalid("vertices must be distinct")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} vertices, need {k}")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(len(c)):
+        for j in range(i + 1, len(c)):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/tests/instance.json b/tasks/construct-rlve-maximum-clique-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..8799bc37bebe5042e49f1af3d4d4e313f654bc1e
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 22, "k": 11, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [0, 20], [0, 21], [1, 2], [1, 3], [1, 4], [1, 6], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [2, 3], [2, 4], [2, 6], [2, 8], [2, 9], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [3, 4], [3, 5], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 19], [3, 21], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [5, 6], [5, 7], [5, 8], [5, 9], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [5, 21], [6, 7], [6, 8], [6, 9], [6, 10], [6, 12], [6, 13], [6, 14], [6, 16], [6, 18], [6, 19], [6, 20], [6, 21], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 14], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 11], [8, 12], [8, 13], [8, 15], [8, 16], [8, 17], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [9, 20], [9, 21], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 19], [10, 20], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [13, 21], [14, 15], [14, 16], [14, 17], [14, 18], [14, 19], [14, 21], [15, 16], [15, 18], [15, 19], [15, 20], [15, 21], [16, 17], [16, 18], [16, 19], [16, 20], [16, 21], [17, 18], [17, 19], [17, 20], [17, 21], [18, 19], [18, 20], [19, 20], [19, 21], [20, 21]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/tests/run.py b/tasks/construct-rlve-maximum-clique-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-maximum-clique-l3-s0/tests/test.sh b/tasks/construct-rlve-maximum-clique-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/environment/instance.json b/tasks/construct-rlve-maximum-clique-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..44b154fefb0960ab1aa08f25c75dfbb7c0a10f29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 22, "k": 11, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 10], [1, 11], [1, 12], [1, 15], [1, 16], [1, 17], [1, 19], [1, 21], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [3, 4], [3, 6], [3, 7], [3, 8], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 19], [3, 20], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 16], [4, 18], [4, 19], [4, 20], [4, 21], [5, 6], [5, 7], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 21], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 18], [6, 19], [6, 20], [6, 21], [7, 8], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [9, 21], [10, 11], [10, 12], [10, 13], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [14, 15], [14, 16], [14, 17], [14, 18], [14, 20], [14, 21], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [16, 17], [16, 19], [16, 21], [17, 18], [17, 20], [17, 21], [18, 19], [18, 20], [18, 21], [19, 20], [19, 21], [20, 21]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/instruction.md b/tasks/construct-rlve-maximum-clique-l3-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..193b284ac0f24783ed732d9e66d54355aaf047a2
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 22 vertices labelled 0..21 and edge list
+[[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 10], [1, 11], [1, 12], [1, 15], [1, 16], [1, 17], [1, 19], [1, 21], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [3, 4], [3, 6], [3, 7], [3, 8], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 19], [3, 20], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 16], [4, 18], [4, 19], [4, 20], [4, 21], [5, 6], [5, 7], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 21], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 18], [6, 19], [6, 20], [6, 21], [7, 8], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [9, 21], [10, 11], [10, 12], [10, 13], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [14, 15], [14, 16], [14, 17], [14, 18], [14, 20], [14, 21], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [16, 17], [16, 19], [16, 21], [17, 18], [17, 20], [17, 21], [18, 19], [18, 20], [18, 21], [19, 20], [19, 21], [20, 21]]
+
+The largest clique in this graph has exactly 11 vertices. Find a clique of size 11: 11 distinct vertices every two of which are adjacent.
+
+Answer format: {"clique": [v_1, ..., v_11]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..47c7b7b08dfa27c65c819725df6b318cf0c4bbb7
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 2, 3, 6, 7, 8, 13, 15, 18, 19, 20]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/task.toml b/tasks/construct-rlve-maximum-clique-l3-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..bf5c292ebfdec09cf59b7498abe0a94cb72feba5
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-maximum-clique-l3-s7"
+version = "0.2.0"
+description = "construct/rlve_maximum_clique"
+authors = []
+keywords = ["rlmath", "construct", "rlve_maximum_clique"]
+
+[metadata]
+subset = "construct"
+family = "rlve_maximum_clique"
+problem_key = "maximum_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/maximum_clique"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/tests/check.py b/tasks/construct-rlve-maximum-clique-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(c)) != len(c):
+        raise Invalid("vertices must be distinct")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} vertices, need {k}")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(len(c)):
+        for j in range(i + 1, len(c)):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/tests/instance.json b/tasks/construct-rlve-maximum-clique-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..44b154fefb0960ab1aa08f25c75dfbb7c0a10f29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 22, "k": 11, "edges": [[0, 1], [0, 2], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 10], [1, 11], [1, 12], [1, 15], [1, 16], [1, 17], [1, 19], [1, 21], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19], [2, 20], [3, 4], [3, 6], [3, 7], [3, 8], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 19], [3, 20], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 16], [4, 18], [4, 19], [4, 20], [4, 21], [5, 6], [5, 7], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 21], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 18], [6, 19], [6, 20], [6, 21], [7, 8], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 16], [9, 17], [9, 18], [9, 19], [9, 21], [10, 11], [10, 12], [10, 13], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [11, 12], [11, 13], [11, 15], [11, 16], [11, 17], [11, 18], [11, 19], [11, 20], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 20], [14, 15], [14, 16], [14, 17], [14, 18], [14, 20], [14, 21], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [16, 17], [16, 19], [16, 21], [17, 18], [17, 20], [17, 21], [18, 19], [18, 20], [18, 21], [19, 20], [19, 21], [20, 21]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/tests/run.py b/tasks/construct-rlve-maximum-clique-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-maximum-clique-l3-s7/tests/test.sh b/tasks/construct-rlve-maximum-clique-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/environment/Dockerfile b/tasks/construct-rlve-maximum-clique-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/environment/instance.json b/tasks/construct-rlve-maximum-clique-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3382765cb53aa72edb7fb22dd97d2af54fefca59
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 22, "k": 10, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 20], [3, 21], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 14], [4, 15], [4, 17], [4, 18], [4, 19], [4, 21], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [6, 7], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 19], [6, 20], [6, 21], [7, 9], [7, 10], [7, 11], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 15], [9, 16], [9, 17], [9, 18], [9, 19], [9, 20], [10, 11], [10, 13], [10, 15], [10, 16], [10, 17], [10, 19], [10, 20], [10, 21], [11, 12], [11, 14], [11, 15], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 21], [14, 15], [14, 18], [14, 19], [14, 21], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [16, 18], [16, 19], [16, 20], [16, 21], [17, 18], [17, 19], [17, 20], [18, 19], [18, 20], [18, 21], [19, 21], [20, 21]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/instruction.md b/tasks/construct-rlve-maximum-clique-l3-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c5e93f07d944060b660a238e3dab8a666b3ec728
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 22 vertices labelled 0..21 and edge list
+[[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 20], [3, 21], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 14], [4, 15], [4, 17], [4, 18], [4, 19], [4, 21], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [6, 7], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 19], [6, 20], [6, 21], [7, 9], [7, 10], [7, 11], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 15], [9, 16], [9, 17], [9, 18], [9, 19], [9, 20], [10, 11], [10, 13], [10, 15], [10, 16], [10, 17], [10, 19], [10, 20], [10, 21], [11, 12], [11, 14], [11, 15], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 21], [14, 15], [14, 18], [14, 19], [14, 21], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [16, 18], [16, 19], [16, 20], [16, 21], [17, 18], [17, 19], [17, 20], [18, 19], [18, 20], [18, 21], [19, 21], [20, 21]]
+
+The largest clique in this graph has exactly 10 vertices. Find a clique of size 10: 10 distinct vertices every two of which are adjacent.
+
+Answer format: {"clique": [v_1, ..., v_10]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/solution/solve.sh b/tasks/construct-rlve-maximum-clique-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f013d097f213b2cd21755983cf2eca1fe221753d
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"clique": [0, 1, 2, 3, 4, 7, 9, 10, 11, 17]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/task.toml b/tasks/construct-rlve-maximum-clique-l3-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..9f798e418da2f1cfc4c8a32f93f4d851c989befb
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-maximum-clique-l3-s9"
+version = "0.2.0"
+description = "construct/rlve_maximum_clique"
+authors = []
+keywords = ["rlmath", "construct", "rlve_maximum_clique"]
+
+[metadata]
+subset = "construct"
+family = "rlve_maximum_clique"
+problem_key = "maximum_clique"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/maximum_clique"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/tests/check.py b/tasks/construct-rlve-maximum-clique-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..95e00c78f7c986ba3aecbdc8af3cf8ed221abd05
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/tests/check.py
@@ -0,0 +1,16 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("clique"), None, 0, n - 1, "clique")
+    if len(set(c)) != len(c):
+        raise Invalid("vertices must be distinct")
+    if len(c) < k:
+        raise Invalid(f"clique has {len(c)} vertices, need {k}")
+    es = {(min(u, v), max(u, v)) for u, v in inst["edges"]}
+    for i in range(len(c)):
+        for j in range(i + 1, len(c)):
+            if (min(c[i], c[j]), max(c[i], c[j])) not in es:
+                raise Invalid(f"{c[i]} and {c[j]} are not adjacent")
+    return None, {}
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/tests/instance.json b/tasks/construct-rlve-maximum-clique-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..3382765cb53aa72edb7fb22dd97d2af54fefca59
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 22, "k": 10, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 17], [2, 18], [2, 19], [2, 20], [2, 21], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 14], [3, 15], [3, 16], [3, 17], [3, 18], [3, 20], [3, 21], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 14], [4, 15], [4, 17], [4, 18], [4, 19], [4, 21], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 16], [5, 17], [5, 18], [5, 19], [5, 20], [6, 7], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 19], [6, 20], [6, 21], [7, 9], [7, 10], [7, 11], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [7, 18], [7, 19], [7, 20], [7, 21], [8, 9], [8, 10], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [8, 18], [8, 19], [8, 20], [8, 21], [9, 10], [9, 11], [9, 12], [9, 15], [9, 16], [9, 17], [9, 18], [9, 19], [9, 20], [10, 11], [10, 13], [10, 15], [10, 16], [10, 17], [10, 19], [10, 20], [10, 21], [11, 12], [11, 14], [11, 15], [11, 17], [11, 18], [11, 19], [11, 20], [11, 21], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 18], [12, 19], [12, 20], [12, 21], [13, 14], [13, 15], [13, 16], [13, 17], [13, 18], [13, 19], [13, 21], [14, 15], [14, 18], [14, 19], [14, 21], [15, 16], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [16, 18], [16, 19], [16, 20], [16, 21], [17, 18], [17, 19], [17, 20], [18, 19], [18, 20], [18, 21], [19, 21], [20, 21]], "family": "rlve_maximum_clique", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/tests/run.py b/tasks/construct-rlve-maximum-clique-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-maximum-clique-l3-s9/tests/test.sh b/tasks/construct-rlve-maximum-clique-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-maximum-clique-l3-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s1/instruction.md b/tasks/construct-rlve-min-harmonious-coloring-l4-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..575ce8a5b9b82999e6d8047fd74bd5729b97efad
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l4-s1/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 12 vertices labelled 0..11 and edge list
+[[0, 2], [0, 4], [0, 6], [0, 11], [1, 4], [1, 10], [2, 4], [2, 5], [2, 11], [3, 7], [3, 9], [4, 8], [4, 11], [5, 8], [5, 10], [6, 7]]
+
+A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minimum number of colours in a harmonious colouring of this graph is 7. Give a harmonious colouring using only colours 0..6.
+
+Answer format: {"colors": [c_0, ..., c_11]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s1/task.toml b/tasks/construct-rlve-min-harmonious-coloring-l4-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..05b6c695305105b98907de60da606c06cab9f1f9
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l4-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-min-harmonious-coloring-l4-s1"
+version = "0.2.0"
+description = "construct/rlve_min_harmonious_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_min_harmonious_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_min_harmonious_coloring"
+problem_key = "harmonious_chromatic_number"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/minimum_harmonious_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s6/instruction.md b/tasks/construct-rlve-min-harmonious-coloring-l4-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..bde41f8f880f79b847cb3c03ca360ba9498e789c
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l4-s6/instruction.md
@@ -0,0 +1,8 @@
+An undirected simple graph has 12 vertices labelled 0..11 and edge list
+[[0, 1], [1, 4], [1, 8], [2, 10], [3, 4], [3, 8], [6, 8], [7, 11], [9, 11]]
+
+A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minimum number of colours in a harmonious colouring of this graph is 5. Give a harmonious colouring using only colours 0..4.
+
+Answer format: {"colors": [c_0, ..., c_11]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-min-harmonious-coloring-l4-s6/task.toml b/tasks/construct-rlve-min-harmonious-coloring-l4-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..e341b1f6cc02c40c702cf2a6ffb23ee7bc6d7a43
--- /dev/null
+++ b/tasks/construct-rlve-min-harmonious-coloring-l4-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-min-harmonious-coloring-l4-s6"
+version = "0.2.0"
+description = "construct/rlve_min_harmonious_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_min_harmonious_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_min_harmonious_coloring"
+problem_key = "harmonious_chromatic_number"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/minimum_harmonious_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s7/instruction.md b/tasks/construct-rlve-pairwise-sums-recovery-l2-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b0ad7e681577e50e63183fb5cb94b8aa6536fb35
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s7/instruction.md
@@ -0,0 +1,6 @@
+Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
+15, 15, 19, 18, 14, 17, 13, 11, 16, 14
+
+Answer format: {"numbers": [x_1, ..., x_5]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s7/task.toml b/tasks/construct-rlve-pairwise-sums-recovery-l2-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..a4e4ccad087bbb622bde12f48c4855d4415a6e43
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-pairwise-sums-recovery-l2-s7"
+version = "0.2.0"
+description = "construct/rlve_pairwise_sums_recovery"
+authors = []
+keywords = ["rlmath", "construct", "rlve_pairwise_sums_recovery"]
+
+[metadata]
+subset = "construct"
+family = "rlve_pairwise_sums_recovery"
+problem_key = "poi_squarks_pairwise_sums"
+domain = "combinatorics"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/squ_squarks"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s9/instruction.md b/tasks/construct-rlve-pairwise-sums-recovery-l2-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..f65373b28b48222243519a564469378c242c7ecd
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s9/instruction.md
@@ -0,0 +1,6 @@
+Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
+10, 13, 11, 11, 8, 9, 12, 10, 9, 7
+
+Answer format: {"numbers": [x_1, ..., x_5]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l2-s9/task.toml b/tasks/construct-rlve-pairwise-sums-recovery-l2-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..e62b312fb20dfdac88c21f556836c361d4a2d82e
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l2-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-pairwise-sums-recovery-l2-s9"
+version = "0.2.0"
+description = "construct/rlve_pairwise_sums_recovery"
+authors = []
+keywords = ["rlmath", "construct", "rlve_pairwise_sums_recovery"]
+
+[metadata]
+subset = "construct"
+family = "rlve_pairwise_sums_recovery"
+problem_key = "poi_squarks_pairwise_sums"
+domain = "combinatorics"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/squ_squarks"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s1/instruction.md b/tasks/construct-rlve-pairwise-sums-recovery-l6-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..58b2db8100bfe13cc62436d5767076f540d2ecf8
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s1/instruction.md
@@ -0,0 +1,6 @@
+Find 26 distinct positive integers whose 325 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
+77, 94, 70, 54, 73, 7, 62, 45, 24, 43, 70, 22, 31, 66, 90, 23, 88, 75, 103, 27, 49, 78, 7, 74, 41, 50, 25, 76, 63, 55, 56, 63, 62, 9, 67, 78, 26, 48, 45, 46, 69, 51, 40, 96, 81, 92, 46, 52, 41, 28, 11, 25, 17, 71, 100, 37, 72, 49, 15, 46, 71, 41, 30, 68, 38, 88, 64, 73, 60, 44, 47, 57, 34, 80, 34, 51, 15, 70, 62, 29, 77, 18, 48, 72, 49, 71, 57, 60, 17, 97, 83, 90, 62, 91, 33, 48, 35, 53, 30, 79, 74, 87, 25, 45, 58, 32, 14, 80, 66, 61, 76, 57, 30, 50, 51, 38, 87, 95, 32, 69, 61, 54, 66, 52, 101, 101, 31, 55, 57, 44, 54, 5, 96, 23, 26, 91, 64, 50, 32, 43, 63, 71, 66, 53, 53, 70, 74, 8, 49, 46, 62, 57, 34, 78, 42, 47, 24, 99, 79, 51, 58, 92, 23, 16, 91, 49, 50, 33, 33, 52, 48, 39, 31, 42, 47, 23, 44, 68, 54, 25, 81, 65, 22, 97, 30, 43, 36, 24, 62, 82, 78, 45, 86, 52, 24, 39, 35, 80, 55, 76, 30, 32, 60, 57, 68, 56, 79, 78, 69, 48, 46, 77, 73, 65, 86, 69, 61, 31, 40, 90, 69, 13, 27, 67, 26, 44, 74, 28, 43, 75, 45, 79, 9, 8, 61, 85, 29, 93, 40, 68, 14, 10, 93, 53, 70, 47, 71, 16, 52, 33, 68, 50, 92, 31, 56, 26, 67, 58, 66, 42, 67, 48, 41, 94, 89, 60, 40, 53, 65, 44, 64, 72, 83, 73, 72, 54, 33, 50, 43, 56, 89, 55, 59, 49, 70, 32, 52, 84, 65, 72, 32, 73, 59, 55, 67, 53, 28, 53, 48, 51, 46, 95, 64, 98, 55, 27, 75, 87, 6, 102, 47, 51, 54, 56, 71, 91, 64, 21, 29, 39, 63, 47, 69, 61, 31
+
+Answer format: {"numbers": [x_1, ..., x_26]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-pairwise-sums-recovery-l6-s1/task.toml b/tasks/construct-rlve-pairwise-sums-recovery-l6-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5c66a9b64fda35ab51ac861398558ce2e2eb78ce
--- /dev/null
+++ b/tasks/construct-rlve-pairwise-sums-recovery-l6-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-pairwise-sums-recovery-l6-s1"
+version = "0.2.0"
+description = "construct/rlve_pairwise_sums_recovery"
+authors = []
+keywords = ["rlmath", "construct", "rlve_pairwise_sums_recovery"]
+
+[metadata]
+subset = "construct"
+family = "rlve_pairwise_sums_recovery"
+problem_key = "poi_squarks_pairwise_sums"
+domain = "combinatorics"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/squ_squarks"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l2-s1/instruction.md b/tasks/construct-rlve-polynomial-global-minimum-l2-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4d08d613ca4a6f8ac95330215d71378fc287cdf7
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l2-s1/instruction.md
@@ -0,0 +1,7 @@
+Let f(x) = (2)*x^0 + (-2)*x^1 + (7)*x^2 + (-4)*x^3 + (1)*x^4.
+
+Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
+
+Answer format: {"x0": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l2-s1/task.toml b/tasks/construct-rlve-polynomial-global-minimum-l2-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..de98018fde90fd12e3b66ba16f629080ee50daf1
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l2-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-global-minimum-l2-s1"
+version = "0.2.0"
+description = "construct/rlve_polynomial_global_minimum"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_global_minimum"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_global_minimum"
+problem_key = "polynomial_global_minimum"
+domain = "analysis"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/polynomial_minimum"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l2-s6/instruction.md b/tasks/construct-rlve-polynomial-global-minimum-l2-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..ae4f7b54b83c29024d37ace1df6c408dc0dc791b
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l2-s6/instruction.md
@@ -0,0 +1,7 @@
+Let f(x) = (4)*x^0 + (4)*x^1 + (14)*x^2 + (8)*x^3 + (2)*x^4.
+
+Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
+
+Answer format: {"x0": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l2-s6/task.toml b/tasks/construct-rlve-polynomial-global-minimum-l2-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..2d00c017aa8edd03fc868efc161fb1d8a05196ca
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l2-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-global-minimum-l2-s6"
+version = "0.2.0"
+description = "construct/rlve_polynomial_global_minimum"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_global_minimum"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_global_minimum"
+problem_key = "polynomial_global_minimum"
+domain = "analysis"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/polynomial_minimum"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s0/instruction.md b/tasks/construct-rlve-polynomial-global-minimum-l6-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4a28d668cc1b29c46886ef934a532f452a70a906
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s0/instruction.md
@@ -0,0 +1,7 @@
+Let f(x) = (8203)*x^0 + (-49144)*x^1 + (135397)*x^2 + (-224960)*x^3 + (254822)*x^4 + (-200902)*x^5 + (121543)*x^6 + (-47360)*x^7 + (18890)*x^8 + (-1528)*x^9 + (1530)*x^10 + (316)*x^11 + (93)*x^12 + (14)*x^13 + (1)*x^14.
+
+Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
+
+Answer format: {"x0": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s0/task.toml b/tasks/construct-rlve-polynomial-global-minimum-l6-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..44f5c9ceb7d745f234db20fab3b0b697af437a18
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-global-minimum-l6-s0"
+version = "0.2.0"
+description = "construct/rlve_polynomial_global_minimum"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_global_minimum"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_global_minimum"
+problem_key = "polynomial_global_minimum"
+domain = "analysis"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/polynomial_minimum"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s9/instruction.md b/tasks/construct-rlve-polynomial-global-minimum-l6-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..2e786ccd32e8bde4545be88ca213a497452aaa8c
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s9/instruction.md
@@ -0,0 +1,7 @@
+Let f(x) = (10252)*x^0 + (-38914)*x^1 + (158359)*x^2 + (-194940)*x^3 + (281423)*x^4 + (-188670)*x^5 + (128025)*x^6 + (-52208)*x^7 + (19204)*x^8 + (-5482)*x^9 + (1531)*x^10 + (-412)*x^11 + (93)*x^12 + (-14)*x^13 + (1)*x^14.
+
+Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
+
+Answer format: {"x0": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-global-minimum-l6-s9/task.toml b/tasks/construct-rlve-polynomial-global-minimum-l6-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..56bbb784a95de3ca3f68c94140508dcaad9a82b4
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-global-minimum-l6-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-global-minimum-l6-s9"
+version = "0.2.0"
+description = "construct/rlve_polynomial_global_minimum"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_global_minimum"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_global_minimum"
+problem_key = "polynomial_global_minimum"
+domain = "analysis"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/polynomial_minimum"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l5-s3/instruction.md b/tasks/construct-rlve-polynomial-integer-roots-l5-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..4e4c95ffde705eceeea1c3586aab7db084a1810c
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l5-s3/instruction.md
@@ -0,0 +1,7 @@
+The degree-16 polynomial
+P(x) = (-187342848000)*x^1 + (172339200)*x^2 + (172308088320)*x^3 + (45623493632)*x^4 + (-25618001376)*x^5 + (-7069926288)*x^6 + (1603594256)*x^7 + (378817032)*x^8 + (-47236038)*x^9 + (-9043269)*x^10 + (622218)*x^11 + (104235)*x^12 + (-3386)*x^13 + (-543)*x^14 + (6)*x^15 + (1)*x^16
+can be written as (x - a_1)(x - a_2)...(x - a_16) with integers a_1, ..., a_16 (not necessarily distinct). Find such integers.
+
+Answer format: {"roots": [a_1, ..., a_16]}  (any order, with multiplicity)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l5-s3/task.toml b/tasks/construct-rlve-polynomial-integer-roots-l5-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..84c17f9e3ac2db318792c022be7731c02768f836
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l5-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-integer-roots-l5-s3"
+version = "0.2.0"
+description = "construct/rlve_polynomial_integer_roots"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_integer_roots"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_integer_roots"
+problem_key = "integer_root_factorization"
+domain = "algebra"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/polynomial_factorization"
+source_license = "MIT"
+tags = ["agentic_trivial", "unique_answer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l5-s4/instruction.md b/tasks/construct-rlve-polynomial-integer-roots-l5-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..8505795defa673d19ee0afaf3eb43331db1037e0
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l5-s4/instruction.md
@@ -0,0 +1,7 @@
+The degree-16 polynomial
+P(x) = (-2421619200000)*x^0 + (2376034080000)*x^1 + (2740686472000)*x^2 + (-2651876902400)*x^3 + (-327815915600)*x^4 + (287240744016)*x^5 + (8672913228)*x^6 + (-11618643384)*x^7 + (81489589)*x^8 + (222898876)*x^9 + (-5840936)*x^10 + (-2187684)*x^11 + (82194)*x^12 + (10596)*x^13 + (-476)*x^14 + (-20)*x^15 + (1)*x^16
+can be written as (x - a_1)(x - a_2)...(x - a_16) with integers a_1, ..., a_16 (not necessarily distinct). Find such integers.
+
+Answer format: {"roots": [a_1, ..., a_16]}  (any order, with multiplicity)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-integer-roots-l5-s4/task.toml b/tasks/construct-rlve-polynomial-integer-roots-l5-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..7d25cbf52d6e2937d9d2157ceed604f318868c81
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-integer-roots-l5-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-integer-roots-l5-s4"
+version = "0.2.0"
+description = "construct/rlve_polynomial_integer_roots"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_integer_roots"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_integer_roots"
+problem_key = "integer_root_factorization"
+domain = "algebra"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/polynomial_factorization"
+source_license = "MIT"
+tags = ["agentic_trivial", "unique_answer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s4/instruction.md b/tasks/construct-rlve-polynomial-interpolation-l2-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..2900db4a89f82fc186feed1ba121f47ff15fa140
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s4/instruction.md
@@ -0,0 +1,12 @@
+A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
+f(-1) = 6
+f(-3) = 108
+f(0) = 3
+f(4) = 731
+f(-2) = 23
+
+Find a_0, ..., a_4.
+
+Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-interpolation-l2-s4/task.toml b/tasks/construct-rlve-polynomial-interpolation-l2-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..95bae21e47e4169ff3fe562787f6bad3ef5224db
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l2-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-interpolation-l2-s4"
+version = "0.2.0"
+description = "construct/rlve_polynomial_interpolation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_interpolation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_interpolation"
+problem_key = "lagrange_interpolation_integer"
+domain = "algebra"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/polynomial_interpolation"
+source_license = "MIT"
+tags = ["agentic_trivial", "unique_answer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-interpolation-l6-s2/instruction.md b/tasks/construct-rlve-polynomial-interpolation-l6-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..e6dbb0132424a991f70efe43d8b89db9f9afffab
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l6-s2/instruction.md
@@ -0,0 +1,26 @@
+A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
+f(16) = 22984652334144338783230
+f(-15) = 7573371106088914393723
+f(2) = 929990
+f(5) = 17244921778523
+f(-9) = 780116823665180755
+f(8) = 85006576829218046
+f(12) = 128309895603341528830
+f(6) = 468331090999990
+f(-12) = 137183918001259586686
+f(1) = -5
+f(11) = 26696864093202199235
+f(-17) = 71872561310905048577971
+f(-11) = 28718516398686658267
+f(14) = 2069057298843034121942
+f(-13) = 578246458095618448355
+f(3) = 1595741731
+f(13) = 543645991581742010011
+f(7) = 7610540807807635
+f(17) = 68563639607499959582075
+
+Find a_0, ..., a_18.
+
+Answer format: {"coeffs": [a_0, a_1, ..., a_18]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-interpolation-l6-s2/task.toml b/tasks/construct-rlve-polynomial-interpolation-l6-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..c2258009fd2c648c1d0d3b40147232e12c51e094
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l6-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-interpolation-l6-s2"
+version = "0.2.0"
+description = "construct/rlve_polynomial_interpolation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_interpolation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_interpolation"
+problem_key = "lagrange_interpolation_integer"
+domain = "algebra"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/polynomial_interpolation"
+source_license = "MIT"
+tags = ["agentic_trivial", "unique_answer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-polynomial-interpolation-l6-s5/instruction.md b/tasks/construct-rlve-polynomial-interpolation-l6-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3159cad4a2b2aacadd2fb502efeb8dd36a3e4a33
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l6-s5/instruction.md
@@ -0,0 +1,26 @@
+A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
+f(-11) = 29019317985182945227
+f(-13) = 582648787508798617703
+f(-8) = 95806704210852493
+f(18) = 193001172415606291797347
+f(-14) = 2205488267735449709059
+f(5) = 18465102485675
+f(-10) = 5244993023345535215
+f(2) = 1561523
+f(-3) = 2339082683
+f(13) = 548559588447494638747
+f(-12) = 138401194700368896497
+f(-16) = 24288593680796977680917
+f(-4) = 394049644649
+f(8) = 87152447366211197
+f(-5) = 21209255486935
+f(9) = 727416764768526467
+f(6) = 490422624769439
+f(-7) = 8749701204957347
+f(16) = 23119540281910414717429
+
+Find a_0, ..., a_18.
+
+Answer format: {"coeffs": [a_0, a_1, ..., a_18]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-polynomial-interpolation-l6-s5/task.toml b/tasks/construct-rlve-polynomial-interpolation-l6-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..0bbbba8fe6d021f3b034c58a9cd694f18a5c80dd
--- /dev/null
+++ b/tasks/construct-rlve-polynomial-interpolation-l6-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-interpolation-l6-s5"
+version = "0.2.0"
+description = "construct/rlve_polynomial_interpolation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_interpolation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_interpolation"
+problem_key = "lagrange_interpolation_integer"
+domain = "algebra"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/polynomial_interpolation"
+source_license = "MIT"
+tags = ["agentic_trivial", "unique_answer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s8/instruction.md b/tasks/construct-rlve-prefix-product-permutation-l2-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b16e8c9905f801fac80a4b692bfe306bcc906990
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-s8/instruction.md
@@ -0,0 +1,5 @@
+Find a permutation p_1, ..., p_79 of the integers 1, 2, ..., 79 such that the 79 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_79 are pairwise distinct modulo 79.
+
+Answer format: {"perm": [p_1, ..., p_79]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prefix-product-permutation-l2-s8/task.toml b/tasks/construct-rlve-prefix-product-permutation-l2-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..97f65f82050762eb91dcbe0f822c70b23998f757
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l2-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prefix-product-permutation-l2-s8"
+version = "0.2.0"
+description = "construct/rlve_prefix_product_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prefix_product_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prefix_product_permutation"
+problem_key = "cf487c_prefix_product_sequence"
+domain = "number_theory"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/prefix_product_mod_distinct_permutation"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s0/instruction.md b/tasks/construct-rlve-prefix-product-permutation-l6-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..5f671f3595eb184d8a04a1309f87ee33e080ebe0
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l6-s0/instruction.md
@@ -0,0 +1,5 @@
+Find a permutation p_1, ..., p_26497 of the integers 1, 2, ..., 26497 such that the 26497 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_26497 are pairwise distinct modulo 26497.
+
+Answer format: {"perm": [p_1, ..., p_26497]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s0/task.toml b/tasks/construct-rlve-prefix-product-permutation-l6-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..64b6275b332dd6d111ca35a92c1194d7ad78adb6
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l6-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prefix-product-permutation-l6-s0"
+version = "0.2.0"
+description = "construct/rlve_prefix_product_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prefix_product_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prefix_product_permutation"
+problem_key = "cf487c_prefix_product_sequence"
+domain = "number_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/prefix_product_mod_distinct_permutation"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s7/instruction.md b/tasks/construct-rlve-prefix-product-permutation-l6-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..999af0e8d1ee204b9f41b5265302b48c5560017c
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l6-s7/instruction.md
@@ -0,0 +1,5 @@
+Find a permutation p_1, ..., p_19531 of the integers 1, 2, ..., 19531 such that the 19531 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_19531 are pairwise distinct modulo 19531.
+
+Answer format: {"perm": [p_1, ..., p_19531]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prefix-product-permutation-l6-s7/task.toml b/tasks/construct-rlve-prefix-product-permutation-l6-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..932ad9ee32cbe43a08318ea4d0f0ca30cb8df5a7
--- /dev/null
+++ b/tasks/construct-rlve-prefix-product-permutation-l6-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prefix-product-permutation-l6-s7"
+version = "0.2.0"
+description = "construct/rlve_prefix_product_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prefix_product_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prefix_product_permutation"
+problem_key = "cf487c_prefix_product_sequence"
+domain = "number_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/prefix_product_mod_distinct_permutation"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..743531810faf0c103c05ac69f0a002e7583f6020
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 78, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/instruction.md b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..0e68bbfbfe937a2087bd0cd68b12a6e2184836a8
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/instruction.md
@@ -0,0 +1,5 @@
+Find a permutation p_1, ..., p_78 of the integers 1, 2, ..., 78 such that the 78 prefix sums p_1, p_1+p_2, ..., p_1+p_2+...+p_78 are pairwise distinct modulo 78.
+
+Answer format: {"perm": [p_1, ..., p_78]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0023d58a9f0b592cce31b65759270555932f24b2
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"perm": [78, 1, 76, 3, 74, 5, 72, 7, 70, 9, 68, 11, 66, 13, 64, 15, 62, 17, 60, 19, 58, 21, 56, 23, 54, 25, 52, 27, 50, 29, 48, 31, 46, 33, 44, 35, 42, 37, 40, 39, 38, 41, 36, 43, 34, 45, 32, 47, 30, 49, 28, 51, 26, 53, 24, 55, 22, 57, 20, 59, 18, 61, 16, 63, 14, 65, 12, 67, 10, 69, 8, 71, 6, 73, 4, 75, 2, 77]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/task.toml b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..f2f0cb120b6f229f67856717faed6eb7711a4c9d
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prefix-sum-permutation-l3-s0"
+version = "0.2.0"
+description = "construct/rlve_prefix_sum_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prefix_sum_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prefix_sum_permutation"
+problem_key = "prefix_sum_mod_distinct_permutation"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/prefix_sum_mod_distinct_permutation"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("perm"), n, 1, n, "perm")
+    if len(set(p)) != n:
+        raise Invalid("not a permutation")
+    seen, acc = set(), 0
+    for v in p:
+        acc = (acc + v) % n
+        if acc in seen:
+            raise Invalid(f"prefix sum residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..743531810faf0c103c05ac69f0a002e7583f6020
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 78, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d3c32961df65744c98c2c30b5473e55d6eb860d
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 214, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/instruction.md b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..ac6c35d913350618046b3ff4c167ab99487043c6
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/instruction.md
@@ -0,0 +1,5 @@
+Find a permutation p_1, ..., p_214 of the integers 1, 2, ..., 214 such that the 214 prefix sums p_1, p_1+p_2, ..., p_1+p_2+...+p_214 are pairwise distinct modulo 214.
+
+Answer format: {"perm": [p_1, ..., p_214]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..c7e6c14374106aa77fb8a79916a0eb9d74c4a818
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"perm": [214, 1, 212, 3, 210, 5, 208, 7, 206, 9, 204, 11, 202, 13, 200, 15, 198, 17, 196, 19, 194, 21, 192, 23, 190, 25, 188, 27, 186, 29, 184, 31, 182, 33, 180, 35, 178, 37, 176, 39, 174, 41, 172, 43, 170, 45, 168, 47, 166, 49, 164, 51, 162, 53, 160, 55, 158, 57, 156, 59, 154, 61, 152, 63, 150, 65, 148, 67, 146, 69, 144, 71, 142, 73, 140, 75, 138, 77, 136, 79, 134, 81, 132, 83, 130, 85, 128, 87, 126, 89, 124, 91, 122, 93, 120, 95, 118, 97, 116, 99, 114, 101, 112, 103, 110, 105, 108, 107, 106, 109, 104, 111, 102, 113, 100, 115, 98, 117, 96, 119, 94, 121, 92, 123, 90, 125, 88, 127, 86, 129, 84, 131, 82, 133, 80, 135, 78, 137, 76, 139, 74, 141, 72, 143, 70, 145, 68, 147, 66, 149, 64, 151, 62, 153, 60, 155, 58, 157, 56, 159, 54, 161, 52, 163, 50, 165, 48, 167, 46, 169, 44, 171, 42, 173, 40, 175, 38, 177, 36, 179, 34, 181, 32, 183, 30, 185, 28, 187, 26, 189, 24, 191, 22, 193, 20, 195, 18, 197, 16, 199, 14, 201, 12, 203, 10, 205, 8, 207, 6, 209, 4, 211, 2, 213]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/task.toml b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..95087110507eb6dcd35907da7a453bb9c0674b7c
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prefix-sum-permutation-l3-s7"
+version = "0.2.0"
+description = "construct/rlve_prefix_sum_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prefix_sum_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prefix_sum_permutation"
+problem_key = "prefix_sum_mod_distinct_permutation"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/prefix_sum_mod_distinct_permutation"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("perm"), n, 1, n, "perm")
+    if len(set(p)) != n:
+        raise Invalid("not a permutation")
+    seen, acc = set(), 0
+    for v in p:
+        acc = (acc + v) % n
+        if acc in seen:
+            raise Invalid(f"prefix sum residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d3c32961df65744c98c2c30b5473e55d6eb860d
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 214, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/environment/Dockerfile b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/environment/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5978e6cb72dffa8192c5d2655d581bec962ac420
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 204, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/instruction.md b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..001106ba646e49104d2fbe7d7c12d87d47b6abbc
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/instruction.md
@@ -0,0 +1,5 @@
+Find a permutation p_1, ..., p_204 of the integers 1, 2, ..., 204 such that the 204 prefix sums p_1, p_1+p_2, ..., p_1+p_2+...+p_204 are pairwise distinct modulo 204.
+
+Answer format: {"perm": [p_1, ..., p_204]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/solution/solve.sh b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..fb9b3fafc72f2bec02b2493259f597d34ba17785
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"perm": [204, 1, 202, 3, 200, 5, 198, 7, 196, 9, 194, 11, 192, 13, 190, 15, 188, 17, 186, 19, 184, 21, 182, 23, 180, 25, 178, 27, 176, 29, 174, 31, 172, 33, 170, 35, 168, 37, 166, 39, 164, 41, 162, 43, 160, 45, 158, 47, 156, 49, 154, 51, 152, 53, 150, 55, 148, 57, 146, 59, 144, 61, 142, 63, 140, 65, 138, 67, 136, 69, 134, 71, 132, 73, 130, 75, 128, 77, 126, 79, 124, 81, 122, 83, 120, 85, 118, 87, 116, 89, 114, 91, 112, 93, 110, 95, 108, 97, 106, 99, 104, 101, 102, 103, 100, 105, 98, 107, 96, 109, 94, 111, 92, 113, 90, 115, 88, 117, 86, 119, 84, 121, 82, 123, 80, 125, 78, 127, 76, 129, 74, 131, 72, 133, 70, 135, 68, 137, 66, 139, 64, 141, 62, 143, 60, 145, 58, 147, 56, 149, 54, 151, 52, 153, 50, 155, 48, 157, 46, 159, 44, 161, 42, 163, 40, 165, 38, 167, 36, 169, 34, 171, 32, 173, 30, 175, 28, 177, 26, 179, 24, 181, 22, 183, 20, 185, 18, 187, 16, 189, 14, 191, 12, 193, 10, 195, 8, 197, 6, 199, 4, 201, 2, 203]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/task.toml b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..40fb370c497fee7e5788de51fce3603f943d26c6
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prefix-sum-permutation-l3-s9"
+version = "0.2.0"
+description = "construct/rlve_prefix_sum_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prefix_sum_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prefix_sum_permutation"
+problem_key = "prefix_sum_mod_distinct_permutation"
+domain = "number_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/prefix_sum_mod_distinct_permutation"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/check.py b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..60c3e0996cdfa8673fd7f34ad70cccb789b17654
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/check.py
@@ -0,0 +1,15 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    p = int_list(ans.get("perm"), n, 1, n, "perm")
+    if len(set(p)) != n:
+        raise Invalid("not a permutation")
+    seen, acc = set(), 0
+    for v in p:
+        acc = (acc + v) % n
+        if acc in seen:
+            raise Invalid(f"prefix sum residue {acc} repeats")
+        seen.add(acc)
+    return None, {}
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/instance.json b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5978e6cb72dffa8192c5d2655d581bec962ac420
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 204, "family": "rlve_prefix_sum_permutation", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/run.py b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/test.sh b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prefix-sum-permutation-l3-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l2-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l2-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1bea5bc48b0a56b4887492a380033d5bf2042643
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/environment/instance.json
@@ -0,0 +1 @@
+{"n": 30, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/instruction.md b/tasks/construct-rlve-prime-graph-coloring-l2-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c17ab0a21c952672629ab901406502ae39a6730e
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/instruction.md
@@ -0,0 +1,5 @@
+Consider the graph on vertices 1, 2, ..., 30 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
+
+Answer format: {"colors": [c_1, c_2, ..., c_30]}  (the i-th entry is the colour of vertex i)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l2-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a45f6ca7251a80f6b37ac0d03a094dc091a0fd59
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/task.toml b/tasks/construct-rlve-prime-graph-coloring-l2-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..aae1a267b412508d472c5a3da782a2fcff6ed25f
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prime-graph-coloring-l2-s1"
+version = "0.2.0"
+description = "construct/rlve_prime_graph_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prime_graph_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prime_graph_coloring"
+problem_key = "prime_distance_graph_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/prime_graph_minimum_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    sieve = [True] * (n + 1)
+    sieve[0] = False
+    if n >= 1:
+        sieve[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if sieve[i]:
+            for j in range(i * i, n + 1, i):
+                sieve[j] = False
+    for p in range(2, n):
+        if sieve[p]:
+            for u in range(n - p):
+                if c[u] == c[u + p]:
+                    raise Invalid(f"vertices {u + 1} and {u + p + 1} (difference {p}) share a colour")
+    return None, {}
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1bea5bc48b0a56b4887492a380033d5bf2042643
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/instance.json
@@ -0,0 +1 @@
+{"n": 30, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l2-s6/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l2-s6/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..18b7eb80791cb7d797f103ba477e088a8b727ad3
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/environment/instance.json
@@ -0,0 +1 @@
+{"n": 21, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/instruction.md b/tasks/construct-rlve-prime-graph-coloring-l2-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..07b581b844068f8123501785e1673e2a79675c90
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/instruction.md
@@ -0,0 +1,5 @@
+Consider the graph on vertices 1, 2, ..., 21 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
+
+Answer format: {"colors": [c_1, c_2, ..., c_21]}  (the i-th entry is the colour of vertex i)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l2-s6/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f73dd23cc5b6f068448088d772071e32709bcb03
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/task.toml b/tasks/construct-rlve-prime-graph-coloring-l2-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..ae8041ecfb04f37f945faee038110e37711caf15
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prime-graph-coloring-l2-s6"
+version = "0.2.0"
+description = "construct/rlve_prime_graph_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prime_graph_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prime_graph_coloring"
+problem_key = "prime_distance_graph_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/prime_graph_minimum_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    sieve = [True] * (n + 1)
+    sieve[0] = False
+    if n >= 1:
+        sieve[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if sieve[i]:
+            for j in range(i * i, n + 1, i):
+                sieve[j] = False
+    for p in range(2, n):
+        if sieve[p]:
+            for u in range(n - p):
+                if c[u] == c[u + p]:
+                    raise Invalid(f"vertices {u + 1} and {u + p + 1} (difference {p}) share a colour")
+    return None, {}
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..18b7eb80791cb7d797f103ba477e088a8b727ad3
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/instance.json
@@ -0,0 +1 @@
+{"n": 21, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s6/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s8/instruction.md b/tasks/construct-rlve-prime-graph-coloring-l2-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..1f36c685cfd40c48d7b815963fb99cc5845a18ce
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s8/instruction.md
@@ -0,0 +1,5 @@
+Consider the graph on vertices 1, 2, ..., 28 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
+
+Answer format: {"colors": [c_1, c_2, ..., c_28]}  (the i-th entry is the colour of vertex i)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prime-graph-coloring-l2-s8/task.toml b/tasks/construct-rlve-prime-graph-coloring-l2-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..d7b805039e367b31431db63d8fd6c774081143c2
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l2-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prime-graph-coloring-l2-s8"
+version = "0.2.0"
+description = "construct/rlve_prime_graph_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prime_graph_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prime_graph_coloring"
+problem_key = "prime_distance_graph_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/prime_graph_minimum_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l6-s0/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l6-s0/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4bb0d2c589f5859e3cf59aa0eed9d5f53cec8404
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/environment/instance.json
@@ -0,0 +1 @@
+{"n": 866, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/instruction.md b/tasks/construct-rlve-prime-graph-coloring-l6-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..c4b49ab6d83deda4c9c185353f18c01f3c131d51
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/instruction.md
@@ -0,0 +1,5 @@
+Consider the graph on vertices 1, 2, ..., 866 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
+
+Answer format: {"colors": [c_1, c_2, ..., c_866]}  (the i-th entry is the colour of vertex i)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l6-s0/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..79f48577eb0c34e88df1ef2c367c09c70fbe50a5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/task.toml b/tasks/construct-rlve-prime-graph-coloring-l6-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..0d1159482095b2cbb6ee0af1ac455292c0c9d1c3
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prime-graph-coloring-l6-s0"
+version = "0.2.0"
+description = "construct/rlve_prime_graph_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prime_graph_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prime_graph_coloring"
+problem_key = "prime_distance_graph_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/prime_graph_minimum_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    sieve = [True] * (n + 1)
+    sieve[0] = False
+    if n >= 1:
+        sieve[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if sieve[i]:
+            for j in range(i * i, n + 1, i):
+                sieve[j] = False
+    for p in range(2, n):
+        if sieve[p]:
+            for u in range(n - p):
+                if c[u] == c[u + p]:
+                    raise Invalid(f"vertices {u + 1} and {u + p + 1} (difference {p}) share a colour")
+    return None, {}
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..4bb0d2c589f5859e3cf59aa0eed9d5f53cec8404
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/instance.json
@@ -0,0 +1 @@
+{"n": 866, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s0/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l6-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l6-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a9c2d73850268bfa7a47d61718b880f617d76db1
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/environment/instance.json
@@ -0,0 +1 @@
+{"n": 1053, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/instruction.md b/tasks/construct-rlve-prime-graph-coloring-l6-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..1ceb27250aeb0ab0ed1add52ff1afc57276a14fb
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/instruction.md
@@ -0,0 +1,5 @@
+Consider the graph on vertices 1, 2, ..., 1053 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
+
+Answer format: {"colors": [c_1, c_2, ..., c_1053]}  (the i-th entry is the colour of vertex i)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l6-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..da092714c58dc74559ce918f27d305b9237d9cc9
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/task.toml b/tasks/construct-rlve-prime-graph-coloring-l6-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..2cfad14fd70a86885a76fab1655bb32234d23c79
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prime-graph-coloring-l6-s7"
+version = "0.2.0"
+description = "construct/rlve_prime_graph_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prime_graph_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prime_graph_coloring"
+problem_key = "prime_distance_graph_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/prime_graph_minimum_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    sieve = [True] * (n + 1)
+    sieve[0] = False
+    if n >= 1:
+        sieve[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if sieve[i]:
+            for j in range(i * i, n + 1, i):
+                sieve[j] = False
+    for p in range(2, n):
+        if sieve[p]:
+            for u in range(n - p):
+                if c[u] == c[u + p]:
+                    raise Invalid(f"vertices {u + 1} and {u + p + 1} (difference {p}) share a colour")
+    return None, {}
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..a9c2d73850268bfa7a47d61718b880f617d76db1
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/instance.json
@@ -0,0 +1 @@
+{"n": 1053, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/environment/Dockerfile b/tasks/construct-rlve-prime-graph-coloring-l6-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/environment/instance.json b/tasks/construct-rlve-prime-graph-coloring-l6-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..282e1c930d5e1918ca7e8b766d61446e52d3be5d
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/environment/instance.json
@@ -0,0 +1 @@
+{"n": 1884, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/instruction.md b/tasks/construct-rlve-prime-graph-coloring-l6-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..390f9c873839933555e902b08202e953e98f063e
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/instruction.md
@@ -0,0 +1,5 @@
+Consider the graph on vertices 1, 2, ..., 1884 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
+
+Answer format: {"colors": [c_1, c_2, ..., c_1884]}  (the i-th entry is the colour of vertex i)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/solution/solve.sh b/tasks/construct-rlve-prime-graph-coloring-l6-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..a70f41ba45299c2f01da2a7c6aa58ac0afe07cad
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 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2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/task.toml b/tasks/construct-rlve-prime-graph-coloring-l6-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..3f112c1b21952723899fd2138677489ff02d4c72
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prime-graph-coloring-l6-s9"
+version = "0.2.0"
+description = "construct/rlve_prime_graph_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prime_graph_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prime_graph_coloring"
+problem_key = "prime_distance_graph_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/prime_graph_minimum_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/check.py b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..b3736f1375f1862241999142c975ced361b8fcb5
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/check.py
@@ -0,0 +1,20 @@
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    n, k = inst["n"], inst["k"]
+    c = int_list(ans.get("colors"), n, 0, k - 1, "colors")
+    sieve = [True] * (n + 1)
+    sieve[0] = False
+    if n >= 1:
+        sieve[1] = False
+    for i in range(2, int(n ** 0.5) + 1):
+        if sieve[i]:
+            for j in range(i * i, n + 1, i):
+                sieve[j] = False
+    for p in range(2, n):
+        if sieve[p]:
+            for u in range(n - p):
+                if c[u] == c[u + p]:
+                    raise Invalid(f"vertices {u + 1} and {u + p + 1} (difference {p}) share a colour")
+    return None, {}
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/instance.json b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..282e1c930d5e1918ca7e8b766d61446e52d3be5d
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/instance.json
@@ -0,0 +1 @@
+{"n": 1884, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/run.py b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/test.sh b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-prime-graph-coloring-l6-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s0/instruction.md b/tasks/construct-rlve-round-robin-scores-l4-s0/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..e154688f32f18679befff29ec75397501c587869
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s0/instruction.md
@@ -0,0 +1,10 @@
+Construct an 13 x 13 matrix A (0-indexed) with entries in {0, 1, 2} such that
+1. A[i][i] = 0 for all i;
+2. A[i][j] + A[j][i] = 2 for all i != j;
+3. W[i] = 3 * #{j : A[i][j] = 2} + 1 * #{j : A[i][j] = 1} equals the target below for every i.
+
+Target W = [22, 20, 11, 20, 22, 13, 13, 12, 10, 15, 11, 13, 14]  (W[0], ..., W[12])
+
+Answer format: {"A": [row_0, ..., row_12]}  where each row is a string of 13 digits from 0/1/2
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s0/task.toml b/tasks/construct-rlve-round-robin-scores-l4-s0/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..7acf4f7e98c01d9f34dff305bef3b4b93fd64d65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s0/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-round-robin-scores-l4-s0"
+version = "0.2.0"
+description = "construct/rlve_round_robin_scores"
+authors = []
+keywords = ["rlmath", "construct", "rlve_round_robin_scores"]
+
+[metadata]
+subset = "construct"
+family = "rlve_round_robin_scores"
+problem_key = "tournament_score_realisation_3_1_0"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/round_robin"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l4-s7/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l4-s7/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b7808a57b2a5daeaaa953bc2ab465c104e55e97a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/environment/instance.json
@@ -0,0 +1 @@
+{"W": [14, 17, 12, 26, 12, 20, 11, 13, 11, 18, 13, 19, 12], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/instruction.md b/tasks/construct-rlve-round-robin-scores-l4-s7/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a713564f6cefa425e7517abc4466a7ac30651fa0
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/instruction.md
@@ -0,0 +1,10 @@
+Construct an 13 x 13 matrix A (0-indexed) with entries in {0, 1, 2} such that
+1. A[i][i] = 0 for all i;
+2. A[i][j] + A[j][i] = 2 for all i != j;
+3. W[i] = 3 * #{j : A[i][j] = 2} + 1 * #{j : A[i][j] = 1} equals the target below for every i.
+
+Target W = [14, 17, 12, 26, 12, 20, 11, 13, 11, 18, 13, 19, 12]  (W[0], ..., W[12])
+
+Answer format: {"A": [row_0, ..., row_12]}  where each row is a string of 13 digits from 0/1/2
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l4-s7/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..0b4b0747b56fccdbfcbf4b76002e5272672911af
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["0121001120012", "1021212121000", "0000212100210", "1120111222222", "2001001112011", "2111201211112", "1001110110112", "1110101021201", "0020111001102", "2120012110112", "2200211011000", "1210111221201", "0220100100210"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/task.toml b/tasks/construct-rlve-round-robin-scores-l4-s7/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..0d8bc6e06327fc0bc30e4063d7766067a90e9c5d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-round-robin-scores-l4-s7"
+version = "0.2.0"
+description = "construct/rlve_round_robin_scores"
+authors = []
+keywords = ["rlmath", "construct", "rlve_round_robin_scores"]
+
+[metadata]
+subset = "construct"
+family = "rlve_round_robin_scores"
+problem_key = "tournament_score_realisation_3_1_0"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/round_robin"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/tests/check.py b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b7808a57b2a5daeaaa953bc2ab465c104e55e97a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/instance.json
@@ -0,0 +1 @@
+{"W": [14, 17, 12, 26, 12, 20, 11, 13, 11, 18, 13, 19, 12], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/tests/run.py b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s7/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s7/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/environment/Dockerfile b/tasks/construct-rlve-round-robin-scores-l4-s9/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/environment/instance.json b/tasks/construct-rlve-round-robin-scores-l4-s9/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..13ebbe9483a7579d5289df9f9dc7a7b518a60a20
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/environment/instance.json
@@ -0,0 +1 @@
+{"W": [10, 12, 12, 12, 12, 12, 12, 14, 12, 12, 16, 12, 11], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/instruction.md b/tasks/construct-rlve-round-robin-scores-l4-s9/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..f85bf9d4b956c77ff0e7672e82ea49af0e5cccfe
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/instruction.md
@@ -0,0 +1,10 @@
+Construct an 13 x 13 matrix A (0-indexed) with entries in {0, 1, 2} such that
+1. A[i][i] = 0 for all i;
+2. A[i][j] + A[j][i] = 2 for all i != j;
+3. W[i] = 3 * #{j : A[i][j] = 2} + 1 * #{j : A[i][j] = 1} equals the target below for every i.
+
+Target W = [10, 12, 12, 12, 12, 12, 12, 14, 12, 12, 16, 12, 11]  (W[0], ..., W[12])
+
+Answer format: {"A": [row_0, ..., row_12]}  where each row is a string of 13 digits from 0/1/2
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/solution/solve.sh b/tasks/construct-rlve-round-robin-scores-l4-s9/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..7fe7955862a9078e255bb072aa7a8ce8c23ba786
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"A": ["0111111011011", "1011111111111", "1101111111111", "1110111111111", "1111011111111", "1111101111111", "1111110111111", "2111111011111", "1111111101111", "1111111110111", "2111111111012", "1111111111101", "1111111111010"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/task.toml b/tasks/construct-rlve-round-robin-scores-l4-s9/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5ab9f752749f3c0d94dd0a86968958559a5a1f73
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-round-robin-scores-l4-s9"
+version = "0.2.0"
+description = "construct/rlve_round_robin_scores"
+authors = []
+keywords = ["rlmath", "construct", "rlve_round_robin_scores"]
+
+[metadata]
+subset = "construct"
+family = "rlve_round_robin_scores"
+problem_key = "tournament_score_realisation_3_1_0"
+domain = "combinatorics"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/round_robin"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/tests/check.py b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..214446acaa90ce170daad3989b42317353060f9d
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/check.py
@@ -0,0 +1,24 @@
+from run import Invalid
+
+
+def check(inst, ans):
+    W = inst["W"]
+    n = len(W)
+    A = ans.get("A")
+    if not isinstance(A, list) or len(A) != n:
+        raise Invalid(f"A must be a list of {n} strings")
+    for r in A:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"0", "1", "2"}:
+            raise Invalid(f"each row must be a string of {n} digits 0/1/2")
+    for i in range(n):
+        if A[i][i] != "0":
+            raise Invalid("diagonal must be 0")
+        w = 0
+        for j in range(n):
+            if i != j:
+                if int(A[i][j]) + int(A[j][i]) != 2:
+                    raise Invalid(f"A[{i}][{j}] + A[{j}][{i}] != 2")
+                w += 3 * (A[i][j] == "2") + (A[i][j] == "1")
+        if w != W[i]:
+            raise Invalid(f"W[{i}] = {w}, need {W[i]}")
+    return None, {}
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/tests/instance.json b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..13ebbe9483a7579d5289df9f9dc7a7b518a60a20
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/instance.json
@@ -0,0 +1 @@
+{"W": [10, 12, 12, 12, 12, 12, 12, 14, 12, 12, 16, 12, 11], "family": "rlve_round_robin_scores", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/tests/run.py b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-round-robin-scores-l4-s9/tests/test.sh b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-round-robin-scores-l4-s9/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l3-s2/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l3-s2/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5cdcbbf9bf6f331f48bf7c5b8c03dc84a1257a49
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/environment/instance.json
@@ -0,0 +1 @@
+{"K": 91760, "n_max": 105, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/instruction.md b/tasks/construct-rlve-shortest-path-count-l3-s2/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..a32f1df03af3bb6f50c0e010b396a276a2309e2f
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/instruction.md
@@ -0,0 +1,5 @@
+Construct a simple undirected graph on N vertices, numbered 1..N, with N < 106, such that the number of shortest paths between vertex 1 and vertex 2 is exactly 91760. (Vertex 2 must be reachable from vertex 1.)
+
+Answer format: {"n": N, "adj": [row_1, ..., row_N]} where row_i is a string of length N over {'Y','N'}; the j-th character of row_i is 'Y' iff vertices i and j are adjacent. The matrix must be symmetric with 'N' on the diagonal.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l3-s2/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..48b1e83f9a080d6e04c9c96c252ef71bb3867e90
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"n": 51, "adj": ["NNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "YNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNN", "NNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNYNNNNNNN", "NNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNYNNNNNNN", "NNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNYNNNNNN", "NNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNYNNNNNN", "NNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNYNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNYNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNY", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNY", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNN", "NNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNN", "NNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNN", "NNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNN", "NNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNN", "NNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNNYNYNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNYNYNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNYNYN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNY", "NYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/task.toml b/tasks/construct-rlve-shortest-path-count-l3-s2/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..5e62d2b6710a7ca0871ed6fee1070a85077395b4
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-shortest-path-count-l3-s2"
+version = "0.2.0"
+description = "construct/rlve_shortest_path_count"
+authors = []
+keywords = ["rlmath", "construct", "rlve_shortest_path_count"]
+
+[metadata]
+subset = "construct"
+family = "rlve_shortest_path_count"
+problem_key = "cf388b_shortest_path_count"
+domain = "combinatorics"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/shortest_path_count_construction"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/tests/check.py b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/check.py
@@ -0,0 +1,34 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    n = as_int(ans.get("n"), "n", lo=2, hi=inst["n_max"])
+    adj = ans.get("adj")
+    if not isinstance(adj, list) or len(adj) != n:
+        raise Invalid(f"adj must be a list of {n} strings")
+    for r in adj:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"Y", "N"}:
+            raise Invalid("each row must be a string of length n over {'Y','N'}")
+    for i in range(n):
+        if adj[i][i] != "N":
+            raise Invalid("self-loop")
+        for j in range(i + 1, n):
+            if adj[i][j] != adj[j][i]:
+                raise Invalid("matrix not symmetric")
+    nb = [[j for j in range(n) if adj[i][j] == "Y"] for i in range(n)]
+    dist = [-1] * n
+    cnt = [0] * n
+    dist[0], cnt[0] = 0, 1
+    q = [0]
+    for u in q:  # BFS with exact (Python int) path counts
+        for v in nb[u]:
+            if dist[v] < 0:
+                dist[v] = dist[u] + 1
+                q.append(v)
+            if dist[v] == dist[u] + 1:
+                cnt[v] += cnt[u]
+    if dist[1] < 0:
+        raise Invalid("vertex 2 is unreachable from vertex 1")
+    if cnt[1] != inst["K"]:
+        raise Invalid(f"{cnt[1]} shortest paths, need {inst['K']}")
+    return None, {}
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5cdcbbf9bf6f331f48bf7c5b8c03dc84a1257a49
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/instance.json
@@ -0,0 +1 @@
+{"K": 91760, "n_max": 105, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/tests/run.py b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s2/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s2/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/environment/Dockerfile b/tasks/construct-rlve-shortest-path-count-l3-s5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/environment/instance.json b/tasks/construct-rlve-shortest-path-count-l3-s5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ffa31d6e8adcd76ac4058601ae01fb7e4742f0db
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/environment/instance.json
@@ -0,0 +1 @@
+{"K": 79878, "n_max": 105, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/instruction.md b/tasks/construct-rlve-shortest-path-count-l3-s5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..499425c7ad22bf83af4c66b470bf721f40efad80
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/instruction.md
@@ -0,0 +1,5 @@
+Construct a simple undirected graph on N vertices, numbered 1..N, with N < 106, such that the number of shortest paths between vertex 1 and vertex 2 is exactly 79878. (Vertex 2 must be reachable from vertex 1.)
+
+Answer format: {"n": N, "adj": [row_1, ..., row_N]} where row_i is a string of length N over {'Y','N'}; the j-th character of row_i is 'Y' iff vertices i and j are adjacent. The matrix must be symmetric with 'N' on the diagonal.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/solution/solve.sh b/tasks/construct-rlve-shortest-path-count-l3-s5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..e0531d8ae9650b9d94355fb0039f4aa02f4ca717
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"n": 51, "adj": ["NNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNY", "YNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNN", "YNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNN", "NNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNYNNNNN", "NNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNNYNNNNN", "NNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNYNNNN", "NNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNYNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNYYNNNNNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNY", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNY", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNNNNN", "NNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNN", "NNNNYYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNN", "NNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNNYNYNNNN", "NNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNNYNYNNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNNNNYNYNN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYN", "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNY", "NYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYYNNNNNNNNNNNNNNNYN"]}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/task.toml b/tasks/construct-rlve-shortest-path-count-l3-s5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..c2c323f0b590e977860f330942ac499ac72a9737
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-shortest-path-count-l3-s5"
+version = "0.2.0"
+description = "construct/rlve_shortest_path_count"
+authors = []
+keywords = ["rlmath", "construct", "rlve_shortest_path_count"]
+
+[metadata]
+subset = "construct"
+family = "rlve_shortest_path_count"
+problem_key = "cf388b_shortest_path_count"
+domain = "combinatorics"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/shortest_path_count_construction"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/tests/check.py b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..c59d4c4f4bb4e824a2019380643a5b3ade0ca974
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/check.py
@@ -0,0 +1,34 @@
+from run import Invalid, as_int
+
+
+def check(inst, ans):
+    n = as_int(ans.get("n"), "n", lo=2, hi=inst["n_max"])
+    adj = ans.get("adj")
+    if not isinstance(adj, list) or len(adj) != n:
+        raise Invalid(f"adj must be a list of {n} strings")
+    for r in adj:
+        if not isinstance(r, str) or len(r) != n or set(r) - {"Y", "N"}:
+            raise Invalid("each row must be a string of length n over {'Y','N'}")
+    for i in range(n):
+        if adj[i][i] != "N":
+            raise Invalid("self-loop")
+        for j in range(i + 1, n):
+            if adj[i][j] != adj[j][i]:
+                raise Invalid("matrix not symmetric")
+    nb = [[j for j in range(n) if adj[i][j] == "Y"] for i in range(n)]
+    dist = [-1] * n
+    cnt = [0] * n
+    dist[0], cnt[0] = 0, 1
+    q = [0]
+    for u in q:  # BFS with exact (Python int) path counts
+        for v in nb[u]:
+            if dist[v] < 0:
+                dist[v] = dist[u] + 1
+                q.append(v)
+            if dist[v] == dist[u] + 1:
+                cnt[v] += cnt[u]
+    if dist[1] < 0:
+        raise Invalid("vertex 2 is unreachable from vertex 1")
+    if cnt[1] != inst["K"]:
+        raise Invalid(f"{cnt[1]} shortest paths, need {inst['K']}")
+    return None, {}
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/tests/instance.json b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ffa31d6e8adcd76ac4058601ae01fb7e4742f0db
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/instance.json
@@ -0,0 +1 @@
+{"K": 79878, "n_max": 105, "family": "rlve_shortest_path_count", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/tests/run.py b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-shortest-path-count-l3-s5/tests/test.sh b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-shortest-path-count-l3-s5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b2b16e4b87fbfd3f4b7263be93dcde2a837cb0bd
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[4, 37], [6, 0], [7, 49], [10, 53], [12, 32], [15, 49], [16, 44], [23, 13], [23, 28], [24, 37], [25, 42], [31, 16], [33, 55], [36, 50], [37, 16], [37, 21], [39, 33], [40, 5], [40, 60], [42, 15], [42, 47], [43, 15], [44, 55], [46, 46], [48, 18], [51, 22], [51, 51], [55, 51], [56, 41], [57, 46]], "r_opt": 35.37334879685318, "r2_num": 50552713, "r2_den": 40401, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/instruction.md b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..3e887a588e13843502da2c2365db6b85f6937c2e
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/instruction.md
@@ -0,0 +1,37 @@
+You are given 30 lattice points in the plane:
+(4, 37)
+(6, 0)
+(7, 49)
+(10, 53)
+(12, 32)
+(15, 49)
+(16, 44)
+(23, 13)
+(23, 28)
+(24, 37)
+(25, 42)
+(31, 16)
+(33, 55)
+(36, 50)
+(37, 16)
+(37, 21)
+(39, 33)
+(40, 5)
+(40, 60)
+(42, 15)
+(42, 47)
+(43, 15)
+(44, 55)
+(46, 46)
+(48, 18)
+(51, 22)
+(51, 51)
+(55, 51)
+(56, 41)
+(57, 46)
+
+Find a circle (centre (x, y), radius r) that contains all of these points and whose radius is minimum possible. Your answer is accepted if every point is within distance r + 1e-6 of the centre and r exceeds the minimum possible radius by at most 1e-6.
+
+Answer format: {"x": <number>, "y": <number>, "r": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..351195511a8faea5bfc1fb5afa328f6f6bd86571
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 29.865671641791046, "y": 26.109452736318406, "r": 35.373348797853176}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/task.toml b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..1e01ab4e44b5830233ad80bb5c25e9798e6619fc
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-smallest-enclosing-circle-l4-s1"
+version = "0.2.0"
+description = "construct/rlve_smallest_enclosing_circle"
+authors = []
+keywords = ["rlmath", "construct", "rlve_smallest_enclosing_circle"]
+
+[metadata]
+subset = "construct"
+family = "rlve_smallest_enclosing_circle"
+problem_key = "minimum_enclosing_circle"
+domain = "geometry"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/smallest_circle"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/check.py
@@ -0,0 +1,17 @@
+import math
+
+from run import Invalid, num
+
+TOL = 1e-6
+
+
+def check(inst, ans):
+    x, y, r = num(ans.get("x"), "x"), num(ans.get("y"), "y"), num(ans.get("r"), "r")
+    if r <= 0:
+        raise Invalid("r must be positive")
+    if r > inst["r_opt"] + TOL:
+        raise Invalid(f"r = {r} exceeds the minimum radius {inst['r_opt']} by more than {TOL}")
+    for px, py in inst["points"]:
+        if math.hypot(px - x, py - y) > r + TOL:
+            raise Invalid(f"point ({px}, {py}) is outside the circle")
+    return None, {"r": r}
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..b2b16e4b87fbfd3f4b7263be93dcde2a837cb0bd
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[4, 37], [6, 0], [7, 49], [10, 53], [12, 32], [15, 49], [16, 44], [23, 13], [23, 28], [24, 37], [25, 42], [31, 16], [33, 55], [36, 50], [37, 16], [37, 21], [39, 33], [40, 5], [40, 60], [42, 15], [42, 47], [43, 15], [44, 55], [46, 46], [48, 18], [51, 22], [51, 51], [55, 51], [56, 41], [57, 46]], "r_opt": 35.37334879685318, "r2_num": 50552713, "r2_den": 40401, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s1/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s6/instruction.md b/tasks/construct-rlve-smallest-enclosing-circle-l4-s6/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..7f934a283e070b5a03b185e4de462f2872e17d33
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s6/instruction.md
@@ -0,0 +1,37 @@
+You are given 30 lattice points in the plane:
+(1, 5)
+(3, 15)
+(3, 27)
+(7, 31)
+(8, 20)
+(10, 9)
+(10, 51)
+(11, 22)
+(14, 45)
+(22, 15)
+(24, 59)
+(26, 30)
+(26, 34)
+(27, 6)
+(30, 18)
+(31, 31)
+(31, 52)
+(45, 24)
+(45, 60)
+(46, 4)
+(47, 8)
+(48, 43)
+(48, 46)
+(49, 32)
+(53, 53)
+(54, 13)
+(54, 47)
+(56, 28)
+(57, 42)
+(59, 4)
+
+Find a circle (centre (x, y), radius r) that contains all of these points and whose radius is minimum possible. Your answer is accepted if every point is within distance r + 1e-6 of the centre and r exceeds the minimum possible radius by at most 1e-6.
+
+Answer format: {"x": <number>, "y": <number>, "r": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s6/task.toml b/tasks/construct-rlve-smallest-enclosing-circle-l4-s6/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..6c0f66b337f8610a94f3eb5260c99e6e782cb121
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s6/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-smallest-enclosing-circle-l4-s6"
+version = "0.2.0"
+description = "construct/rlve_smallest_enclosing_circle"
+authors = []
+keywords = ["rlmath", "construct", "rlve_smallest_enclosing_circle"]
+
+[metadata]
+subset = "construct"
+family = "rlve_smallest_enclosing_circle"
+problem_key = "minimum_enclosing_circle"
+domain = "geometry"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/smallest_circle"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/environment/Dockerfile b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/environment/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e2bd3c9c8f8859f32a1f3540ddca07c15d913538
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/environment/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 56], [3, 5], [3, 8], [4, 43], [5, 18], [8, 23], [11, 37], [15, 21], [17, 4], [19, 37], [20, 18], [20, 35], [22, 52], [26, 20], [30, 1], [30, 22], [34, 16], [40, 59], [41, 45], [42, 53], [48, 27], [49, 27], [49, 38], [50, 26], [50, 54], [51, 4], [53, 22], [53, 31], [55, 28], [60, 26]], "r_opt": 36.41771546926029, "r2_num": 5305, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/instruction.md b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..b17bcf40db311db5ac3b1247c5b33476e68c6437
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/instruction.md
@@ -0,0 +1,37 @@
+You are given 30 lattice points in the plane:
+(0, 56)
+(3, 5)
+(3, 8)
+(4, 43)
+(5, 18)
+(8, 23)
+(11, 37)
+(15, 21)
+(17, 4)
+(19, 37)
+(20, 18)
+(20, 35)
+(22, 52)
+(26, 20)
+(30, 1)
+(30, 22)
+(34, 16)
+(40, 59)
+(41, 45)
+(42, 53)
+(48, 27)
+(49, 27)
+(49, 38)
+(50, 26)
+(50, 54)
+(51, 4)
+(53, 22)
+(53, 31)
+(55, 28)
+(60, 26)
+
+Find a circle (centre (x, y), radius r) that contains all of these points and whose radius is minimum possible. Your answer is accepted if every point is within distance r + 1e-6 of the centre and r exceeds the minimum possible radius by at most 1e-6.
+
+Answer format: {"x": <number>, "y": <number>, "r": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/solution/solve.sh b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..b3699d9da8115f635be1fec8e519d548ae728654
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": 25.5, "y": 30.0, "r": 36.41771547026028}
+RLMATH_EOF
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/task.toml b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..46836964672b734cade7b773588356383d75afa8
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-smallest-enclosing-circle-l4-s8"
+version = "0.2.0"
+description = "construct/rlve_smallest_enclosing_circle"
+authors = []
+keywords = ["rlmath", "construct", "rlve_smallest_enclosing_circle"]
+
+[metadata]
+subset = "construct"
+family = "rlve_smallest_enclosing_circle"
+problem_key = "minimum_enclosing_circle"
+domain = "geometry"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/smallest_circle"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/check.py b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0eabf3219588f98db42bf5fd305dc24ce21ca495
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/check.py
@@ -0,0 +1,17 @@
+import math
+
+from run import Invalid, num
+
+TOL = 1e-6
+
+
+def check(inst, ans):
+    x, y, r = num(ans.get("x"), "x"), num(ans.get("y"), "y"), num(ans.get("r"), "r")
+    if r <= 0:
+        raise Invalid("r must be positive")
+    if r > inst["r_opt"] + TOL:
+        raise Invalid(f"r = {r} exceeds the minimum radius {inst['r_opt']} by more than {TOL}")
+    for px, py in inst["points"]:
+        if math.hypot(px - x, py - y) > r + TOL:
+            raise Invalid(f"point ({px}, {py}) is outside the circle")
+    return None, {"r": r}
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/instance.json b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e2bd3c9c8f8859f32a1f3540ddca07c15d913538
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/instance.json
@@ -0,0 +1 @@
+{"points": [[0, 56], [3, 5], [3, 8], [4, 43], [5, 18], [8, 23], [11, 37], [15, 21], [17, 4], [19, 37], [20, 18], [20, 35], [22, 52], [26, 20], [30, 1], [30, 22], [34, 16], [40, 59], [41, 45], [42, 53], [48, 27], [49, 27], [49, 38], [50, 26], [50, 54], [51, 4], [53, 22], [53, 31], [55, 28], [60, 26]], "r_opt": 36.41771546926029, "r2_num": 5305, "r2_den": 4, "family": "rlve_smallest_enclosing_circle", "subset": "construct"}
\ No newline at end of file
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/run.py b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/test.sh b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/construct-rlve-smallest-enclosing-circle-l4-s8/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l4-s3/instruction.md b/tasks/construct-rlve-subgraph-isomorphism-l4-s3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..869b9af10cf6ac62fa1ab031302457396d7e7488
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l4-s3/instruction.md
@@ -0,0 +1,10 @@
+G1 is an undirected simple graph on vertices 0..17 with edges
+[[10, 11], [14, 17], [3, 17], [1, 16], [9, 17], [5, 6], [0, 7], [7, 11], [6, 10], [5, 11], [2, 17], [10, 14], [2, 16], [13, 14], [5, 16], [1, 5], [8, 17], [4, 15], [8, 11], [5, 14], [4, 14], [5, 13], [3, 11], [12, 14], [16, 17], [1, 13], [1, 3], [10, 16], [0, 17], [5, 8], [1, 2], [7, 15], [4, 7], [2, 13], [2, 11], [3, 15], [4, 8], [7, 10], [4, 10], [1, 14], [0, 1], [0, 15], [6, 9], [0, 16], [0, 6], [12, 16], [2, 6], [1, 15], [2, 5], [6, 12], [5, 12], [7, 8], [8, 12], [13, 15], [5, 9], [6, 17], [8, 16], [9, 10], [3, 5], [8, 15], [6, 15], [7, 17], [1, 8], [3, 16], [0, 4], [3, 9], [0, 11], [14, 16]]
+G2 is an undirected simple graph on vertices 0..17 with edges
+[[0, 13], [5, 13], [6, 10], [3, 16], [5, 16], [10, 12], [0, 11], [2, 12], [5, 15], [6, 14], [5, 9], [12, 15], [8, 15], [0, 15], [11, 16], [0, 10], [9, 10], [9, 17], [0, 16], [4, 12], [0, 1], [1, 16], [5, 12], [0, 2], [6, 8], [2, 6], [9, 13], [13, 14], [0, 9], [1, 8], [7, 13], [4, 14], [14, 17], [4, 10], [6, 15], [10, 17], [5, 8], [1, 17], [4, 11], [4, 17], [1, 12], [4, 9], [11, 14], [2, 7], [2, 17], [11, 12], [4, 7], [11, 17], [1, 6], [7, 9], [2, 8], [2, 15], [3, 5], [7, 16], [1, 9], [2, 4], [6, 17], [4, 16], [1, 15], [9, 11], [3, 4], [6, 16], [13, 17], [2, 9], [4, 13], [0, 3], [8, 13], [3, 10]]
+
+Find an injective map p from the vertices of G1 to the vertices of G2 such that for every pair u != v of G1 vertices, (u, v) is an edge of G1 if and only if (p(u), p(v)) is an edge of G2 (i.e. G1 is isomorphic to the subgraph of G2 induced by the image of p).
+
+Answer format: {"p": [p(0), ..., p(17)]}  (distinct integers in 0..17)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l4-s3/task.toml b/tasks/construct-rlve-subgraph-isomorphism-l4-s3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..bb62639fa851e1c008391e591886bd44b457f632
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l4-s3/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-subgraph-isomorphism-l4-s3"
+version = "0.2.0"
+description = "construct/rlve_subgraph_isomorphism"
+authors = []
+keywords = ["rlmath", "construct", "rlve_subgraph_isomorphism"]
+
+[metadata]
+subset = "construct"
+family = "rlve_subgraph_isomorphism"
+problem_key = "induced_subgraph_isomorphism"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/subgraph_isomorphism"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l4-s4/instruction.md b/tasks/construct-rlve-subgraph-isomorphism-l4-s4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..db8bd0648861156fdc25d132afb0f711d21f332e
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l4-s4/instruction.md
@@ -0,0 +1,10 @@
+G1 is an undirected simple graph on vertices 0..17 with edges
+[[6, 16], [8, 15], [0, 12], [7, 13], [8, 13], [13, 16], [0, 1], [1, 6], [3, 13], [11, 14], [6, 7], [8, 16], [8, 12], [2, 7], [6, 8], [4, 17], [10, 12], [0, 10], [12, 16], [7, 10], [2, 6], [15, 16], [8, 11], [12, 13], [11, 12], [2, 3], [1, 5], [3, 7], [14, 15], [4, 7], [2, 4], [1, 9], [3, 16], [2, 14], [11, 16], [4, 11], [12, 15], [2, 9], [6, 10], [4, 5], [7, 15], [0, 6], [12, 14], [4, 9], [6, 14], [0, 8], [0, 4], [2, 12], [6, 13], [9, 15], [5, 15], [5, 6], [2, 15], [9, 12], [5, 8], [11, 15], [9, 17], [7, 16], [1, 14], [0, 14], [2, 11], [5, 12], [0, 11], [5, 7], [13, 14], [0, 15], [2, 10], [6, 9], [4, 12], [5, 16], [1, 17], [3, 11], [4, 6], [5, 14], [5, 11], [1, 7], [1, 16], [2, 16], [7, 17], [4, 15], [1, 11], [7, 12], [0, 16], [5, 17], [1, 4], [8, 9], [6, 12], [9, 16], [2, 8], [7, 9], [7, 11], [0, 13], [3, 5], [9, 11], [14, 17], [1, 13], [0, 2], [0, 7], [3, 8], [4, 13], [2, 5], [7, 14], [6, 15], [1, 8], [5, 13], [0, 5], [1, 2], [12, 17], [9, 13], [8, 14], [0, 17], [10, 16], [10, 17], [3, 6]]
+G2 is an undirected simple graph on vertices 0..17 with edges
+[[0, 2], [0, 7], [6, 9], [3, 16], [6, 17], [11, 13], [1, 14], [2, 16], [7, 11], [6, 15], [0, 16], [10, 14], [6, 16], [14, 17], [7, 12], [7, 14], [8, 11], [2, 13], [7, 10], [2, 4], [8, 13], [10, 13], [13, 15], [1, 4], [2, 6], [10, 11], [8, 16], [1, 3], [2, 8], [3, 14], [2, 3], [3, 15], [16, 17], [2, 5], [12, 15], [6, 14], [1, 16], [2, 15], [11, 15], [1, 17], [9, 15], [14, 16], [0, 11], [1, 11], [14, 15], [7, 15], [11, 17], [5, 12], [3, 6], [10, 12], [6, 7], [4, 16], [0, 14], [5, 9], [0, 17], [10, 17], [2, 10], [5, 17], [4, 13], [11, 14], [11, 12], [9, 11], [9, 12], [1, 2], [12, 14], [3, 9], [3, 12], [7, 8], [8, 9], [2, 11], [3, 17], [0, 8], [8, 17], [5, 16], [1, 13], [0, 3], [5, 11], [6, 13], [1, 6], [15, 17], [2, 7], [1, 15], [1, 9], [0, 10], [12, 17], [1, 12], [6, 12], [2, 17], [6, 11], [4, 12], [12, 13], [5, 6], [12, 16], [3, 8], [3, 10], [6, 10], [4, 14], [2, 12], [4, 17], [7, 16], [0, 6], [0, 1], [0, 4], [1, 10], [8, 12], [11, 16], [1, 7], [3, 13], [9, 10], [13, 16], [8, 14], [7, 17], [0, 13], [8, 15]]
+
+Find an injective map p from the vertices of G1 to the vertices of G2 such that for every pair u != v of G1 vertices, (u, v) is an edge of G1 if and only if (p(u), p(v)) is an edge of G2 (i.e. G1 is isomorphic to the subgraph of G2 induced by the image of p).
+
+Answer format: {"p": [p(0), ..., p(17)]}  (distinct integers in 0..17)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/construct-rlve-subgraph-isomorphism-l4-s4/task.toml b/tasks/construct-rlve-subgraph-isomorphism-l4-s4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..83df451d8c71158a4ef97dc0660973df15e43caa
--- /dev/null
+++ b/tasks/construct-rlve-subgraph-isomorphism-l4-s4/task.toml
@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-subgraph-isomorphism-l4-s4"
+version = "0.2.0"
+description = "construct/rlve_subgraph_isomorphism"
+authors = []
+keywords = ["rlmath", "construct", "rlve_subgraph_isomorphism"]
+
+[metadata]
+subset = "construct"
+family = "rlve_subgraph_isomorphism"
+problem_key = "induced_subgraph_isomorphism"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/subgraph_isomorphism"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ae-p1-ff-kakeya-d4-p3/instruction.md b/tasks/optimize-ae-p1-ff-kakeya-d4-p3/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..38494f1f8aae4cd47bc4868fe2c3f51152159fba
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d4-p3/instruction.md
@@ -0,0 +1,16 @@
+Kakeya sets over a finite field.
+
+Let p = 3 (a prime) and F_p = {0, 1, ..., p-1} with arithmetic mod p. A set K of points of F_p^4 is a
+Kakeya set if it contains a full line in every direction: for every non-zero direction v in F_p^4 there is a
+point x in K such that x + t*v (coordinates mod p) lies in K for all t in F_p.
+
+Find a Kakeya set in F_p^4 with as few points as possible. (The whole space trivially works; the classical
+Dvir / Saraf-Sudan construction has p^4/2^3 + O(p^3) points; can you do better?)
+
+Answer format: {"points": [[x_1, ..., x_4], ...]}  -- each point is a list of 4 integers in [0, 2],
+no point may appear twice.
+Score (minimize): the number of points |K|. An answer that misses some direction is invalid.
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ae-p1-ff-kakeya-d4-p3/task.toml b/tasks/optimize-ae-p1-ff-kakeya-d4-p3/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..6f3c82f7792b1ae4a1d99d035b4561ac1d268c9a
--- /dev/null
+++ b/tasks/optimize-ae-p1-ff-kakeya-d4-p3/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ae-p1-ff-kakeya-d4-p3"
+version = "0.2.0"
+description = "optimize/ae_p1_ff_kakeya"
+authors = []
+keywords = ["rlmath", "optimize", "ae_p1_ff_kakeya"]
+
+[metadata]
+subset = "optimize"
+family = "ae_p1_ff_kakeya"
+problem_key = "finite_field_kakeya_min_size"
+domain = "combinatorics"
+tier = "research"
+level = "research"
+source = "AlphaEvolve-Repository-of-Problems/1-finite-field-kakeya"
+source_license = "CC-BY-4.0"
+tags = ["exact_integer", "finite_fields"]
+direction = "minimize"
+baseline = 81
+best_known = 31
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ae-p16-gagliardo-nirenberg-p4/instruction.md b/tasks/optimize-ae-p16-gagliardo-nirenberg-p4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..aebfce6c3b169712afeeeabe007b6418bc42ddb1
--- /dev/null
+++ b/tasks/optimize-ae-p16-gagliardo-nirenberg-p4/instruction.md
@@ -0,0 +1,19 @@
+Sharp constant in a Gagliardo-Nirenberg (Nagy) inequality, p = 4.
+
+For a non-zero function f on the real line consider
+    Q(f) = ||f||_p^{4p} / ( ||f||_2^{2(p+2)} * ||f'||_2^{2(p-2)} ),      p = 4,
+where ||.||_s is the L^s norm on R. The supremum C(p) of Q is the sharp constant of the inequality. Make Q(f)
+as large as possible.
+
+Your f must be a non-negative, continuous, piecewise-linear function with unit knot spacing: f(0) = 0,
+f(k) = values[k-1] for k = 1, ..., m, f(m+1) = 0, linear in between and zero outside [0, m+1]. (Q is unchanged
+by scaling f or dilating x, so unit spacing costs nothing if you use many knots.) The three norms are
+integrated exactly for this f.
+
+Constraints: 1 <= m <= 200000; every value in [0, 1e6], not all zero.
+Answer format: {"values": [f(1), f(2), ..., f(m)]}
+Score (maximize): Q(f).
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ae-p16-gagliardo-nirenberg-p4/task.toml b/tasks/optimize-ae-p16-gagliardo-nirenberg-p4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..a3b0838d2933faff373cb6cfe54225639751bb64
--- /dev/null
+++ b/tasks/optimize-ae-p16-gagliardo-nirenberg-p4/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ae-p16-gagliardo-nirenberg-p4"
+version = "0.2.0"
+description = "optimize/ae_p16_gagliardo_nirenberg"
+authors = []
+keywords = ["rlmath", "optimize", "ae_p16_gagliardo_nirenberg"]
+
+[metadata]
+subset = "optimize"
+family = "ae_p16_gagliardo_nirenberg"
+problem_key = "nagy_gagliardo_nirenberg_sharp_constant"
+domain = "analysis"
+tier = "research"
+level = "research"
+source = "AlphaEvolve-Repository-of-Problems/16-gagliardo-nirenberg-special-case"
+source_license = "CC-BY-4.0"
+tags = ["float_objective", "known_optimum"]
+direction = "maximize"
+baseline = 0.07290000000000005
+best_known = 0.11111111111111113
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/environment/Dockerfile b/tasks/optimize-ae-p29-block-stacking-n100/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/environment/instance.json b/tasks/optimize-ae-p29-block-stacking-n100/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..9103149553b1e38db08947fc3461ac9947655717
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/environment/instance.json
@@ -0,0 +1 @@
+{"n": 100, "direction": "maximize", "family": "ae_p29_block_stacking", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/instruction.md b/tasks/optimize-ae-p29-block-stacking-n100/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..d14a5cbc487838bfc0e908c262a874d2e67ff6d3
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/instruction.md
@@ -0,0 +1,18 @@
+Block stacking (maximum overhang with one block per level).
+
+Let n = 100. Find real numbers 0 = x_0 <= x_1 <= x_2 <= ... <= x_n satisfying, for every 0 <= i < n,
+
+    (x_{i+1} + x_{i+2} + ... + x_n) / (n - i)  <=  x_i + 1/2,
+
+and make x_n as large as possible. (This is the stability condition for a stack of n unit-width blocks over a
+table edge: the centre of mass of the blocks above each block must lie over its support.)
+
+The constraints are checked exactly: every submitted number is converted to the exact rational value of its
+binary floating-point representation, so leave yourself a tiny safety margin if you round.
+
+Answer format: {"x": [x_1, x_2, ..., x_100]}   (n numbers; x_0 = 0 is implicit)
+Score (maximize): x_n.
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/solution/solve.sh b/tasks/optimize-ae-p29-block-stacking-n100/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..48ff696665d17f5701034e0995047e96a295e426
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"x": [0.004999999995, 0.010050505040454545, 0.015152545851679034, 0.020307185021782127, 0.02551551834990713, 0.03077867623938081, 0.03609782517023188, 0.04147416925087704, 0.046908951854137904, 0.0524034573431489, 0.0579590128931489, 0.0635769904156208, 0.06925880859175718, 0.07500593502279165, 0.0808198885053498, 0.08670224144064391, 0.09265462238707248, 0.09867871876659055, 0.10477627973610275, 0.11094911923610275, 0.11719911922985275, 0.12352823314757427, 0.12993848955142043, 0.1364319960384334, 0.1430109434002755, 0.14967761006027552, 0.1564343668102755, 0.16328368187191936, 0.17022812630941936, 0.17727037982350385, 0.18441323695921813, 0.19165961376356597, 0.1990125549326836, 0.2064752414923851, 0.21405099906056693, 0.2217433067451823, 0.2295558067373698, 0.23749231466594123, 0.245556830786909, 0.2537535520901877, 0.26208688541518765, 0.2705614616778995, 0.27918215132445123, 0.28795408114024074, 0.2968826525598836, 0.30597356164170175, 0.3152328208917018, 0.3246667831464187, 0.334282167752188, 0.34408608931101153, 0.3540860893010115, 0.3642901709234605, 0.3747068375797105, 0.38534513544141263, 0.39621470064793435, 0.40732581174793436, 0.4186894481002071, 0.43031735506532337, 0.44222211695818053, 0.4544172388972049, 0.4669172388847049, 0.4797377516923972, 0.4928956464160814, 0.5064091599160814, 0.5202980487910814, 0.53458376306251, 0.5492896454007453, 0.5644411605371089, 0.580066160521484, 0.5961951927634194, 0.6128618594134194, 0.6301032387065229, 0.6479603815458086, 0.6664789000458086, 0.685709669257347, 0.705709669237347, 0.726543002549847, 0.7482821329628905, 0.7710094056674359, 0.7948189294531502, 0.8198189294281503, 0.8461347188755187, 0.8739124966255186, 0.9033242613019893, 0.9345742612707393, 0.9679075945707393, 1.0036218802493106, 1.0420834186723875, 1.0837500852973876, 1.1292046307064785, 1.1792046306564785, 1.2347601861564785, 1.2972601860939785, 1.3686887574511213, 1.4520220907011214, 1.5520220906011213, 1.6770220904761213, 1.8436887569761213, 2.0936887567261215, 2.5936887562261215]}
+RLMATH_EOF
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/task.toml b/tasks/optimize-ae-p29-block-stacking-n100/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..d96a4cf3f96bde3f3c1fa9bb1e3068b9e3c0cdd8
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ae-p29-block-stacking-n100"
+version = "0.2.0"
+description = "optimize/ae_p29_block_stacking"
+authors = []
+keywords = ["rlmath", "optimize", "ae_p29_block_stacking"]
+
+[metadata]
+subset = "optimize"
+family = "ae_p29_block_stacking"
+problem_key = "block_stacking_overhang_one_per_level"
+domain = "analysis"
+tier = "competition"
+level = "competition"
+source = "AlphaEvolve-Repository-of-Problems/29-block-stacking"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial", "exact_rational", "known_optimum"]
+direction = "maximize"
+baseline = 0.0
+best_known = 2.5936887588198103
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/tests/check.py b/tasks/optimize-ae-p29-block-stacking-n100/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..0936f9a12cbe14efd9acc0331b8d8feef14c7ad6
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/tests/check.py
@@ -0,0 +1,23 @@
+"""Block stacking (overhang) problem, closed form of the constraints; checked in exact rational arithmetic.
+
+Upstream (block_stacking_problem.ipynb) used a float tolerance of 100*eps on every constraint, which lets a
+submission exceed the true optimum H_n/2 by accumulated slack; here all constraints are exact (non-strict).
+"""
+from fractions import Fraction
+
+from run import Invalid, float_list
+
+
+def check(inst, ans):
+    n = inst["n"]
+    x = [Fraction(v) for v in float_list(ans.get("x"), n, "x")]
+    xs = [Fraction(0)] + x  # x_0 = 0
+    for i in range(n):
+        if xs[i + 1] < xs[i]:
+            raise Invalid(f"need x_{i} <= x_{i + 1}")
+    tail = Fraction(0)
+    for i in range(n - 1, -1, -1):  # tail = x_{i+1} + ... + x_n
+        tail += xs[i + 1]
+        if tail > (n - i) * (xs[i] + Fraction(1, 2)):
+            raise Invalid(f"stability constraint violated at i = {i}")
+    return float(xs[n]), {}
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/tests/instance.json b/tasks/optimize-ae-p29-block-stacking-n100/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..5916d45c61e735eeace1e5c76b9cd3f1f7e72996
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/tests/instance.json
@@ -0,0 +1 @@
+{"n": 100, "direction": "maximize", "best_known": 2.5936887588198103, "baseline": 0.0, "family": "ae_p29_block_stacking", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/tests/run.py b/tasks/optimize-ae-p29-block-stacking-n100/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ae-p29-block-stacking-n100/tests/test.sh b/tasks/optimize-ae-p29-block-stacking-n100/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ae-p29-block-stacking-n100/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-ae-p30-arithmetic-kakeya-3slopes/instruction.md b/tasks/optimize-ae-p30-arithmetic-kakeya-3slopes/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..2ea3ae800193a08ae60d08a38f974a4e94de5559
--- /dev/null
+++ b/tasks/optimize-ae-p30-arithmetic-kakeya-3slopes/instruction.md
@@ -0,0 +1,18 @@
+Arithmetic Kakeya conjecture: entropic sum-difference ratio with 3 slopes.
+
+For a real r let pi_r(a, b) = a + r*b, and pi_inf(a, b) = b. Let (X, Y) be a pair of integer-valued random
+variables with finitely many values (X and Y need not be independent) and let H denote Shannon entropy.
+The constant C({0, 1, infinity}; -1) is the least C with
+    H(X - Y) <= C * max( H(X), H(X+Y), H(Y) )
+for all such (X, Y); every distribution gives the lower bound C >= H(X - Y) / max( H(X), H(X+Y), H(Y) ).
+Find a joint distribution making this ratio as large as possible.
+
+Constraints: 2 <= number of support points <= 20000; support points are distinct integer pairs (x, y)
+with |x|, |y| <= 1000000; weights are non-negative floats with positive sum (they are normalised to
+probabilities). Entropies use the natural logarithm (the ratio does not depend on the base).
+Answer format: {"support": [[x_1, y_1], [x_2, y_2], ...], "weights": [w_1, w_2, ...]}
+Score (maximize): H(X - Y) / max( H(X), H(X+Y), H(Y) ).
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ae-p30-arithmetic-kakeya-3slopes/task.toml b/tasks/optimize-ae-p30-arithmetic-kakeya-3slopes/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..40fdee4f4994bfefa73219557d810e07ab6e84e1
--- /dev/null
+++ b/tasks/optimize-ae-p30-arithmetic-kakeya-3slopes/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ae-p30-arithmetic-kakeya-3slopes"
+version = "0.2.0"
+description = "optimize/ae_p30_arithmetic_kakeya"
+authors = []
+keywords = ["rlmath", "optimize", "ae_p30_arithmetic_kakeya"]
+
+[metadata]
+subset = "optimize"
+family = "ae_p30_arithmetic_kakeya"
+problem_key = "arithmetic_kakeya_entropy_sum_difference"
+domain = "combinatorics"
+tier = "research"
+level = "research"
+source = "AlphaEvolve-Repository-of-Problems/30-arithmetic-kakeya"
+source_license = "CC-BY-4.0"
+tags = ["additive_combinatorics", "entropy", "float_objective"]
+direction = "maximize"
+baseline = 1.0
+best_known = 1.77898
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ea-circle-packing-n26/environment/Dockerfile b/tasks/optimize-ea-circle-packing-n26/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ea-circle-packing-n26/environment/instance.json b/tasks/optimize-ea-circle-packing-n26/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e00a54f423886213ab0105261c8aef49f6bf20c1
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/environment/instance.json
@@ -0,0 +1 @@
+{"n": 26, "direction": "maximize", "family": "ea_circle_packing_26", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-circle-packing-n26/instruction.md b/tasks/optimize-ea-circle-packing-n26/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..17a56a5f5e5470f2218714ae8b719ed79c794964
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/instruction.md
@@ -0,0 +1,22 @@
+## Problem
+
+Pack $n = 26$ non-overlapping circles inside the unit square $[0, 1]^2$ to **maximize** the sum of their
+radii $S = \sum_{i=1}^{26} r_i$. Each circle has center $(x_i, y_i)$ and radius $r_i > 0$, subject to
+
+- **Containment:** $r_i \le x_i \le 1 - r_i$ and $r_i \le y_i \le 1 - r_i$;
+- **Non-overlap:** $\|c_i - c_j\| \ge r_i + r_j$ for all $i \ne j$ (touching is allowed).
+
+## Verification
+
+Both constraints are checked **exactly** on the rational values of the submitted floating-point numbers
+(no tolerance): a pair overlapping by 1e-16 is rejected. Leave a tiny safety margin if you optimise
+numerically.
+
+## Answer format
+
+`{"circles": [[x_1, y_1, r_1], ..., [x_26, y_26, r_26]]}`: exactly 26 triples of finite numbers. The score
+is the sum of the radii.
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ea-circle-packing-n26/solution/solve.sh b/tasks/optimize-ea-circle-packing-n26/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..f923c39a3bfa08b9ef6bbe69b85d6ae112605dae
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"circles": [[0.7026096036990247, 0.3816658444526457, 0.11514888015902278], [0.31311580997040145, 0.9076084484290411, 0.0923915515699589], [0.726905714311596, 0.5960427019081348, 0.1006003678177114], [0.894817439731251, 0.27395283962395217, 0.10518256026774886], [0.9038486659542352, 0.6820800429325902, 0.09615133404476481], [0.10306052014158237, 0.48460080265191496, 0.10306052014058237], [0.2716298514860014, 0.5976347963876618, 0.09989835059175478], [0.23971052792753603, 0.7636735693833854, 0.0691806763562347], [0.759352401560932, 0.7629588636539982, 0.06944019371025845], [0.915073737545101, 0.084926262454899, 0.08492626245389895], [0.4955317606743583, 0.2753426167714399, 0.11762968804554108], [0.896532766642048, 0.48259558221054216, 0.10346723335695204], [0.49728444620411005, 0.07886037291596384, 0.07886037291496378], [0.11077901279071568, 0.8892209872092842, 0.11077901278971568], [0.8888438205895552, 0.8888438205895551, 0.11115617940944475], [0.49942836913903915, 0.9060726627225563, 0.09392733727644359], [0.4986680755034023, 0.5299634197531913, 0.13701043012274758], [0.08463950069577313, 0.08463950069577317, 0.0846395006947731], [0.2946094887818273, 0.1302211010652256, 0.1302211010642249], [0.4033587836026808, 0.742417049501635, 0.09584232574450488], [0.6859430219867827, 0.9074079050485644, 0.09259209495043558], [0.7023095250891603, 0.13325857277081155, 0.1332585727698113], [0.5952197329397327, 0.742049443460592, 0.09601897575725388], [0.09573232930702141, 0.6832585349730799, 0.09573232930602141], [0.29474605904894957, 0.38692355340959994, 0.11207708894925691], [0.10679014462858022, 0.2747832833508202, 0.10679014462758021]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ea-circle-packing-n26/task.toml b/tasks/optimize-ea-circle-packing-n26/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..f7c9f6192d5f71a3cbddeae564d6cfd5eaf5a725
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ea-circle-packing-n26"
+version = "0.2.0"
+description = "optimize/ea_circle_packing_26"
+authors = []
+keywords = ["rlmath", "optimize", "ea_circle_packing_26"]
+
+[metadata]
+subset = "optimize"
+family = "ea_circle_packing_26"
+problem_key = "circle_packing_square_sum_radii_n26"
+domain = "discrete_geometry"
+tier = "research"
+level = "research"
+source = "EinsteinArena/circle-packing"
+source_license = "MIT"
+tags = ["exact_check", "float_objective"]
+direction = "maximize"
+baseline = 2.38375
+best_known = 2.6359830849176076
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ea-circle-packing-n26/tests/check.py b/tasks/optimize-ea-circle-packing-n26/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..018159b91112bc76f2410da3995e5cea7fd7b438
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/tests/check.py
@@ -0,0 +1,26 @@
+"""Circle packing in the unit square, n = 26, maximize the sum of radii (EinsteinArena circle-packing, MIT).
+
+Upstream bug fixed: containment and non-overlap were tested in float64 (sqrt of a float distance), so
+configurations with overlaps of ~1e-16 were accepted (the AlphaEvolve seed itself overlaps by that much in
+exact arithmetic). Here both constraints are checked exactly on the rational values of the floats."""
+from fractions import Fraction
+
+from run import Invalid, float_matrix
+
+
+def check(inst, ans):
+    n = inst["n"]
+    c = float_matrix(ans.get("circles"), n, 3, "circles")
+    F = [tuple(Fraction(v) for v in row) for row in c]
+    for x, y, r in F:
+        if r <= 0:
+            raise Invalid("radii must be positive")
+        if not (r <= x <= 1 - r and r <= y <= 1 - r):
+            raise Invalid("a circle is not contained in the unit square")
+    for i in range(n):
+        xi, yi, ri = F[i]
+        for j in range(i + 1, n):
+            xj, yj, rj = F[j]
+            if (xi - xj) ** 2 + (yi - yj) ** 2 < (ri + rj) ** 2:
+                raise Invalid(f"circles {i} and {j} overlap")
+    return sum(r for _, _, r in c), {}
diff --git a/tasks/optimize-ea-circle-packing-n26/tests/instance.json b/tasks/optimize-ea-circle-packing-n26/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ba1444cf3413ac74264b2efc7cb15bfb0e7257f2
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/tests/instance.json
@@ -0,0 +1 @@
+{"n": 26, "direction": "maximize", "best_known": 2.6359830849176076, "baseline": 2.38375, "family": "ea_circle_packing_26", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-circle-packing-n26/tests/run.py b/tasks/optimize-ea-circle-packing-n26/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ea-circle-packing-n26/tests/test.sh b/tasks/optimize-ea-circle-packing-n26/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ea-circle-packing-n26/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-ea-erdos-min-overlap/instruction.md b/tasks/optimize-ea-erdos-min-overlap/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..f32e5808da2947ec71845533fc9d02e55deff69f
--- /dev/null
+++ b/tasks/optimize-ea-erdos-min-overlap/instruction.md
@@ -0,0 +1,21 @@
+## Problem
+
+Find a step function $h: [0, 2] \to [0, 1]$ with $\int_0^2 h = 1$ that **minimizes** the overlap
+$$C = \max_k \int h(x)\,(1 - h(x+k))\, dx .$$
+This gives an upper bound for Erdős' minimum overlap constant.
+
+## Scoring
+
+Represent $h$ by $n$ equally spaced samples on $[0, 2]$ (you choose $n$, at most 20000), $dx = 2/n$. All
+values must lie in $[0, 1]$. The grader rescales the samples so that their sum is $n/2$ (the rescaled
+values must still lie in $[0,1]$) and computes
+$$C = \max\bigl(\texttt{numpy.correlate}(h,\; 1-h,\; \texttt{mode="full"})\bigr) \cdot dx .$$
+Lower is better. (The best known value is about 0.38087.)
+
+## Answer format
+
+`{"values": [h_0, ..., h_{n-1}]}`: 1 to 20000 finite numbers in [0, 1].
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ea-erdos-min-overlap/task.toml b/tasks/optimize-ea-erdos-min-overlap/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..1b1687c112f684d11b8984b7be8d973af798a530
--- /dev/null
+++ b/tasks/optimize-ea-erdos-min-overlap/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ea-erdos-min-overlap"
+version = "0.2.0"
+description = "optimize/ea_erdos_min_overlap"
+authors = []
+keywords = ["rlmath", "optimize", "ea_erdos_min_overlap"]
+
+[metadata]
+subset = "optimize"
+family = "ea_erdos_min_overlap"
+problem_key = "erdos_minimum_overlap_upper"
+domain = "analysis"
+tier = "research"
+level = "research"
+source = "EinsteinArena/erdos-min-overlap"
+source_license = "MIT"
+tags = ["float_objective"]
+direction = "minimize"
+baseline = 0.5
+best_known = 0.3808703105862199
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ea-first-autocorrelation/environment/Dockerfile b/tasks/optimize-ea-first-autocorrelation/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ea-first-autocorrelation/environment/instance.json b/tasks/optimize-ea-first-autocorrelation/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..898d826a7dab21773b621ce2adc8efd910c016bd
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/environment/instance.json
@@ -0,0 +1 @@
+{"max_len": 30000, "direction": "minimize", "family": "ea_first_autocorrelation", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-first-autocorrelation/instruction.md b/tasks/optimize-ea-first-autocorrelation/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..7752f5964ad292b720eade32c43f04ae0f737a34
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/instruction.md
@@ -0,0 +1,20 @@
+## Problem
+
+Find a non-negative function $f: \mathbb{R} \to \mathbb{R}$ that **minimizes** the constant $C$ in the
+autocorrelation inequality
+$$\max_{t}\; (f * f)(t) \;\ge\; C \left(\int f\right)^2 ,\qquad (f*f)(t) = \int f(t-x)\,f(x)\,dx .$$
+
+## Scoring
+
+Discretize $f$ on $[-1/4, 1/4]$ into $n$ equally spaced values (you choose $n$, at most 30000). All values
+must be non-negative with positive sum. The grader computes
+$$dx = \frac{0.5}{n}, \qquad C = \frac{\max\bigl(\texttt{numpy.convolve}(f, f) \cdot dx\bigr)}{\bigl(\sum f \cdot dx\bigr)^2}.$$
+Lower is better. (The best known value is about 1.5029.)
+
+## Answer format
+
+`{"values": [f_0, f_1, ..., f_{n-1}]}`: 1 to 30000 finite non-negative numbers.
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ea-first-autocorrelation/solution/solve.sh b/tasks/optimize-ea-first-autocorrelation/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..d8cdec24798f292852b2dd329ae2fd1a82164daf
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"values": [0.00046823520640991233, 0.0004997266321609107, 0.0005068554357726596, 0.0005098150459737163, 0.000513159605650718, 0.0005181627696931539, 0.0005250803892046767, 0.0005296664909247913, 0.0005320519229336151, 0.0005327476658663981, 0.0005332838785931339, 0.0005324102072049723, 0.0005297110551020049, 0.0005268697353022721, 0.0005243376960275314, 0.0005232792092153603, 0.0005235296669783454, 0.0005243263781747899, 0.0005243584178015957, 0.0005242830085656002, 0.0005246327516992215, 0.0005250188469123379, 0.0005206392429057127, 0.0005059822301346624, 0.0004902475346456187, 0.0004813419788150537, 0.0004801807500430878, 0.000483958327960289, 0.0004988395932952718, 0.0005154171293410447, 0.0005243110238569309, 0.000529398669874208, 0.0005330704535271074, 0.0005371286471732931, 0.0005354745794998277, 0.0005018657258855667, 0.0004495943985846874, 0.00044498170976055616, 0.0004708057125982386, 0.0004930820772277026, 0.0005023374609755128, 0.0005104969014454413, 0.0005166913803666308, 0.0005166094539447708, 0.0005121549147705164, 0.0004923096587665936, 0.0004999681765952735, 0.0005028748222312704, 0.0005043582861001582, 0.0005166511531892378, 0.0005118797076909724, 0.0004989847215042363, 0.0004912799652647474, 0.00048793847861710677, 0.0004850146733087113, 0.0004902694503999967, 0.0004990187258354423, 0.0004887375789472924, 0.00048551282205740816, 0.0004860919578008146, 0.0004883509530028154, 0.0004915007677479014, 0.0004937802678441638, 0.0004960878577351591, 0.0004983000967753561, 0.0004987795992897033, 0.0004972687809251705, 0.0004946693439580432, 0.0004914248834549501, 0.0004871751864411113, 0.0004836813724754751, 0.00048036202378137446, 0.00047812410959417734, 0.0004791025578437194, 0.00048131348222799905, 0.00048149170293041853, 0.00047966290766966204, 0.0004764242574787247, 0.0004720353888135095, 0.0004676802419138645, 0.00046439956331833967, 0.00046191488649216175, 0.00046074480733246956, 0.0004606713683128964, 0.0004628518773385476, 0.0004657169196558225, 0.00046710006741816314, 0.0004651220474248415, 0.00046456803072201933, 0.0004674755405513536, 0.0004738088032270523, 0.0004786179986320034, 0.0004805172544703165, 0.0004812090045896603, 0.0004819829671132178, 0.00048205864005076727, 0.0004784929461068502, 0.00047640148742405413, 0.000477651004954414, 0.00047816175499237537, 0.00047991601931321015, 0.0005070890124777704, 1.5467394363280336e-11, 2.010205186385574e-11, 1.720418920649495e-12, 7.401314336582802e-13, 5.371688847868184e-12, 4.066360056344697e-15, 6.238224768863693e-12, 4.066120759872003e-15, 1.714356791293513e-12, 8.729531259519884e-12, 5.631740716923679e-13, 4.09506093998417e-12, 9.582515881159292e-12, 3.921248571131906e-12, 4.068545954820349e-15, 4.072494176883259e-15, 1.3921093249817332e-11, 1.6555450369638088e-13, 1.3858215060563634e-11, 4.072216217774333e-15, 1.0092028326373728e-11, 9.07492814127154e-12, 5.540651627415828e-06, 2.554489170447029e-05, 4.850650100996895e-05, 6.296189215537122e-05, 6.910464483786877e-05, 6.978420146610119e-05, 5.3862593641463176e-05, 3.4759928024035985e-05, 2.54417696467699e-05, 2.0769214596727677e-05, 1.6817081635020424e-05, 1.1776543619976978e-05, 1.0863454952611323e-05, 4.070165550311133e-05, 8.219702671623441e-05, 8.450031336574359e-05, 6.050054122373988e-05, 3.82395440844448e-05, 2.257234200699501e-05, 8.984920223496603e-06, 7.595524129425397e-08, 1.5591955512216987e-08, 2.8575084402714612e-06, 1.1796989105786692e-05, 3.463341058694425e-06, 2.200909976523644e-08, 2.0212892664444638e-08, 2.735562496126767e-09, 6.739957547650371e-06, 2.2500679512155038e-05, 3.36050306786808e-05, 4.138962871001753e-05, 4.6494803633375116e-05, 3.907974326155378e-05, 2.660180385885794e-05, 4.204764898021493e-05, 4.45455499381318e-05, 4.247489320823645e-05, 3.992005714419979e-05, 3.680894983002033e-05, 3.342919711939416e-05, 2.9818987757121774e-05, 2.6526590959040827e-05, 2.548403160257353e-05, 2.7099016622595714e-05, 2.899696564912648e-05, 2.988475354475491e-05, 3.012631173813578e-05, 3.0260132058681022e-05, 3.047938116118693e-05, 2.9938318807693014e-05, 2.7428809683137837e-05, 2.4553869339994665e-05, 2.3087556470203143e-05, 2.3357175029170753e-05, 2.4875393823283434e-05, 2.692621228816746e-05, 2.9223293134349183e-05, 3.211099391155126e-05, 3.395415839612163e-05, 3.368208018579851e-05, 3.171497038191695e-05, 2.917748610488832e-05, 2.6589348161023133e-05, 2.5725816003308982e-05, 2.7040861873938665e-05, 2.6806636558642542e-05, 2.4459837944475482e-05, 2.3671880642313268e-05, 2.3168153522139523e-05, 2.2248390384449923e-05, 1.9660531476477535e-05, 1.5593905825452032e-05, 1.1396343390518966e-05, 8.461341110574527e-06, 5.899930538201212e-06, 1.7997608234468992e-06, 2.4454649631194754e-13, 1.5260570169758907e-11, 1.2636542968275046e-11, 1.1180628051752818e-11, 5.43417214274716e-11, 7.44466359062827e-11, 4.334284128485743e-11, 4.287480788631322e-12, 1.3373194338526269e-11, 4.250251594637655e-12, 6.647924637292243e-12, 4.07010038090474e-15, 4.080477650689342e-15, 3.82616871880365e-12, 1.4909863156873225e-11, 1.28004166343561e-11, 2.210170744086095e-12, 4.073910955749621e-15, 3.404536704460424e-14, 4.068800782040155e-15, 4.083604477529354e-15, 3.558711700774471e-11, 1.0084223521983843e-11, 9.576956020103822e-12, 4.049876005425899e-15, 2.766260479501606e-07, 1.2603997132653207e-06, 1.7278074147333478e-06, 9.13475914747689e-07, 4.062355743390715e-15, 1.0193785583264075e-11, 4.506227655116012e-12, 1.9430613183184473e-12, 2.5477934711991394e-12, 2.6839500983365816e-13, 6.429831308195772e-11, 6.3085065473815284e-12, 3.777182004012213e-12, 1.0298091209085614e-11, 2.5996665996011663e-11, 1.9399417999094057e-12, 7.909643931014447e-12, 4.0771066382594095e-15, 7.988064267878021e-12, 2.493381571606508e-13, 1.1586110395071399e-11, 4.081677747116201e-15, 3.194998244269358e-12, 3.2060357047343172e-12, 8.116839074855466e-10, 3.861365612750472e-07, 7.931897818106147e-07, 2.4660447321950316e-07, 9.901215928378203e-12, 4.8426666430999284e-12, 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7.133909670598812e-05, 4.406353355801957e-05, 4.8703507314269374e-05, 6.457300829311543e-05, 7.700134811594729e-05, 8.00947818507305e-05, 5.26944862841488e-05, 7.482024316165973e-05, 5.973012810903456e-05, 5.801301447664533e-05, 7.37635395482621e-05, 5.7971348048234775e-05, 6.754070709739842e-05, 9.250985518856266e-05, 0.0001106409626297461, 9.963783749180866e-05, 9.56348063333784e-05, 0.00010678096867995398, 0.00010878040293529065, 9.891404875454979e-05, 8.330337068906743e-05, 6.845738835786609e-05, 6.765280922810532e-05, 6.41182048921048e-05, 6.710434564840873e-05, 6.882668782969031e-05, 7.480203411472743e-05, 7.961205899723373e-05, 7.468173149758173e-05, 7.378448585728753e-05, 6.234274558596225e-05, 5.607528426510457e-05, 6.194397897748338e-05, 7.636152978254385e-05, 8.550849078466127e-05, 7.925430913126948e-05, 5.823277048844432e-05, 5.415164198361705e-05, 6.18627972439852e-05, 6.608876167048331e-05, 5.904126907996631e-05, 5.2710942007229133e-05, 5.909596858638335e-05, 8.841913434789214e-05, 9.796409781416714e-05, 0.00010754001185184504, 0.00010599807016556692, 9.889333493910366e-05, 8.577655478676866e-05, 0.00010311217559870491, 0.00013050111855034103, 0.0001562353197275561, 0.0001493839402897504, 0.00014779143452081834, 0.00014973736178065748, 0.00011407019069777507, 7.22574571888421e-05, 3.560797389726914e-05, 5.939347416617311e-05, 8.685034637663116e-05, 0.0001006044378818663, 0.00017399057196307836, 0.0004445148437677233, 0.0019872184870793905, 0.00032998099724890293, 0.00010661834171691197, 6.799295553641755e-05, 7.480572397632029e-05, 9.066207497578926e-05, 0.00010259294983292668, 7.822579441787978e-05, 6.183097830141213e-05, 4.464508118995846e-05, 4.393033652991865e-05, 3.566254117094561e-05, 2.668418752055547e-05, 2.9682066497808248e-05, 3.461847712882693e-05, 4.8459113922293316e-05, 5.309680199769452e-05, 4.9762913811580424e-05, 5.468283696728826e-05, 6.789397175160145e-05, 7.427858237615397e-05, 8.11557815408687e-05, 0.0001041172650445048, 0.000138061038355448, 0.0001558006683236242, 0.00012457119867842646, 9.608630556846945e-05, 7.023324767590049e-05, 5.4660717135316146e-05, 5.0186352005979876e-05, 5.534130169269308e-05, 7.489783131030483e-05, 8.177789265763897e-05, 8.418450720444216e-05, 7.996458177490804e-05, 5.6246275935027855e-05, 2.5570298982623155e-05, 3.8058157923240186e-05, 5.8831140269316554e-05, 5.4277076540592416e-05, 3.944146210957903e-05, 4.3947358241010944e-05, 6.379464738748105e-05, 7.469155758856661e-05, 7.208966661089571e-05, 4.326403158116993e-05, 4.2428987041868386e-05, 3.34841939669851e-05, 3.060352144161952e-05, 4.712563684492946e-05, 4.750899242525289e-05, 5.89664904482853e-05, 8.21703091432304e-05, 0.00010998746860877456, 9.754895580357212e-05, 8.407708644089981e-05, 7.706202329096118e-05, 7.035886463916572e-05, 6.475143273518234e-05, 5.5257125424894405e-05, 4.6562564804765124e-05, 4.026082608850498e-05, 3.7741268694666184e-05, 5.1146209896726866e-05, 5.5722696313889746e-05, 6.0753118382835516e-05, 6.902175565384613e-05, 8.148558411210398e-05, 7.771377402553917e-05, 6.287845248919436e-05, 5.654008591405626e-05, 5.375783954868032e-05, 5.924557949859115e-05, 7.204755195042673e-05, 7.265418651133788e-05, 6.533286944462345e-05, 7.709568205189855e-05, 7.974222530924832e-05, 7.395128537097728e-05, 6.657016476302227e-05, 5.69173434610792e-05, 5.8780755043942235e-05, 8.768921223927363e-05, 0.00010528687137146367, 0.00011727069635280954, 0.00010982193664897713, 9.781725351872797e-05, 8.194451802666461e-05, 9.259899521730156e-05, 0.00011437963012029809, 0.0001446066839723951, 0.00013820945286033767, 0.0001443568461423454, 0.00015693343244988682, 0.0001293308827516323, 9.143099319443105e-05, 5.027271678500283e-05, 5.813921372090864e-05, 7.6633346996537e-05, 0.0001097606316575667, 0.00016049534516335924, 0.00037826574485727723, 0.0030247549255100056, 0.00017384093720462427, 3.095608591523488e-05, 1.764326432572223e-05, 2.6124599260641207e-05, 3.714218358817632e-05, 4.632680660430944e-05, 2.8350654305773236e-05, 2.2373158893352886e-05, 1.4440307390360613e-05, 2.046733893014437e-05, 1.5631560183805057e-05, 1.170347132550106e-05, 1.132817664352069e-05, 9.978803401305664e-06, 1.5779537686838808e-05, 2.3187435844935074e-05, 2.90860490787183e-05, 3.147374152726317e-05, 3.8763788745064204e-05, 4.282642837508508e-05, 5.08345657420735e-05, 7.516544645062106e-05, 9.893850381745732e-05, 0.00010376905581333849, 8.417343898194407e-05, 6.805166695615442e-05, 5.404269495196107e-05, 3.093598340919066e-05, 2.324807151008422e-05, 3.3854735731703206e-05, 4.952916741839992e-05, 5.917464087578994e-05, 6.370844689335137e-05, 5.768535500535781e-05, 3.8636681581693165e-05, 4.714857497019652e-05, 2.327071588980181e-05, 2.7554081378002153e-05, 3.3265489528425284e-05, 3.776628209118478e-05, 4.3100328922012136e-05, 5.885796460808312e-05, 6.197386399097269e-05, 5.434409575481636e-05, 5.266362809807043e-05, 3.1790196840541546e-05, 3.5897313506950996e-05, 3.392615455104314e-05, 2.8195621048952164e-05, 3.68057686045643e-05, 4.7143326771744435e-05, 6.116643520299204e-05, 7.672493362077605e-05, 6.564325963198104e-05, 4.4895638356546784e-05, 3.8342720179222715e-05, 6.435992599981887e-05, 5.462617597352854e-05, 4.7337583014054065e-05, 3.70800429057102e-05, 2.084909911324265e-05, 9.771037167684825e-06, 1.103856775437892e-05, 1.7524790284164803e-05, 3.678993582971535e-05, 5.0653318598248055e-05, 4.98792716349228e-05, 4.768273314171177e-05, 3.790302527273071e-05, 2.9762269378145282e-05, 3.2370874382539074e-05, 3.869134841771552e-05, 4.5236479998547784e-05, 4.89256591557294e-05, 4.98675369323716e-05, 5.589316521644329e-05, 6.148876940575709e-05, 5.72670656889753e-05, 6.036787990054452e-05, 6.0466652618119004e-05, 6.888082267289854e-05, 8.716480660909032e-05, 9.206056129242097e-05, 9.594949339172422e-05, 8.361143169543651e-05, 7.589308542723449e-05, 6.734100123095177e-05, 7.418051015141635e-05, 9.076489373432337e-05, 0.00011590201138056377, 0.00011033214796907344, 0.000117650749487373, 0.00013596302287705, 0.00010945070301139293, 8.927073625441885e-05, 7.040003955449563e-05, 7.949407242046349e-05, 9.432690615993019e-05, 0.00012960277886082784, 0.00018226032093539136, 0.0003709150293716709, 0.003718513596155081]}
+RLMATH_EOF
diff --git a/tasks/optimize-ea-first-autocorrelation/task.toml b/tasks/optimize-ea-first-autocorrelation/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..858b590f43b6e2cfff2458bdf09ad73ff7d4486d
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ea-first-autocorrelation"
+version = "0.2.0"
+description = "optimize/ea_first_autocorrelation"
+authors = []
+keywords = ["rlmath", "optimize", "ea_first_autocorrelation"]
+
+[metadata]
+subset = "optimize"
+family = "ea_first_autocorrelation"
+problem_key = "first_autocorrelation_inequality_upper"
+domain = "analysis"
+tier = "research"
+level = "research"
+source = "EinsteinArena/first-autocorrelation-inequality"
+source_license = "MIT"
+tags = ["float_objective"]
+direction = "minimize"
+baseline = 2.0
+best_known = 1.5028628587053106
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ea-first-autocorrelation/tests/check.py b/tasks/optimize-ea-first-autocorrelation/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..2c08b4ef2afb69e7113612f5da3fe62d83576de9
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/tests/check.py
@@ -0,0 +1,24 @@
+"""First autocorrelation inequality, upper bound (EinsteinArena first-autocorrelation-inequality, MIT).
+
+C = max(conv(f, f) * dx) / (sum(f) * dx)^2 with dx = 0.5 / n, f >= 0 (minimize). Ported from the upstream
+verifier (np.convolve). Change: the length is capped at inst["max_len"] so grading stays fast (upstream
+has no cap), and NaN/inf are rejected explicitly."""
+import numpy as np
+
+from run import Invalid, float_list
+
+
+def check(inst, ans):
+    v = ans.get("values")
+    if not isinstance(v, list) or not 1 <= len(v) <= inst["max_len"]:
+        raise Invalid(f"values must be a list of 1..{inst['max_len']} numbers")
+    f = np.array(float_list(v, None, "values"))
+    if np.any(f < 0):
+        raise Invalid("all values must be non-negative")
+    if np.sum(f) <= 0:
+        raise Invalid("the integral of f must be positive")
+    dx = 0.5 / len(f)
+    c = float(np.max(np.convolve(f, f) * dx) / (np.sum(f) * dx) ** 2)
+    if not np.isfinite(c):
+        raise Invalid("non-finite score")
+    return c, {}
diff --git a/tasks/optimize-ea-first-autocorrelation/tests/instance.json b/tasks/optimize-ea-first-autocorrelation/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ae276c4967a46b4bf63d21d43d73f90c3e4a8f03
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/tests/instance.json
@@ -0,0 +1 @@
+{"max_len": 30000, "direction": "minimize", "best_known": 1.5028628587053106, "baseline": 2.0, "family": "ea_first_autocorrelation", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-first-autocorrelation/tests/run.py b/tasks/optimize-ea-first-autocorrelation/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ea-first-autocorrelation/tests/test.sh b/tasks/optimize-ea-first-autocorrelation/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ea-first-autocorrelation/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-ea-kakeya-needle-n128/instruction.md b/tasks/optimize-ea-kakeya-needle-n128/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..75313002ec9182c2291ec3caef6b7bde08a278ca
--- /dev/null
+++ b/tasks/optimize-ea-kakeya-needle-n128/instruction.md
@@ -0,0 +1,23 @@
+## Problem
+
+For $j = 1, \ldots, 128$ choose a real horizontal offset $x_j$ and define the triangle
+$$T_j(x_j) = \operatorname{conv}\left\{ (x_j, 0),\ \left(x_j + \tfrac{1}{128}, 0\right),\ \left(x_j + \tfrac{j}{128}, 1\right) \right\}.$$
+**Minimize the area of the union** $\left| \bigcup_{j=1}^{128} T_j(x_j) \right|$ (finite Kakeya needle problem).
+
+The best known value is $0.10706663656\ldots$ (the Station, August 2026).
+
+## Scoring
+
+At height $y\in[0,1]$ the section of $T_j$ is $[x_j + \tfrac{j}{128}y,\ x_j + \tfrac{1}{128} + \tfrac{j-1}{128}y]$.
+The grader reads every offset as an exact rational, finds every height where two section endpoints
+cross, and integrates the (piecewise affine) union length exactly slab by slab. Only the final value is
+converted to a float. A common translation of all offsets does not change the area. Lower is better.
+
+## Answer format
+
+`{"offsets": ["x_1", ..., "x_128"]}`: exactly 128 JSON **strings**, each a base-10 decimal with an
+optional sign, at most 4 integer digits and at most 25 fractional digits (e.g. "-0.0123").
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ea-kakeya-needle-n128/task.toml b/tasks/optimize-ea-kakeya-needle-n128/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..f04aa81e123d168106903db7fb82c69c4ac881f7
--- /dev/null
+++ b/tasks/optimize-ea-kakeya-needle-n128/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ea-kakeya-needle-n128"
+version = "0.2.0"
+description = "optimize/ea_kakeya_needle_128"
+authors = []
+keywords = ["rlmath", "optimize", "ea_kakeya_needle_128"]
+
+[metadata]
+subset = "optimize"
+family = "ea_kakeya_needle_128"
+problem_key = "kakeya_needle_triangles_n128"
+domain = "geometry"
+tier = "research"
+level = "research"
+source = "EinsteinArena/kakeya-needle-128"
+source_license = "MIT"
+tags = ["ea_under_review", "exact_check"]
+direction = "minimize"
+baseline = 0.251953125
+best_known = 0.10706663656163481
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ea-spencer-discrepancy/environment/Dockerfile b/tasks/optimize-ea-spencer-discrepancy/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-ea-spencer-discrepancy/environment/instance.json b/tasks/optimize-ea-spencer-discrepancy/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..e34c1283b8d80b48f13e5c030458b638a023bc79
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/environment/instance.json
@@ -0,0 +1 @@
+{"max_order": 20, "direction": "maximize", "family": "ea_spencer_discrepancy", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-spencer-discrepancy/instruction.md b/tasks/optimize-ea-spencer-discrepancy/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..abddb0e5954c7ebdfbf94e9248bf380766eb9ea9
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/instruction.md
@@ -0,0 +1,23 @@
+## Problem
+
+For an $n\times n$ sign matrix $A\in\{-1,1\}^{n\times n}$ define
+$\operatorname{disc}(A)=\min_{x\in\{-1,1\}^{n}}\lVert Ax\rVert_\infty$.
+
+**Maximize $\operatorname{disc}(A)/\sqrt n$** over sign matrices of order $1\le n\le20$.
+
+The best known witness in this range is a $17\times17$ matrix with discrepancy 7, proving
+$C_{10c}\ge7/\sqrt{17}\approx1.697749$; the best proven asymptotic upper bound is
+$\operatorname{disc}(A)\le4.1\sqrt n+O(1)$.
+
+## Verification
+
+The grader evaluates all $2^n$ sign vectors exactly with integer arithmetic.
+
+## Answer format
+
+`{"matrix": [[a_11, ..., a_1n], ..., [a_n1, ..., a_nn]]}`: a square matrix of order 1..20 whose entries
+are the JSON integers 1 or -1. The score is disc(A)/sqrt(n).
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-ea-spencer-discrepancy/solution/solve.sh b/tasks/optimize-ea-spencer-discrepancy/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..2ee527b5278dcc6243506a91f1473e2641691042
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"matrix": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [-1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], [1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1], [-1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1], [1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1], [1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1], [-1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], [1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1], [-1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1], [1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1], [-1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1], [-1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1], [1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1], [1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1], [-1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}
+RLMATH_EOF
diff --git a/tasks/optimize-ea-spencer-discrepancy/task.toml b/tasks/optimize-ea-spencer-discrepancy/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..da5af65eb5e63c5e13cb6d08831a758a6522874c
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ea-spencer-discrepancy"
+version = "0.2.0"
+description = "optimize/ea_spencer_discrepancy"
+authors = []
+keywords = ["rlmath", "optimize", "ea_spencer_discrepancy"]
+
+[metadata]
+subset = "optimize"
+family = "ea_spencer_discrepancy"
+problem_key = "spencer_discrepancy_square_n_le20"
+domain = "combinatorics"
+tier = "research"
+level = "research"
+source = "EinsteinArena/spencer-discrepancy"
+source_license = "MIT"
+tags = ["ea_under_review", "exact_check"]
+direction = "maximize"
+baseline = 1.0
+best_known = 1.697749375254331
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-ea-spencer-discrepancy/tests/check.py b/tasks/optimize-ea-spencer-discrepancy/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..7b5b2016ea7084a3d98b8cb89dadb432e60d0ce5
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/tests/check.py
@@ -0,0 +1,42 @@
+"""Spencer discrepancy constant witness (EinsteinArena spencer-discrepancy, MIT).
+Score disc(A)/sqrt(n) with disc(A) = min_{x in {-1,1}^n} ||Ax||_inf (maximize).
+
+Audit: upstream verifier enumerates all 2^n sign vectors exactly; sound. Re-implemented with numpy
+(vectorised popcounts; x and -x give the same value so half the vectors suffice)."""
+import math
+
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def _popcount(a):
+    a = a - ((a >> 1) & 0x55555555)
+    a = (a & 0x33333333) + ((a >> 2) & 0x33333333)
+    a = (a + (a >> 4)) & 0x0F0F0F0F
+    return (a * 0x01010101 & 0xFFFFFFFF) >> 24
+
+
+def check(inst, ans):
+    m = ans.get("matrix")
+    cap = inst["max_order"]
+    if not isinstance(m, list) or not 1 <= len(m) <= cap:
+        raise Invalid(f"matrix order must be between 1 and {cap}")
+    n = len(m)
+    masks = []
+    for row in m:
+        int_list(row, n, -1, 1, "matrix row")
+        if any(v == 0 for v in row):
+            raise Invalid("entries must be exactly -1 or 1")
+        masks.append(sum(1 << j for j, v in enumerate(row) if v == -1))
+    disc = n
+    total = 1 << max(n - 1, 0)  # fix the top sign (x ~ -x)
+    step = 1 << 18
+    for s0 in range(0, total, step):
+        x = np.arange(s0, min(total, s0 + step), dtype=np.uint64)
+        worst = np.zeros(len(x), dtype=np.int64)
+        for r in masks:
+            pc = _popcount((x ^ np.uint64(r)) & np.uint64(0xFFFFFFFF)).astype(np.int64)
+            worst = np.maximum(worst, np.abs(n - 2 * pc))
+        disc = min(disc, int(worst.min()))
+    return disc / math.sqrt(n), {"disc": disc, "order": n}
diff --git a/tasks/optimize-ea-spencer-discrepancy/tests/instance.json b/tasks/optimize-ea-spencer-discrepancy/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..d665a44e4fc3700d337829d789cf6f4e80e830d8
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/tests/instance.json
@@ -0,0 +1 @@
+{"max_order": 20, "direction": "maximize", "best_known": 1.697749375254331, "baseline": 1.0, "family": "ea_spencer_discrepancy", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-ea-spencer-discrepancy/tests/run.py b/tasks/optimize-ea-spencer-discrepancy/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-ea-spencer-discrepancy/tests/test.sh b/tasks/optimize-ea-spencer-discrepancy/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-ea-spencer-discrepancy/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/environment/Dockerfile b/tasks/optimize-fs-cycle-indep-c11-n4/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/environment/instance.json b/tasks/optimize-fs-cycle-indep-c11-n4/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..1484765b9f2719e6d7224a421687b6d546427977
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/environment/instance.json
@@ -0,0 +1 @@
+{"m": 11, "n": 4, "direction": "maximize", "family": "fs_cycle_independent_set", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/instruction.md b/tasks/optimize-fs-cycle-indep-c11-n4/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..8468c73e0654f7a5bde25289018e0191ebbc2c80
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/instruction.md
@@ -0,0 +1,7 @@
+Let C_11 be the cycle graph on vertices 0..10 (i adjacent to i+1 mod 11). Its 4-th strong power C_11^4 has vertex set {0..10}^4; two distinct vertices x, y are adjacent iff for every coordinate i, x_i - y_i is -1, 0 or 1 modulo 11. Find an independent set in C_11^4 (no two of its vertices adjacent) that is as large as possible; this gives the Shannon capacity lower bound Theta(C_11) >= |S|^(1/4). The score is |S|.
+
+Answer format: {"vertices": [[x_1, ..., x_4], ...]}: a list of distinct length-4 lists with integer entries in 0..10.
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/solution/solve.sh b/tasks/optimize-fs-cycle-indep-c11-n4/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..9760ffae0c44c08108b84f54be9829d1fe3f0121
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"vertices": [[0, 0, 0, 8], [0, 0, 0, 10], [0, 0, 1, 6], [0, 0, 2, 4], [0, 0, 3, 2], [0, 0, 4, 0], [0, 0, 5, 7], [0, 0, 6, 5], [0, 0, 7, 3], [0, 0, 8, 1], [0, 0, 9, 8], [0, 0, 9, 10], [0, 0, 10, 1], [0, 1, 0, 4], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 3, 7], [0, 1, 4, 5], [0, 1, 5, 3], [0, 1, 6, 1], [0, 1, 7, 8], [0, 1, 7, 10], [0, 1, 8, 6], [0, 1, 9, 4], [0, 1, 10, 6], [0, 2, 0, 0], [0, 2, 1, 7], [0, 2, 2, 5], [0, 2, 3, 3], [0, 2, 4, 1], [0, 2, 5, 8], [0, 2, 5, 10], [0, 2, 6, 6], [0, 2, 7, 4], [0, 2, 8, 2], [0, 2, 9, 0], [0, 2, 10, 2], [0, 3, 0, 5], [0, 3, 1, 3], [0, 3, 2, 1], [0, 3, 3, 8], [0, 3, 3, 10], [0, 3, 4, 6], [0, 3, 5, 4], [0, 3, 6, 2], [0, 3, 7, 0], [0, 3, 8, 7], [0, 3, 9, 5], [0, 3, 10, 7], [0, 4, 0, 1], [0, 4, 1, 8], [0, 4, 1, 10], [0, 4, 2, 6], [0, 4, 3, 4], [0, 4, 4, 2], [0, 4, 5, 0], [0, 4, 6, 7], [0, 4, 7, 5], [0, 4, 8, 3], [0, 4, 9, 1], [0, 4, 10, 3], [0, 5, 0, 6], [0, 5, 1, 4], [0, 5, 2, 2], [0, 5, 3, 0], [0, 5, 4, 7], [0, 5, 5, 5], [0, 5, 6, 3], [0, 5, 7, 1], [0, 5, 8, 8], [0, 5, 8, 10], [0, 5, 9, 6], [0, 5, 10, 8], [0, 5, 10, 10], [0, 6, 0, 2], [0, 6, 1, 0], [0, 6, 2, 7], [0, 6, 3, 5], [0, 6, 4, 3], [0, 6, 5, 1], [0, 6, 6, 8], [0, 6, 6, 10], [0, 6, 7, 6], [0, 6, 8, 4], [0, 6, 9, 2], [0, 6, 10, 4], [0, 7, 0, 7], [0, 7, 1, 5], [0, 7, 2, 3], [0, 7, 3, 1], [0, 7, 4, 8], [0, 7, 4, 10], [0, 7, 5, 6], [0, 7, 6, 4], [0, 7, 7, 2], [0, 7, 8, 0], [0, 7, 9, 7], [0, 7, 10, 0], [0, 8, 0, 3], [0, 8, 1, 1], [0, 8, 2, 8], [0, 8, 2, 10], [0, 8, 3, 6], [0, 8, 4, 4], [0, 8, 5, 2], [0, 8, 6, 0], [0, 8, 7, 7], [0, 8, 8, 5], [0, 8, 9, 3], [0, 8, 10, 5], [0, 9, 0, 8], [0, 9, 0, 10], [0, 9, 1, 6], [0, 9, 2, 4], [0, 9, 3, 2], [0, 9, 4, 0], [0, 9, 5, 7], [0, 9, 6, 5], [0, 9, 7, 3], [0, 9, 8, 1], [0, 9, 9, 7], [0, 9, 10, 1], [0, 10, 0, 3], [0, 10, 1, 1], [0, 10, 2, 8], [0, 10, 2, 10], [0, 10, 3, 6], [0, 10, 4, 4], [0, 10, 5, 2], [0, 10, 6, 0], [0, 10, 7, 7], [0, 10, 8, 5], [0, 10, 9, 3], [0, 10, 10, 5], [1, 0, 5, 9], [1, 1, 3, 9], [1, 2, 1, 9], [1, 3, 8, 9], [1, 3, 10, 9], [1, 4, 6, 9], [1, 5, 4, 9], [1, 6, 2, 9], [1, 7, 0, 9], [1, 7, 9, 9], [1, 8, 7, 9], [1, 9, 5, 9], [1, 9, 9, 9], [1, 10, 7, 9], [2, 0, 0, 1], [2, 0, 1, 8], [2, 0, 1, 10], [2, 0, 2, 6], [2, 0, 3, 4], [2, 0, 4, 2], [2, 0, 5, 0], [2, 0, 6, 7], [2, 0, 7, 5], [2, 0, 8, 3], [2, 0, 9, 1], [2, 0, 10, 3], [2, 1, 0, 6], [2, 1, 1, 4], [2, 1, 2, 2], [2, 1, 3, 0], [2, 1, 4, 7], [2, 1, 5, 5], [2, 1, 6, 3], [2, 1, 7, 1], [2, 1, 8, 8], [2, 1, 8, 10], [2, 1, 9, 6], [2, 1, 10, 8], [2, 1, 10, 10], [2, 2, 0, 2], [2, 2, 1, 0], [2, 2, 2, 7], [2, 2, 3, 5], [2, 2, 4, 3], [2, 2, 5, 1], [2, 2, 6, 8], [2, 2, 6, 10], [2, 2, 7, 6], [2, 2, 8, 4], [2, 2, 9, 2], [2, 2, 10, 4], [2, 3, 0, 7], [2, 3, 1, 5], [2, 3, 2, 3], [2, 3, 3, 1], [2, 3, 4, 8], [2, 3, 4, 10], [2, 3, 5, 6], [2, 3, 6, 4], [2, 3, 7, 2], [2, 3, 8, 0], [2, 3, 9, 7], [2, 3, 10, 0], [2, 4, 0, 3], [2, 4, 1, 1], [2, 4, 2, 8], [2, 4, 2, 10], [2, 4, 3, 6], [2, 4, 4, 4], [2, 4, 5, 2], [2, 4, 6, 0], [2, 4, 7, 7], [2, 4, 8, 5], [2, 4, 9, 3], [2, 4, 10, 5], [2, 5, 0, 8], [2, 5, 0, 10], [2, 5, 1, 6], [2, 5, 2, 4], [2, 5, 3, 2], [2, 5, 4, 0], [2, 5, 5, 7], [2, 5, 6, 5], [2, 5, 7, 3], [2, 5, 8, 1], [2, 5, 9, 8], [2, 5, 9, 10], [2, 5, 10, 1], [2, 6, 0, 4], [2, 6, 1, 2], [2, 6, 2, 0], [2, 6, 3, 7], [2, 6, 4, 5], [2, 6, 5, 3], [2, 6, 6, 1], [2, 6, 7, 8], [2, 6, 7, 10], [2, 6, 8, 6], [2, 6, 9, 4], [2, 6, 10, 6], [2, 7, 0, 0], [2, 7, 1, 7], [2, 7, 2, 5], [2, 7, 3, 3], [2, 7, 4, 1], [2, 7, 5, 8], [2, 7, 5, 10], [2, 7, 6, 6], [2, 7, 7, 4], [2, 7, 8, 2], [2, 7, 9, 0], [2, 7, 10, 2], [2, 8, 0, 5], [2, 8, 1, 3], [2, 8, 2, 1], [2, 8, 3, 8], [2, 8, 3, 10], [2, 8, 4, 6], [2, 8, 5, 4], [2, 8, 6, 2], [2, 8, 7, 0], [2, 8, 8, 7], [2, 8, 9, 5], [2, 8, 10, 7], [2, 9, 0, 1], [2, 9, 1, 8], [2, 9, 1, 10], [2, 9, 2, 6], [2, 9, 3, 4], [2, 9, 4, 2], [2, 9, 5, 0], [2, 9, 6, 7], [2, 9, 7, 5], [2, 9, 8, 3], [2, 9, 9, 0], [2, 9, 10, 3], [2, 10, 0, 5], [2, 10, 1, 3], [2, 10, 2, 1], [2, 10, 3, 8], [2, 10, 3, 10], [2, 10, 4, 6], [2, 10, 5, 4], [2, 10, 6, 2], [2, 10, 7, 0], [2, 10, 8, 7], [2, 10, 9, 5], [2, 10, 10, 7], [3, 0, 6, 9], [3, 1, 4, 9], [3, 2, 2, 9], [3, 3, 0, 9], [3, 3, 9, 9], [3, 4, 7, 9], [3, 5, 5, 9], [3, 6, 3, 9], [3, 7, 1, 9], [3, 8, 8, 9], [3, 8, 10, 9], [3, 9, 6, 9], [3, 10, 8, 9], [3, 10, 10, 9], [4, 0, 0, 3], [4, 0, 1, 1], [4, 0, 2, 8], [4, 0, 2, 10], [4, 0, 3, 6], [4, 0, 4, 4], [4, 0, 5, 2], [4, 0, 6, 0], [4, 0, 7, 7], [4, 0, 8, 5], [4, 0, 9, 3], [4, 0, 10, 5], [4, 1, 0, 8], [4, 1, 0, 10], [4, 1, 1, 6], [4, 1, 2, 4], [4, 1, 3, 2], [4, 1, 4, 0], [4, 1, 5, 7], [4, 1, 6, 5], [4, 1, 7, 3], [4, 1, 8, 1], [4, 1, 9, 8], [4, 1, 9, 10], [4, 1, 10, 1], [4, 2, 0, 4], [4, 2, 1, 2], [4, 2, 2, 0], [4, 2, 3, 7], [4, 2, 4, 5], [4, 2, 5, 3], [4, 2, 6, 1], [4, 2, 7, 8], [4, 2, 7, 10], [4, 2, 8, 6], [4, 2, 9, 4], [4, 2, 10, 6], [4, 3, 0, 0], [4, 3, 1, 7], [4, 3, 2, 5], [4, 3, 3, 3], [4, 3, 4, 1], [4, 3, 5, 8], [4, 3, 5, 10], [4, 3, 6, 6], [4, 3, 7, 4], [4, 3, 8, 2], [4, 3, 9, 0], [4, 3, 10, 2], [4, 4, 0, 5], [4, 4, 1, 3], [4, 4, 2, 1], [4, 4, 3, 8], [4, 4, 3, 10], [4, 4, 4, 6], [4, 4, 5, 4], [4, 4, 6, 2], [4, 4, 7, 0], [4, 4, 8, 7], [4, 4, 9, 5], [4, 4, 10, 7], [4, 5, 0, 1], [4, 5, 1, 8], [4, 5, 1, 10], [4, 5, 2, 6], [4, 5, 3, 4], [4, 5, 4, 2], [4, 5, 5, 0], [4, 5, 6, 7], [4, 5, 7, 5], [4, 5, 8, 3], [4, 5, 9, 1], [4, 5, 10, 3], [4, 6, 0, 6], [4, 6, 1, 4], [4, 6, 2, 2], [4, 6, 3, 0], [4, 6, 4, 7], [4, 6, 5, 5], [4, 6, 6, 3], [4, 6, 7, 1], [4, 6, 8, 8], [4, 6, 8, 10], [4, 6, 9, 6], [4, 6, 10, 8], [4, 6, 10, 10], [4, 7, 0, 2], [4, 7, 1, 0], [4, 7, 2, 7], [4, 7, 3, 5], [4, 7, 4, 3], [4, 7, 5, 1], [4, 7, 6, 8], [4, 7, 6, 10], [4, 7, 7, 6], [4, 7, 8, 4], [4, 7, 9, 2], [4, 7, 10, 4], [4, 8, 0, 7], [4, 8, 1, 5], [4, 8, 2, 3], [4, 8, 3, 1], [4, 8, 4, 8], [4, 8, 4, 10], [4, 8, 5, 6], [4, 8, 6, 4], [4, 8, 7, 2], [4, 8, 8, 0], [4, 8, 9, 7], [4, 8, 10, 0], [4, 9, 0, 3], [4, 9, 1, 1], [4, 9, 2, 8], [4, 9, 2, 10], [4, 9, 3, 6], [4, 9, 4, 4], [4, 9, 5, 2], [4, 9, 6, 0], [4, 9, 7, 7], [4, 9, 8, 5], [4, 9, 9, 2], [4, 9, 10, 5], [4, 10, 0, 7], [4, 10, 1, 5], [4, 10, 2, 3], [4, 10, 3, 1], [4, 10, 4, 8], [4, 10, 4, 10], [4, 10, 5, 6], [4, 10, 6, 4], [4, 10, 7, 2], [4, 10, 8, 0], [4, 10, 9, 7], [4, 10, 10, 0], [5, 0, 7, 9], [5, 1, 5, 9], [5, 2, 3, 9], [5, 3, 1, 9], [5, 4, 8, 9], [5, 4, 10, 9], [5, 5, 6, 9], [5, 6, 4, 9], [5, 7, 2, 9], [5, 8, 0, 9], [5, 8, 9, 9], [5, 9, 7, 9], [5, 10, 0, 9], [5, 10, 9, 9], [6, 0, 0, 5], [6, 0, 1, 3], [6, 0, 2, 1], [6, 0, 3, 8], [6, 0, 3, 10], [6, 0, 4, 6], [6, 0, 5, 4], [6, 0, 6, 2], [6, 0, 7, 0], [6, 0, 8, 7], [6, 0, 9, 5], [6, 0, 10, 7], [6, 1, 0, 1], [6, 1, 1, 8], [6, 1, 1, 10], [6, 1, 2, 6], [6, 1, 3, 4], [6, 1, 4, 2], [6, 1, 5, 0], [6, 1, 6, 7], [6, 1, 7, 5], [6, 1, 8, 3], [6, 1, 9, 1], [6, 1, 10, 3], [6, 2, 0, 6], [6, 2, 1, 4], [6, 2, 2, 2], [6, 2, 3, 0], [6, 2, 4, 7], [6, 2, 5, 5], [6, 2, 6, 3], [6, 2, 7, 1], [6, 2, 8, 8], [6, 2, 8, 10], [6, 2, 9, 6], [6, 2, 10, 8], [6, 2, 10, 10], [6, 3, 0, 2], [6, 3, 1, 0], [6, 3, 2, 7], [6, 3, 3, 5], [6, 3, 4, 3], [6, 3, 5, 1], [6, 3, 6, 8], [6, 3, 6, 10], [6, 3, 7, 6], [6, 3, 8, 4], [6, 3, 9, 2], [6, 3, 10, 4], [6, 4, 0, 7], [6, 4, 1, 5], [6, 4, 2, 3], [6, 4, 3, 1], [6, 4, 4, 8], [6, 4, 4, 10], [6, 4, 5, 6], [6, 4, 6, 4], [6, 4, 7, 2], [6, 4, 8, 0], [6, 4, 9, 7], [6, 4, 10, 0], [6, 5, 0, 3], [6, 5, 1, 1], [6, 5, 2, 8], [6, 5, 2, 10], [6, 5, 3, 6], [6, 5, 4, 4], [6, 5, 5, 2], [6, 5, 6, 0], [6, 5, 7, 7], [6, 5, 8, 5], [6, 5, 9, 3], [6, 5, 10, 5], [6, 6, 0, 8], [6, 6, 0, 10], [6, 6, 1, 6], [6, 6, 2, 4], [6, 6, 3, 2], [6, 6, 4, 0], [6, 6, 5, 7], [6, 6, 6, 5], [6, 6, 7, 3], [6, 6, 8, 1], [6, 6, 9, 8], [6, 6, 9, 10], [6, 6, 10, 1], [6, 7, 0, 4], [6, 7, 1, 2], [6, 7, 2, 0], [6, 7, 3, 7], [6, 7, 4, 5], [6, 7, 5, 3], [6, 7, 6, 1], [6, 7, 7, 8], [6, 7, 7, 10], [6, 7, 8, 6], [6, 7, 9, 4], [6, 7, 10, 6], [6, 8, 0, 0], [6, 8, 1, 7], [6, 8, 2, 5], [6, 8, 3, 3], [6, 8, 4, 1], [6, 8, 5, 8], [6, 8, 5, 10], [6, 8, 6, 6], [6, 8, 7, 4], [6, 8, 8, 2], [6, 8, 9, 0], [6, 8, 10, 2], [6, 9, 0, 5], [6, 9, 1, 3], [6, 9, 2, 1], [6, 9, 3, 8], [6, 9, 3, 10], [6, 9, 4, 6], [6, 9, 5, 4], [6, 9, 6, 2], [6, 9, 7, 0], [6, 9, 8, 7], [6, 9, 9, 4], [6, 9, 10, 7], [6, 10, 0, 0], [6, 10, 1, 7], [6, 10, 2, 5], [6, 10, 3, 3], [6, 10, 4, 1], [6, 10, 5, 8], [6, 10, 5, 10], [6, 10, 6, 6], [6, 10, 7, 4], [6, 10, 8, 2], [6, 10, 9, 0], [6, 10, 10, 2], [7, 0, 8, 9], [7, 0, 10, 9], [7, 1, 6, 9], [7, 2, 4, 9], [7, 3, 2, 9], [7, 4, 0, 9], [7, 4, 9, 9], [7, 5, 7, 9], [7, 6, 5, 9], [7, 7, 3, 9], [7, 8, 1, 9], [7, 9, 8, 9], [7, 9, 10, 9], [7, 10, 1, 9], [8, 0, 0, 7], [8, 0, 1, 5], [8, 0, 2, 3], [8, 0, 3, 1], [8, 0, 4, 8], [8, 0, 4, 10], [8, 0, 5, 6], [8, 0, 6, 4], [8, 0, 7, 2], [8, 0, 8, 0], [8, 0, 9, 7], [8, 0, 10, 0], [8, 1, 0, 3], [8, 1, 1, 1], [8, 1, 2, 8], [8, 1, 2, 10], [8, 1, 3, 6], [8, 1, 4, 4], [8, 1, 5, 2], [8, 1, 6, 0], [8, 1, 7, 7], [8, 1, 8, 5], [8, 1, 9, 3], [8, 1, 10, 5], [8, 2, 0, 8], [8, 2, 0, 10], [8, 2, 1, 6], [8, 2, 2, 4], [8, 2, 3, 2], [8, 2, 4, 0], [8, 2, 5, 7], [8, 2, 6, 5], [8, 2, 7, 3], [8, 2, 8, 1], [8, 2, 9, 8], [8, 2, 9, 10], [8, 2, 10, 1], [8, 3, 0, 4], [8, 3, 1, 2], [8, 3, 2, 0], [8, 3, 3, 7], [8, 3, 4, 5], [8, 3, 5, 3], [8, 3, 6, 1], [8, 3, 7, 8], [8, 3, 7, 10], [8, 3, 8, 6], [8, 3, 9, 4], [8, 3, 10, 6], [8, 4, 0, 0], [8, 4, 1, 7], [8, 4, 2, 5], [8, 4, 3, 3], [8, 4, 4, 1], [8, 4, 5, 8], [8, 4, 5, 10], [8, 4, 6, 6], [8, 4, 7, 4], [8, 4, 8, 2], [8, 4, 9, 0], [8, 4, 10, 2], [8, 5, 0, 5], [8, 5, 1, 3], [8, 5, 2, 1], [8, 5, 3, 8], [8, 5, 3, 10], [8, 5, 4, 6], [8, 5, 5, 4], [8, 5, 6, 2], [8, 5, 7, 0], [8, 5, 8, 7], [8, 5, 9, 5], [8, 5, 10, 7], [8, 6, 0, 1], [8, 6, 1, 8], [8, 6, 1, 10], [8, 6, 2, 6], [8, 6, 3, 4], [8, 6, 4, 2], [8, 6, 5, 0], [8, 6, 6, 7], [8, 6, 7, 5], [8, 6, 8, 3], [8, 6, 9, 1], [8, 6, 10, 3], [8, 7, 0, 6], [8, 7, 1, 4], [8, 7, 2, 2], [8, 7, 3, 0], [8, 7, 4, 7], [8, 7, 5, 5], [8, 7, 6, 3], [8, 7, 7, 1], [8, 7, 8, 8], [8, 7, 8, 10], [8, 7, 9, 6], [8, 7, 10, 8], [8, 7, 10, 10], [8, 8, 0, 2], [8, 8, 1, 0], [8, 8, 2, 7], [8, 8, 3, 5], [8, 8, 4, 3], [8, 8, 5, 1], [8, 8, 6, 8], [8, 8, 6, 10], [8, 8, 7, 6], [8, 8, 8, 4], [8, 8, 9, 2], [8, 8, 10, 4], [8, 9, 0, 7], [8, 9, 1, 5], [8, 9, 2, 3], [8, 9, 3, 1], [8, 9, 4, 8], [8, 9, 4, 10], [8, 9, 5, 6], [8, 9, 6, 4], [8, 9, 7, 2], [8, 9, 8, 0], [8, 9, 9, 6], [8, 9, 10, 0], [8, 10, 0, 2], [8, 10, 1, 0], [8, 10, 2, 7], [8, 10, 3, 5], [8, 10, 4, 3], [8, 10, 5, 1], [8, 10, 6, 8], [8, 10, 6, 10], [8, 10, 7, 6], [8, 10, 8, 4], [8, 10, 9, 2], [8, 10, 10, 4], [9, 0, 0, 9], [9, 0, 9, 9], [9, 1, 7, 9], [9, 2, 5, 9], [9, 3, 3, 9], [9, 4, 1, 9], [9, 5, 8, 9], [9, 5, 10, 9], [9, 6, 6, 9], [9, 7, 4, 9], [9, 8, 2, 9], [9, 9, 0, 9], [9, 9, 8, 8], [9, 10, 2, 9], [10, 0, 4, 9], [10, 1, 2, 9], [10, 2, 0, 9], [10, 2, 9, 9], [10, 3, 7, 9], [10, 4, 5, 9], [10, 5, 3, 9], [10, 6, 1, 9], [10, 7, 8, 9], [10, 7, 10, 9], [10, 8, 6, 9], [10, 9, 4, 9], [10, 9, 8, 10], [10, 10, 6, 9]]}
+RLMATH_EOF
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/task.toml b/tasks/optimize-fs-cycle-indep-c11-n4/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..514f3ba127cc52eeed832098389789c68fca3a55
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-fs-cycle-indep-c11-n4"
+version = "0.2.0"
+description = "optimize/fs_cycle_independent_set"
+authors = []
+keywords = ["rlmath", "optimize", "fs_cycle_independent_set"]
+
+[metadata]
+subset = "optimize"
+family = "fs_cycle_independent_set"
+problem_key = "independent_set_strong_power_odd_cycle"
+domain = "graph_theory"
+tier = "research"
+level = "c11_n4"
+source = "FunSearch/cyclic_graphs"
+source_license = "Apache-2.0"
+tags = ["integer_objective"]
+direction = "maximize"
+baseline = 625
+best_known = 754
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/tests/check.py b/tasks/optimize-fs-cycle-indep-c11-n4/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..18467766f4b39df02d00aad7ae384bd83e857320
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/tests/check.py
@@ -0,0 +1,38 @@
+"""Independent set in the strong product C_m^{⊠n}. Score = size.
+
+Two distinct vertices x, y of C_m^{⊠n} (n-tuples over Z_m) are adjacent iff x_i - y_i ∈ {-1, 0, 1} (mod m)
+for every i. Check: mark the answer in a boolean table of size m^n and look up all 3^n - 1 neighbours of
+every answer vertex (vectorised; 26244 vertices of C_9^7 take ~1 s).
+"""
+import itertools
+
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    m, n = inst["m"], inst["n"]
+    vecs = ans.get("vertices")
+    # alpha(C_m^{⊠n}) <= (m/2)^n (fractional independence number is multiplicative under strong products),
+    # so longer lists are invalid; rejecting them early also bounds grading time
+    if not isinstance(vecs, list) or not vecs or 2 ** n * len(vecs) > m ** n:
+        raise Invalid(f"vertices must be a non-empty list of at most ({m}/2)^{n} tuples")
+    for v in vecs:
+        int_list(v, n, 0, m - 1, "vertex")
+    A = np.array(vecs, dtype=np.int64)
+    pw = m ** np.arange(n - 1, -1, -1, dtype=np.int64)
+    codes = A @ pw
+    if len(np.unique(codes)) != len(codes):
+        raise Invalid("duplicate vertices")
+    table = np.zeros(m ** n, bool)
+    table[codes] = True
+    for off in itertools.product((-1, 0, 1), repeat=n):
+        if not any(off):
+            continue
+        nb = ((A + np.array(off)) % m) @ pw
+        hit = table[nb]
+        if hit.any():
+            k = int(np.nonzero(hit)[0][0])
+            raise Invalid(f"vertices {vecs[k]} and {[(x + o) % m for x, o in zip(vecs[k], off)]} are adjacent")
+    return float(len(vecs)), {"size": len(vecs)}
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/tests/instance.json b/tasks/optimize-fs-cycle-indep-c11-n4/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..ff924cd67488b471cc11152e2b91de3537218eba
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/tests/instance.json
@@ -0,0 +1 @@
+{"m": 11, "n": 4, "direction": "maximize", "best_known": 754, "baseline": 625, "family": "fs_cycle_independent_set", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/tests/run.py b/tasks/optimize-fs-cycle-indep-c11-n4/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-fs-cycle-indep-c11-n4/tests/test.sh b/tasks/optimize-fs-cycle-indep-c11-n4/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c11-n4/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/environment/Dockerfile b/tasks/optimize-fs-cycle-indep-c7-n5/environment/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..06d0365485bd1fc9437a07fafe38cb8333e9ac65
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/environment/Dockerfile
@@ -0,0 +1,7 @@
+FROM python:3.11.16-slim
+RUN apt-get update && apt-get install -y --no-install-recommends tmux curl git procps build-essential \
+    && rm -rf /var/lib/apt/lists/*
+RUN pip install --no-cache-dir numpy==2.4.6 scipy==1.17.1 sympy==1.14.0 networkx==3.6.1 \
+    python-sat==1.9.dev15 z3-solver==5.1.0.0 PuLP==3.3.2 ortools==9.15.6755
+WORKDIR /workdir
+COPY instance.json /workdir/instance.json
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/environment/instance.json b/tasks/optimize-fs-cycle-indep-c7-n5/environment/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..0ae21f09a85667140d2893fbf833c4339b6cd7c3
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/environment/instance.json
@@ -0,0 +1 @@
+{"m": 7, "n": 5, "direction": "maximize", "family": "fs_cycle_independent_set", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/instruction.md b/tasks/optimize-fs-cycle-indep-c7-n5/instruction.md
new file mode 100644
index 0000000000000000000000000000000000000000..9574e609853686fb15f45ac18b71d3bd76c9bf20
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/instruction.md
@@ -0,0 +1,7 @@
+Let C_7 be the cycle graph on vertices 0..6 (i adjacent to i+1 mod 7). Its 5-th strong power C_7^5 has vertex set {0..6}^5; two distinct vertices x, y are adjacent iff for every coordinate i, x_i - y_i is -1, 0 or 1 modulo 7. Find an independent set in C_7^5 (no two of its vertices adjacent) that is as large as possible; this gives the Shannon capacity lower bound Theta(C_7) >= |S|^(1/5). The score is |S|.
+
+Answer format: {"vertices": [[x_1, ..., x_5], ...]}: a list of distinct length-5 lists with integer entries in 0..6.
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/solution/solve.sh b/tasks/optimize-fs-cycle-indep-c7-n5/solution/solve.sh
new file mode 100644
index 0000000000000000000000000000000000000000..1e6eb0fcc9d16535521f87ab749e9bf3acef5b33
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/solution/solve.sh
@@ -0,0 +1,5 @@
+#!/bin/bash
+# oracle: a known valid construction (planted witness or published solution)
+cat > /workdir/answer.json <<'RLMATH_EOF'
+{"vertices": [[1, 1, 1, 1, 1], [2, 3, 2, 2, 4], [2, 4, 2, 3, 2], [3, 2, 2, 4, 2], [2, 2, 4, 2, 3], [4, 2, 3, 2, 2], [1, 1, 2, 2, 3], [1, 2, 2, 3, 1], [2, 2, 3, 1, 1], [2, 3, 1, 1, 2], [3, 1, 1, 2, 2], [1, 2, 3, 4, 3], [3, 1, 2, 3, 4], [2, 3, 4, 3, 1], [3, 4, 3, 1, 2], [4, 3, 1, 2, 3], [2, 4, 3, 4, 4], [3, 4, 4, 2, 4], [4, 2, 4, 3, 4], [4, 3, 4, 4, 2], [4, 4, 2, 4, 3], [1, 1, 3, 3, 5], [1, 3, 3, 5, 1], [3, 3, 5, 1, 1], [3, 5, 1, 1, 3], [5, 1, 1, 3, 3], [0, 3, 1, 0, 1], [1, 0, 1, 0, 3], [0, 1, 0, 3, 1], [1, 0, 3, 1, 0], [3, 1, 0, 1, 0], [2, 5, 3, 5, 2], [3, 3, 6, 2, 3], [3, 5, 2, 2, 5], [2, 2, 5, 3, 5], [2, 3, 3, 3, 6], [3, 3, 3, 6, 2], [3, 6, 2, 3, 3], [5, 2, 2, 5, 3], [5, 3, 5, 2, 2], [6, 2, 3, 3, 3], [2, 3, 5, 4, 3], [3, 2, 3, 5, 4], [4, 3, 2, 3, 5], [5, 4, 3, 2, 3], [3, 5, 4, 3, 2], [0, 3, 2, 1, 3], [2, 1, 3, 0, 3], [3, 0, 3, 2, 1], [3, 2, 1, 3, 0], [1, 3, 0, 3, 2], [0, 0, 0, 2, 3], [0, 2, 3, 0, 0], [1, 3, 4, 6, 3], [2, 3, 0, 0, 0], [3, 0, 0, 0, 2], [0, 0, 2, 3, 0], [3, 1, 3, 4, 6], [3, 4, 6, 3, 1], [4, 6, 3, 1, 3], [6, 3, 1, 3, 4], [0, 2, 4, 1, 2], [1, 2, 0, 2, 4], [2, 0, 2, 4, 1], [2, 4, 1, 2, 0], [4, 1, 2, 0, 2], [1, 5, 1, 0, 2], [0, 2, 1, 5, 1], [1, 0, 2, 1, 5], [2, 1, 5, 1, 0], [5, 1, 0, 2, 1], [2, 4, 5, 5, 1], [4, 5, 5, 1, 2], [5, 5, 1, 2, 4], [1, 2, 4, 5, 5], [5, 1, 2, 4, 5], [1, 5, 2, 1, 4], [4, 1, 5, 2, 1], [4, 2, 2, 1, 0], [0, 4, 2, 2, 1], [1, 0, 4, 2, 2], [1, 4, 1, 5, 2], [2, 1, 0, 4, 2], [2, 2, 1, 0, 4], [5, 2, 1, 4, 1], [2, 1, 4, 1, 5], [0, 4, 3, 3, 3], [1, 4, 4, 1, 3], [3, 0, 4, 3, 3], [3, 1, 4, 4, 1], [3, 3, 0, 4, 3], [4, 1, 3, 1, 4], [4, 3, 3, 3, 0], [4, 4, 1, 3, 1], [1, 3, 1, 4, 4], [3, 3, 3, 0, 4], [2, 5, 2, 4, 0], [3, 0, 1, 1, 4], [4, 3, 0, 1, 1], [4, 5, 3, 6, 3], [5, 2, 4, 0, 2], [5, 3, 6, 3, 4], [0, 1, 1, 4, 3], [0, 2, 5, 2, 4], [1, 1, 4, 3, 0], [1, 4, 3, 0, 1], [1, 6, 2, 2, 2], [2, 1, 6, 2, 2], [2, 2, 1, 6, 2], [2, 2, 2, 1, 6], [2, 4, 0, 2, 5], [3, 6, 3, 4, 5], [3, 4, 5, 3, 6], [4, 0, 2, 5, 2], [6, 2, 2, 2, 1], [6, 3, 4, 5, 3], [5, 5, 5, 5, 5], [1, 3, 6, 1, 2], [2, 0, 0, 3, 4], [2, 1, 3, 6, 1], [4, 2, 0, 0, 3], [0, 0, 3, 4, 2], [0, 3, 3, 2, 5], [0, 3, 4, 2, 0], [1, 2, 1, 3, 6], [2, 5, 0, 3, 3], [2, 5, 4, 6, 4], [3, 2, 5, 0, 3], [3, 3, 2, 5, 0], [3, 4, 2, 0, 0], [3, 6, 1, 2, 1], [4, 2, 5, 4, 6], [4, 6, 4, 2, 5], [5, 4, 6, 4, 2], [5, 0, 3, 3, 2], [6, 1, 2, 1, 3], [6, 4, 2, 5, 4], [0, 1, 3, 5, 0], [1, 3, 5, 0, 0], [3, 5, 0, 0, 1], [0, 0, 1, 3, 5], [5, 0, 0, 1, 3], [0, 3, 5, 3, 2], [2, 0, 3, 5, 3], [3, 2, 0, 3, 5], [5, 3, 2, 0, 3], [3, 5, 3, 2, 0], [4, 3, 5, 5, 4], [4, 4, 3, 5, 5], [5, 4, 4, 3, 5], [5, 5, 4, 4, 3], [3, 5, 5, 4, 4], [0, 5, 3, 4, 1], [4, 4, 5, 6, 2], [5, 3, 4, 1, 0], [5, 6, 2, 4, 4], [1, 0, 5, 3, 4], [2, 4, 4, 5, 6], [3, 4, 1, 0, 5], [4, 5, 6, 2, 4], [6, 2, 4, 4, 5], [4, 1, 0, 5, 3], [4, 5, 2, 5, 1], [0, 4, 0, 1, 4], [1, 4, 0, 4, 0], [1, 5, 4, 2, 1], [2, 1, 1, 5, 4], [4, 0, 4, 0, 1], [4, 2, 1, 1, 5], [5, 2, 5, 1, 4], [5, 4, 2, 1, 1], [0, 1, 4, 0, 4], [1, 1, 5, 4, 2], [1, 4, 5, 2, 5], [2, 5, 1, 4, 5], [4, 0, 1, 4, 0], [5, 1, 4, 5, 2], [0, 4, 5, 4, 0], [2, 6, 3, 0, 2], [3, 0, 2, 2, 6], [5, 4, 0, 0, 4], [5, 5, 2, 3, 6], [6, 5, 5, 2, 3], [0, 0, 4, 5, 4], [0, 2, 2, 6, 3], [2, 2, 6, 3, 0], [2, 3, 6, 5, 5], [3, 6, 5, 5, 2], [4, 0, 0, 4, 5], [4, 5, 4, 0, 0], [5, 2, 3, 6, 5], [6, 3, 0, 2, 2], [2, 6, 4, 1, 4], [4, 1, 4, 2, 6], [4, 2, 6, 4, 1], [4, 4, 4, 5, 0], [4, 5, 0, 4, 4], [0, 4, 4, 4, 5], [1, 4, 2, 6, 4], [4, 4, 5, 0, 4], [5, 0, 4, 4, 4], [6, 4, 1, 4, 2], [2, 5, 5, 0, 1], [3, 2, 4, 6, 6], [5, 5, 0, 1, 2], [0, 1, 2, 5, 5], [1, 2, 5, 5, 0], [1, 5, 3, 2, 6], [2, 4, 6, 6, 3], [2, 6, 1, 5, 3], [3, 2, 6, 1, 5], [4, 6, 6, 3, 2], [5, 0, 1, 2, 5], [5, 3, 2, 6, 1], [6, 1, 5, 3, 2], [6, 3, 2, 4, 6], [6, 6, 3, 2, 4], [0, 2, 6, 3, 6], [2, 6, 3, 6, 0], [3, 6, 0, 2, 6], [6, 0, 2, 6, 3], [6, 3, 6, 0, 2], [0, 5, 0, 2, 2], [0, 5, 4, 5, 3], [1, 6, 3, 3, 4], [2, 0, 5, 0, 2], [2, 2, 0, 5, 0], [3, 0, 5, 4, 5], [3, 4, 1, 6, 3], [4, 1, 6, 3, 3], [5, 4, 5, 3, 0], [0, 2, 2, 0, 5], [3, 3, 4, 1, 6], [4, 5, 3, 0, 5], [5, 0, 2, 2, 0], [5, 3, 0, 5, 4], [6, 3, 3, 4, 1], [0, 1, 4, 6, 2], [1, 4, 6, 2, 0], [2, 0, 1, 4, 6], [4, 6, 2, 0, 1], [6, 2, 0, 1, 4], [0, 1, 6, 1, 1], [1, 0, 1, 6, 1], [1, 6, 1, 1, 0], [5, 6, 3, 5, 6], [5, 6, 5, 6, 3], [6, 5, 6, 3, 5], [1, 1, 0, 1, 6], [3, 5, 6, 5, 6], [6, 1, 1, 0, 1], [6, 3, 5, 6, 5], [1, 5, 5, 3, 3], [3, 1, 5, 5, 3], [3, 3, 1, 5, 5], [5, 3, 3, 1, 5], [5, 5, 3, 3, 1], [0, 6, 4, 6, 1], [6, 4, 6, 1, 0], [1, 0, 6, 4, 6], [4, 6, 1, 0, 6], [6, 1, 0, 6, 4], [2, 5, 6, 1, 3], [2, 6, 2, 6, 5], [2, 6, 5, 2, 6], [3, 2, 5, 6, 1], [5, 2, 6, 2, 6], [5, 6, 1, 3, 2], [6, 5, 2, 6, 2], [1, 3, 2, 5, 6], [6, 1, 3, 2, 5], [6, 2, 6, 5, 2], [1, 3, 5, 0, 5], [3, 5, 0, 5, 1], [5, 0, 5, 1, 3], [0, 5, 1, 3, 5], [5, 1, 3, 5, 0], [3, 0, 6, 4, 0], [4, 0, 3, 0, 6], [0, 3, 0, 6, 4], [0, 6, 4, 0, 3], [6, 4, 0, 3, 0], [0, 3, 6, 4, 4], [1, 2, 6, 6, 2], [2, 1, 2, 6, 6], [2, 6, 6, 2, 1], [3, 6, 4, 4, 0], [4, 4, 0, 3, 6], [6, 4, 4, 0, 3], [6, 6, 2, 1, 2], [4, 0, 3, 6, 4], [6, 2, 1, 2, 6], [1, 6, 0, 1, 5], [5, 1, 6, 0, 1], [0, 1, 5, 1, 6], [1, 5, 1, 6, 0], [6, 0, 1, 5, 1], [6, 4, 4, 6, 1], [1, 1, 6, 5, 4], [1, 6, 4, 4, 6], [1, 6, 5, 4, 1], [3, 6, 6, 6, 4], [4, 3, 6, 6, 6], [4, 6, 1, 6, 4], [5, 4, 1, 1, 6], [6, 1, 6, 4, 4], [6, 4, 3, 6, 6], [6, 5, 4, 1, 1], [6, 6, 4, 3, 6], [6, 6, 6, 4, 3], [4, 1, 1, 6, 5], [4, 4, 6, 1, 6], [2, 0, 5, 6, 0], [6, 0, 2, 0, 5], [0, 2, 0, 5, 6], [0, 5, 6, 0, 2], [5, 6, 0, 2, 0], [0, 5, 5, 6, 5], [0, 4, 6, 5, 2], [2, 0, 4, 6, 5], [4, 6, 5, 2, 0], [5, 0, 5, 5, 6], [5, 5, 6, 5, 0], [5, 6, 5, 0, 5], [6, 5, 0, 5, 5], [6, 5, 2, 0, 4], [5, 2, 0, 4, 6], [1, 5, 6, 4, 5], [4, 5, 1, 5, 6], [5, 1, 5, 6, 4], [5, 6, 4, 5, 1], [6, 4, 5, 1, 5], [5, 0, 6, 5, 1], [5, 1, 5, 0, 6], [6, 5, 1, 5, 0], [0, 6, 5, 1, 5], [1, 5, 0, 6, 5], [0, 0, 5, 6, 6], [0, 5, 6, 6, 0], [5, 6, 6, 0, 0], [6, 0, 0, 5, 6], [6, 6, 0, 0, 5], [3, 1, 6, 6, 5], [1, 6, 6, 5, 3], [5, 3, 1, 6, 6], [6, 6, 5, 3, 1], [6, 5, 3, 1, 6], [0, 6, 2, 5, 5], [5, 0, 6, 2, 5], [6, 2, 5, 5, 0], [2, 5, 5, 0, 6], [5, 5, 0, 6, 2], [0, 0, 6, 6, 1], [1, 0, 0, 6, 6], [0, 6, 6, 1, 0], [6, 1, 0, 0, 6], [6, 6, 1, 0, 0], [0, 6, 1, 4, 3], [3, 0, 6, 1, 4], [4, 3, 0, 6, 1], [6, 1, 4, 3, 0], [1, 4, 3, 0, 6], [1, 6, 0, 4, 1], [4, 1, 1, 6, 0], [6, 0, 4, 1, 1], [0, 4, 1, 1, 6], [1, 1, 6, 0, 4]]}
+RLMATH_EOF
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/task.toml b/tasks/optimize-fs-cycle-indep-c7-n5/task.toml
new file mode 100644
index 0000000000000000000000000000000000000000..6764fbd2ee03ea6ab79d0f72899eae7440942bb6
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/task.toml
@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-fs-cycle-indep-c7-n5"
+version = "0.2.0"
+description = "optimize/fs_cycle_independent_set"
+authors = []
+keywords = ["rlmath", "optimize", "fs_cycle_independent_set"]
+
+[metadata]
+subset = "optimize"
+family = "fs_cycle_independent_set"
+problem_key = "independent_set_strong_power_odd_cycle"
+domain = "graph_theory"
+tier = "research"
+level = "c7_n5"
+source = "FunSearch/cyclic_graphs"
+source_license = "Apache-2.0"
+tags = ["integer_objective"]
+direction = "maximize"
+baseline = 243
+best_known = 367
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/tests/check.py b/tasks/optimize-fs-cycle-indep-c7-n5/tests/check.py
new file mode 100644
index 0000000000000000000000000000000000000000..18467766f4b39df02d00aad7ae384bd83e857320
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/tests/check.py
@@ -0,0 +1,38 @@
+"""Independent set in the strong product C_m^{⊠n}. Score = size.
+
+Two distinct vertices x, y of C_m^{⊠n} (n-tuples over Z_m) are adjacent iff x_i - y_i ∈ {-1, 0, 1} (mod m)
+for every i. Check: mark the answer in a boolean table of size m^n and look up all 3^n - 1 neighbours of
+every answer vertex (vectorised; 26244 vertices of C_9^7 take ~1 s).
+"""
+import itertools
+
+import numpy as np
+
+from run import Invalid, int_list
+
+
+def check(inst, ans):
+    m, n = inst["m"], inst["n"]
+    vecs = ans.get("vertices")
+    # alpha(C_m^{⊠n}) <= (m/2)^n (fractional independence number is multiplicative under strong products),
+    # so longer lists are invalid; rejecting them early also bounds grading time
+    if not isinstance(vecs, list) or not vecs or 2 ** n * len(vecs) > m ** n:
+        raise Invalid(f"vertices must be a non-empty list of at most ({m}/2)^{n} tuples")
+    for v in vecs:
+        int_list(v, n, 0, m - 1, "vertex")
+    A = np.array(vecs, dtype=np.int64)
+    pw = m ** np.arange(n - 1, -1, -1, dtype=np.int64)
+    codes = A @ pw
+    if len(np.unique(codes)) != len(codes):
+        raise Invalid("duplicate vertices")
+    table = np.zeros(m ** n, bool)
+    table[codes] = True
+    for off in itertools.product((-1, 0, 1), repeat=n):
+        if not any(off):
+            continue
+        nb = ((A + np.array(off)) % m) @ pw
+        hit = table[nb]
+        if hit.any():
+            k = int(np.nonzero(hit)[0][0])
+            raise Invalid(f"vertices {vecs[k]} and {[(x + o) % m for x, o in zip(vecs[k], off)]} are adjacent")
+    return float(len(vecs)), {"size": len(vecs)}
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/tests/instance.json b/tasks/optimize-fs-cycle-indep-c7-n5/tests/instance.json
new file mode 100644
index 0000000000000000000000000000000000000000..cc75642394f7b33c1176a8027e38a40712ee4d7a
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/tests/instance.json
@@ -0,0 +1 @@
+{"m": 7, "n": 5, "direction": "maximize", "best_known": 367, "baseline": 243, "family": "fs_cycle_independent_set", "subset": "optimize"}
\ No newline at end of file
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/tests/run.py b/tasks/optimize-fs-cycle-indep-c7-n5/tests/run.py
new file mode 100644
index 0000000000000000000000000000000000000000..9f6db6107aa1f8132aeb1abdcf9bbf100792e48a
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/tests/run.py
@@ -0,0 +1,127 @@
+"""rlmath runtime grader. Copied into every task as /tests/run.py next to /tests/check.py.
+
+Deterministic; no LLM in the reward path. Runs with python3 + numpy/scipy/sympy/networkx only.
+
+    python3 /tests/run.py /tests/instance.json /workdir/answer.json
+
+Prints the reward in [0, 1] and writes /logs/verifier/details.json when that directory exists.
+
+check.py must define  check(inst, ans) -> (value, extra_dict)  and raise Invalid for a bad answer.
+  construct : value is ignored; a returned check means the witness is valid -> reward 1.0
+  optimize  : value is the raw objective; reward = 0.1 + 0.9 * progress, where
+              progress = clip((s - baseline) / (best_known - baseline), 0, 1)       (maximize)
+                         clip((baseline - s) / (baseline - best_known), 0, 1)       (minimize)
+              inst must carry "direction", "baseline", "best_known".
+"""
+import json
+import math
+import os
+import sys
+
+VALID_FLOOR = 0.1
+
+
+class Invalid(Exception):
+    pass
+
+
+# ------------------------------------------------------------ input helpers
+
+def int_list(v, n=None, lo=None, hi=None, name="list"):
+    if not isinstance(v, list):
+        raise Invalid(f"{name} must be a list")
+    if n is not None and len(v) != n:
+        raise Invalid(f"{name} must have length {n}, got {len(v)}")
+    for x in v:
+        if isinstance(x, bool) or not isinstance(x, int):
+            raise Invalid(f"{name} must contain integers only")
+        if (lo is not None and x < lo) or (hi is not None and x > hi):
+            raise Invalid(f"{name} entry {x} out of range [{lo}, {hi}]")
+    return v
+
+
+def as_int(x, name="value", lo=None, hi=None):
+    return int_list([x], 1, lo, hi, name)[0]
+
+
+def num(x, name="value"):
+    if isinstance(x, bool) or not isinstance(x, (int, float)):
+        raise Invalid(f"{name} must be a number")
+    if not math.isfinite(x):
+        raise Invalid(f"{name} is not finite")
+    return float(x)
+
+
+def float_matrix(v, rows=None, cols=None, name="matrix"):
+    if not isinstance(v, list) or (rows is not None and len(v) != rows):
+        raise Invalid(f"{name} must be a list of {rows} rows")
+    out = []
+    for r in v:
+        if not isinstance(r, list) or (cols is not None and len(r) != cols):
+            raise Invalid(f"each row of {name} must have {cols} numbers")
+        out.append([num(x, name) for x in r])
+    return out
+
+
+def float_list(v, n=None, name="list"):
+    if not isinstance(v, list) or (n is not None and len(v) != n):
+        raise Invalid(f"{name} must be a list of length {n}")
+    return [num(x, name) for x in v]
+
+
+# ------------------------------------------------------------------ reward
+
+def optimize_reward(inst, s):
+    b, best = inst["baseline"], inst["best_known"]
+    if inst.get("progress_scale") == "log":
+        # for non-negative losses spanning orders of magnitude (e.g. overlap loss -> 0);
+        # progress is measured in log10(value + floor)
+        f = inst.get("log_floor", 1e-3)
+        b, best, s = (math.log10(max(x, 0.0) + f) for x in (b, best, s))
+    if inst["direction"] == "maximize":
+        p = (s - b) / (best - b)
+    else:
+        p = (b - s) / (b - best)
+    return VALID_FLOOR + (1 - VALID_FLOOR) * max(0.0, min(1.0, p))
+
+
+def grade(inst, ans, check):
+    try:
+        if not isinstance(ans, dict):
+            raise Invalid("answer must be a JSON object")
+        value, extra = check(inst, ans)
+        if inst.get("subset") == "optimize":
+            s = float(value)
+            if not math.isfinite(s):
+                raise Invalid("non-finite score")
+            return optimize_reward(inst, s), {"valid": True, "raw_score": s, **(extra or {})}
+        return 1.0, {"valid": True, **(extra or {})}
+    except Invalid as e:
+        return 0.0, {"valid": False, "error": str(e)}
+    except Exception as e:  # any malformed answer
+        return 0.0, {"valid": False, "error": f"{type(e).__name__}: {e}"}
+
+
+def main():
+    here = os.path.dirname(os.path.abspath(__file__))
+    sys.path.insert(0, here)
+    # import ourselves as `run` so check.py's `from run import Invalid` is the same class
+    import run as R  # noqa: E402
+    import check as family  # noqa: E402
+
+    inst = json.load(open(sys.argv[1]))
+    try:
+        ans = json.load(open(sys.argv[2]))
+    except Exception as e:
+        reward, det = 0.0, {"valid": False, "error": f"unreadable answer: {e}"}
+    else:
+        reward, det = R.grade(inst, ans, family.check)
+    det["reward"] = reward
+    if os.path.isdir("/logs/verifier"):
+        with open("/logs/verifier/details.json", "w") as f:
+            json.dump(det, f)
+    print(reward)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tasks/optimize-fs-cycle-indep-c7-n5/tests/test.sh b/tasks/optimize-fs-cycle-indep-c7-n5/tests/test.sh
new file mode 100644
index 0000000000000000000000000000000000000000..648521fa89684f62943a573f74ce3cb75cd3ae29
--- /dev/null
+++ b/tasks/optimize-fs-cycle-indep-c7-n5/tests/test.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+mkdir -p /logs/verifier
+if [ ! -s /workdir/answer.json ]; then
+  echo '{"valid": false, "error": "no /workdir/answer.json"}' > /logs/verifier/details.json
+  echo 0 > /logs/verifier/reward.txt
+  exit 0
+fi
+timeout 290 python3 /tests/run.py /tests/instance.json /workdir/answer.json \
+  > /logs/verifier/reward.txt 2> /logs/verifier/grader.log || echo 0 > /logs/verifier/reward.txt