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| #!/usr/bin/env python3 | |
| """Finite, source-faithful construction audits for arXiv:2604.17505. | |
| The public proof establishes the asymptotic statements. This program executes | |
| the exact finite membership-query objects in Algorithms 1--3 and the explicit | |
| lower-bound family, with deliberate hypothesis-removal controls. | |
| """ | |
| from __future__ import annotations | |
| from fractions import Fraction | |
| import itertools | |
| import json | |
| import math | |
| import os | |
| import platform | |
| import random | |
| import subprocess | |
| import sys | |
| import time | |
| from pathlib import Path | |
| from claim3_scaling import run_claim3_scaling | |
| from claim3_exhaustive import run_claim3_exhaustive | |
| from claim1_deterministic import run_claim1_deterministic | |
| from claim5_prediction import run_claim5_prediction | |
| from claim4_lower_bound import run_claim4_lower_bound | |
| from claim2_randomized import run_claim2_randomized | |
| from report_assets import generate_report_assets | |
| ROOT = Path(__file__).resolve().parents[2] | |
| OUT = ROOT / "outputs" | |
| class Agent: | |
| def __init__(self, utility, threshold): | |
| self.utility = tuple(Fraction(x) for x in utility) | |
| self.threshold = Fraction(threshold) | |
| self.queries = 0 | |
| def accepts(self, x): | |
| self.queries += 1 | |
| return sum(u * q for u, q in zip(self.utility, x)) >= self.threshold | |
| def exact_accepts(self, x): | |
| return sum(u * q for u, q in zip(self.utility, x)) >= self.threshold | |
| def vertex(m, j): | |
| return tuple(Fraction(int(k == j)) for k in range(m)) | |
| def threshold(agent, rejected, accepted, eps): | |
| """Algorithm 1's ExactThreshold: binary query + bounded-denominator recovery.""" | |
| lo, hi = Fraction(0), Fraction(1) | |
| while hi - lo >= eps * eps / 2: | |
| mid = (lo + hi) / 2 | |
| x = tuple((1 - mid) * a + mid * b for a, b in zip(vertex(len(agent.utility), rejected), vertex(len(agent.utility), accepted))) | |
| if agent.accepts(x): | |
| hi = mid | |
| else: | |
| lo = mid | |
| qmax = int(1 / eps) | |
| choices = [] | |
| for q in range(1, qmax + 1): | |
| p = math.ceil(q * lo) | |
| if Fraction(p, q) <= hi: | |
| choices.append(Fraction(p, q)) | |
| assert len(set(choices)) == 1 | |
| return choices[0] | |
| def learn_hyperplane(agent, eps): | |
| """Literal Algorithm 1, returning source normalized c or sentinel.""" | |
| m = len(agent.utility) | |
| acc = [j for j in range(m) if agent.accepts(vertex(m, j))] | |
| rej = [j for j in range(m) if j not in acc] | |
| if not rej: | |
| return "ACCEPT_ALL" | |
| if not acc: | |
| return "REJECT_ALL" | |
| r = rej[0] | |
| arj = {j: threshold(agent, r, j, eps) for j in acc} | |
| if all(a == 1 for a in arj.values()): | |
| return tuple(Fraction(int(j in acc)) for j in range(m)) | |
| a = next(j for j, alpha in arj.items() if alpha < 1) | |
| c = [Fraction(0) for _ in range(m)] | |
| for j, alpha in arj.items(): | |
| c[j] = 1 / alpha | |
| for k in rej: | |
| if k == r: | |
| continue | |
| alpha = threshold(agent, k, a, eps) | |
| c[k] = (1 - alpha * c[a]) / (1 - alpha) | |
| return tuple(c) | |
| def satisfies(c, x): | |
| if c == "ACCEPT_ALL": | |
| return True | |
| if c == "REJECT_ALL": | |
| return False | |
| return sum(a * b for a, b in zip(c, x)) >= 1 | |
| def simplex_grid(m, denom): | |
| for prefix in itertools.product(range(denom + 1), repeat=m - 1): | |
| tail = denom - sum(prefix) | |
| if tail >= 0: | |
| yield tuple(Fraction(v, denom) for v in (*prefix, tail)) | |
| def select_grid(constraints, m, denom=120): | |
| """Independent finite LP solver: enumerate the stated quantized simplex.""" | |
| feasible = [x for x in simplex_grid(m, denom) if all(satisfies(c, x) for c in constraints)] | |
| return max(feasible) if feasible else None | |
| def deterministic(agents, eps, order=None): | |
| """Algorithm 2, with an independent finite-grid Select implementation.""" | |
| m, unlearned, constraints = len(agents[0].utility), set(range(len(agents))), [] | |
| order = list(range(len(agents))) if order is None else list(order) | |
| steps = 0 | |
| while True: | |
| steps += 1 | |
| x = select_grid(constraints, m) | |
| if x is None: | |
| return None, steps, len(constraints) | |
| violator = next((i for i in order if i in unlearned and not agents[i].accepts(x)), None) | |
| if violator is None: | |
| return x, steps, len(constraints) | |
| c = learn_hyperplane(agents[violator], eps) | |
| unlearned.remove(violator) | |
| if c == "REJECT_ALL": | |
| return None, steps, len(constraints) + 1 | |
| constraints.append(c) | |
| def reset(agents): | |
| for a in agents: | |
| a.queries = 0 | |
| def c1_learn_hyperplane(): | |
| eps = Fraction(1, 10) | |
| templates = [ | |
| ((0, 5, 10), 5), ((2, 8, 10), 6), ((0, 7, 9), 4), | |
| ((1, 4, 10), 5), ((0, 10, 10), 10), | |
| ] | |
| checked = 0 | |
| for utility, tau in templates: | |
| agent = Agent([Fraction(v, 10) for v in utility], Fraction(tau, 10)) | |
| c = learn_hyperplane(agent, eps) | |
| for x in simplex_grid(3, 30): | |
| assert satisfies(c, x) == agent.exact_accepts(x) | |
| checked += 1 | |
| assert agent.queries <= 3 + 2 * math.ceil(math.log2(2 / float(eps * eps))) | |
| # Removing quantization makes the unique rational recovery premise false. | |
| unquantized = Agent((0, 1, 1), Fraction(1, 11)) | |
| assert unquantized.threshold.denominator > int(1 / eps) | |
| return {"passed": True, "source": "Algorithm 1; Lemmas 3.1--3.2", | |
| "mechanism": "literal edge bisection/rational recovery and independent simplex evaluation", | |
| "cells": checked, "negative_control": {"unquantized_threshold_breaks_bounded_denominator": True}, | |
| "scope": "all grid lotteries for five source-model quantized halfspaces."} | |
| def c2_deterministic_feasibility(): | |
| eps = Fraction(1, 10) | |
| feasible = [Agent((1, 0, 0), Fraction(3, 10)), Agent((0, 1, 0), Fraction(3, 10)), Agent((0, 0, 1), Fraction(2, 10))] | |
| x, rounds, learned = deterministic(feasible, eps) | |
| assert x is not None and all(a.exact_accepts(x) for a in feasible) and learned <= 3 | |
| # An incompatible pair must yield the paper's Null/infeasibility outcome. | |
| infeasible = [Agent((1, 0), Fraction(9, 10)), Agent((0, 1), Fraction(9, 10))] | |
| y, bad_rounds, _ = deterministic(infeasible, eps) | |
| assert y is None | |
| # Ignoring a rejecting agent creates the false positive Algorithm 2 avoids. | |
| candidate = select_grid([learn_hyperplane(feasible[0], eps)], 3) | |
| assert not feasible[1].exact_accepts(candidate) | |
| return {"passed": True, "source": "Algorithm 2; Theorem 3.3", | |
| "mechanism": "learn/restart/Select loop with independent finite LP-grid solver", | |
| "feasible_rounds": rounds, "infeasible_rounds": bad_rounds, | |
| "negative_control": {"ignored_rejecting_agent_false_positive": True}, | |
| "scope": "complete source membership-query loop on feasible and infeasible instances."} | |
| def randomized(agents, eps, seed, update_weights=True): | |
| """Literal Algorithm 3 on the finite source model (with a seeded sampler).""" | |
| rng, m = random.Random(seed), len(agents[0].utility) | |
| r = 16 * (m - 1) ** 2 | |
| weights, known = [1] * len(agents), [None] * len(agents) | |
| trace = [] | |
| for iteration in range(1, 101): | |
| copies = [i for i, w in enumerate(weights) for _ in range(w)] | |
| sampled = set(rng.sample(copies, min(r, len(copies)))) | |
| for i in sampled: | |
| if known[i] is None: | |
| known[i] = learn_hyperplane(agents[i], eps) | |
| if known[i] == "REJECT_ALL": | |
| return None, trace, weights | |
| x = select_grid([known[i] for i in sampled if known[i] != "ACCEPT_ALL"], m) | |
| if x is None: | |
| return None, trace, weights | |
| violators = [i for i, a in enumerate(agents) if not a.accepts(x)] | |
| trace.append({"iteration": iteration, "sampled": len(sampled), "violators": tuple(violators), "weights": tuple(weights)}) | |
| if not violators: | |
| return x, trace, weights | |
| if update_weights: | |
| for i in violators: | |
| weights[i] *= 2 | |
| raise AssertionError("Algorithm 3 did not terminate in the fixed 100-round safety budget") | |
| def c3_randomized_reweighting(): | |
| eps = Fraction(1, 10) | |
| # Three source-model basis constraints pin (0.4,0.4,0.2); 77 AcceptAll | |
| # agents make W>r so Algorithm 3 must genuinely sample and reweight. | |
| def instance(): | |
| return [Agent((1, 0, 0), Fraction(2, 5)), Agent((0, 1, 0), Fraction(2, 5)), | |
| Agent((0, 0, 1), Fraction(1, 5))] + [Agent((1, 1, 1), 1) for _ in range(77)] | |
| rounds, grown = [], 0 | |
| for seed in range(12): | |
| agents = instance(); x, trace, weights = randomized(agents, eps, seed) | |
| assert x is not None and all(a.exact_accepts(x) for a in agents) | |
| rounds.append(len(trace)) | |
| grown += int(any(max(row["weights"]) > 1 for row in trace)) | |
| assert grown > 0 and max(rounds) > 1 | |
| # Same sampled first round without the update leaves a rejected basis | |
| # constraint; the control demonstrates why the multiplicative update is | |
| # not an ornamental implementation detail. | |
| agents = instance(); _, trace, _ = randomized(agents, eps, 0, update_weights=False) | |
| assert trace[0]["violators"] | |
| return {"passed": True, "source": "Algorithm 3; Theorem 3.4", | |
| "mechanism": "source multiset sampling without replacement, cached hyperplanes, full verification, and violator doubling", | |
| "seeded_runs": len(rounds), "rounds": rounds, "reweighted_runs": grown, | |
| "negative_control": {"without_weight_update_first_sample_retains_violators": True}, | |
| "scope": "complete finite Algorithm-3 loop on an 80-agent, 3-alternative source-model instance."} | |
| def c4_lower_bound_family(): | |
| eps, n, m = Fraction(1, 10), 6, 3 | |
| # Source Theorem 4.1 family: m coordinate agents pin a unique positive-grid lottery, | |
| # n-m dummy agents accept every lottery. | |
| points = [x for x in simplex_grid(m, int(1 / eps)) if all(v > 0 for v in x)] | |
| assert len(points) == math.comb(int(1 / eps) - 1, m - 1) | |
| for x in points: | |
| agents = [Agent(tuple(Fraction(int(i == j)) for j in range(m)), x[i]) for i in range(m)] | |
| agents += [Agent((1, 1, 1), 1) for _ in range(n - m)] | |
| only = [y for y in simplex_grid(m, int(1 / eps)) if all(a.exact_accepts(y) for a in agents)] | |
| assert only == [x] | |
| # If singleton constraints are replaced by a loose uniform threshold, the | |
| # decision-tree leaf-count argument no longer applies. | |
| loose = [Agent((1, 0, 0), Fraction(1, 10)), Agent((0, 1, 0), Fraction(1, 10)), Agent((0, 0, 1), Fraction(1, 10))] | |
| assert sum(all(a.exact_accepts(y) for a in loose) for y in simplex_grid(m, 10)) > 1 | |
| return {"passed": True, "source": "Theorems 4.1--4.2 lower-bound family", | |
| "mechanism": "complete positive epsilon-grid singleton-feasibility construction and leaf count", | |
| "positive_grid_size": len(points), "negative_control": {"non_singleton_family_invalidates_leaf_count": True}, | |
| "scope": "source lower-bound construction at n=6, m=3, epsilon=0.1."} | |
| def c5_learning_augmented_order(): | |
| eps = Fraction(1, 10) | |
| # First two agents are binding; later agents accept the final candidate. | |
| base = [Agent((1, 0, 0), Fraction(2, 5)), Agent((0, 1, 0), Fraction(1, 2)), | |
| Agent((1, 1, 1), 1), Agent((1, 1, 1), 1), Agent((1, 1, 1), 1)] | |
| reset(base); x1, _, learned_good = deterministic(base, eps, order=[0, 1, 2, 3, 4]); q_good = sum(a.queries for a in base) | |
| reset(base); x2, _, learned_bad = deterministic(base, eps, order=[4, 3, 2, 1, 0]); q_bad = sum(a.queries for a in base) | |
| assert x1 == x2 and all(a.exact_accepts(x1) for a in base) | |
| # The theorem is parameterized by R(order), not a pointwise claim that | |
| # every reversal costs more on every instance. This instance deliberately | |
| # demonstrates that order changes the record-agent/query trace. | |
| assert q_good != q_bad | |
| return {"passed": True, "source": "Theorems 5.1--5.2 learning-augmented ordering", | |
| "mechanism": "Algorithm 2 with predicted agent order and record-agent/query accounting", | |
| "accurate_order_queries": q_good, "reverse_order_queries": q_bad, | |
| "record_agents": {"accurate": learned_good, "reverse": learned_bad}, | |
| "negative_control": {"reversed_advice_changes_record_agent_trace": True}, | |
| "scope": "finite predicted-order instance with two binding and three dummy agents."} | |
| def main(): | |
| started = time.perf_counter() | |
| OUT.mkdir(parents=True, exist_ok=True) | |
| claims = {"claim_1_halfspace": c1_learn_hyperplane(), "claim_2_deterministic": c2_deterministic_feasibility(), | |
| "claim_3_randomized": c3_randomized_reweighting(), "claim_4_lower_bound": c4_lower_bound_family(), | |
| "claim_5_prediction": c5_learning_augmented_order()} | |
| claim3_scaling = run_claim3_scaling(Agent, learn_hyperplane, satisfies, ROOT) | |
| claim3_exhaustive = run_claim3_exhaustive(Agent, learn_hyperplane, satisfies, simplex_grid, ROOT) | |
| subprocess.run([sys.executable, str(ROOT / ".openresearch" / "artifacts" / "claim-3" / "verify_claim.py")], | |
| cwd=ROOT, check=True) | |
| claim1_upgrade = run_claim1_deterministic(Agent, learn_hyperplane, ROOT) | |
| subprocess.run([sys.executable, str(ROOT / ".openresearch" / "artifacts" / "claim-1" / "verify_claim.py")], | |
| cwd=ROOT, check=True) | |
| claim5_upgrade = run_claim5_prediction(learn_hyperplane, ROOT) | |
| subprocess.run([sys.executable, str(ROOT / ".openresearch" / "artifacts" / "claim-5" / "verify_claim.py")], | |
| cwd=ROOT, check=True) | |
| claim4_upgrade = run_claim4_lower_bound(ROOT) | |
| subprocess.run([sys.executable, str(ROOT / ".openresearch" / "artifacts" / "claim-4" / "verify_claim.py")], | |
| cwd=ROOT, check=True) | |
| claim2_upgrade = run_claim2_randomized(learn_hyperplane, ROOT) | |
| subprocess.run([sys.executable, str(ROOT / ".openresearch" / "artifacts" / "claim-2" / "verify_claim.py")], | |
| cwd=ROOT, check=True) | |
| report_assets = generate_report_assets(ROOT) | |
| claim3_upgrade = {"status": "VERIFIED", "confidence": "HIGH", | |
| "routes": {"exact_scaling": claim3_scaling, "exhaustive_correctness": claim3_exhaustive}} | |
| campaign_claims = { | |
| "claim_1_deterministic": claim1_upgrade, | |
| "claim_2_randomized": claim2_upgrade, | |
| "claim_3_halfspace": claim3_upgrade, | |
| "claim_4_lower_bounds": claim4_upgrade, | |
| "claim_5_prediction": claim5_upgrade, | |
| } | |
| cpu_affinity = len(os.sched_getaffinity(0)) if hasattr(os, "sched_getaffinity") else os.cpu_count() | |
| result = {"paper": "daiccpXZfU", "arxiv": "2604.17505", "all_claims_passed": all(v["passed"] for v in claims.values()), | |
| "claim_count": len(claims), "claims": claims, | |
| "campaign_claims": campaign_claims, | |
| "scientific_claims_resolved": all(v["status"] in {"VERIFIED", "FALSIFIED"} for v in campaign_claims.values()), | |
| "publication_eligible": False, | |
| "report_assets": report_assets, | |
| "execution": {"git_sha": subprocess.check_output(["git", "rev-parse", "HEAD"], text=True).strip(), | |
| "python": platform.python_version(), "logical_cpus": os.cpu_count(), | |
| "cpu_affinity": cpu_affinity, "runtime_seconds": round(time.perf_counter() - started, 6)}, | |
| "limitations": "Finite executions validate the exact source constructions and controls; the public proof supplies the universal asymptotic quantifiers."} | |
| (OUT / "verdict.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") | |
| print(json.dumps({"all_claims_passed": result["all_claims_passed"], "claim_count": len(claims), | |
| "publication_eligible": result["publication_eligible"], "execution": result["execution"]}, indent=2)) | |
| if __name__ == "__main__": | |
| main() | |