Document curated SODA final-answer release

README.md

@@ -74,3 +74,31 @@ configs:
   - split: test
     path: SODA_2026/test-*
 ---
+
+# TCSBench 2026: Final-answer problems
+
+This release contains **290 exact-answer problems** from **142 SODA 2026 paper DAGs**. It is SODA-only, and answers are visible. The public config/split is `SODA_2026` / `test`.
+
+## Coverage and curation
+
+The generator requested three problems per DAG, each with a distinct theorem-like target node; quality gates did not force-fill unsuitable papers. After curation, 62 papers have three questions, 38 have two, 28 have one, and 14 have none. Thus 128 papers appear in the question rows. [`paper_coverage.json`](./paper_coverage.json) lists all source papers and their final counts.
+
+This release was copied from the [original AI-Math-TCS release](https://huggingface.co/datasets/AI-Math-TCS/TCSBench_2026_ans), then the trailing answer-format instruction was removed from **every** public `problem`. The mathematical question, canonical answer, reference solution, audit fields, and `question_id` were otherwise preserved. **41 rows were excluded** because their canonical `answer` contains an integer literal of six or more decimal digits anywhere in the expression, including inside fractions or radicals. This is a textual literal rule, not an evaluation of symbolic expressions. The original source release remains available; this copy is the curated evaluation set.
+
+Remaining answer types: 133 integer, 86 rational, 41 rational-expression, and 30 algebraic-expression. 1 retained row(s) have a `unicode_math` formatting flag, recorded in `format_issues`.
+
+## Generation and checks
+
+Problems were generated with `gpt-5.6-sol` at `xhigh` effort from a target node and its proof-relevant DAG context. Each accepted problem passed context and exact-answer eligibility checks, scaffold reduction, a proceduralness audit, an independent solve, answer-equivalence review, and a final content audit. The post-generation removal of the response-format instruction changes no mathematical assumptions or requested quantity, but these audits were not rerun on the edited string. Model-assisted audits are not a formal guarantee of mathematical correctness.
+
+The `answer` column is the canonical closed-form answer; `reference_solution` explains it. `answer_symbols` and `answer_assumptions` are JSON strings used by the 0/1 grader. Exact symbolic comparison is attempted first, with `gpt-5.6-luna` at medium effort used only when exact comparison is unresolved. See the [grader](https://github.com/CohenQU/AI-Math-TCS/blob/6c1dc00/scripts/synthetic/final_answer_grader.py) and [equivalence fallback](https://github.com/CohenQU/AI-Math-TCS/blob/6c1dc00/scripts/synthetic/final_answer_equivalence.py).
+
+## Provenance
+
+Each row records its source paper and target node, generation settings, audit records, and the SHA-256 of the exact source DAG payload. The source is the [structurally validated SODA 2026 DAG split](https://huggingface.co/datasets/AI-Math-TCS/tcs_dags/viewer/SODA_2026/legacy_v1_6_structurally_repaired_gemini_3_8_flash) at revision `4ccf1e006ac1d6f3053049b7fcc5aa47cec8a6f8`.
+
+```python
+from datasets import load_dataset
+
+ds = load_dataset("HerrHruby/TCSBench_2026_ans", "SODA_2026", split="test")
+```

paper_coverage.json

@@ -0,0 +1,860 @@
+{
+  "conference": "SODA_2026",
+  "paper_count": 142,
+  "question_count": 290,
+  "papers": [
+    {
+      "paper_id": "-approximation_algorithm_general",
+      "title": "A $(2 + \\epsilon)$-approximation algorithm for the general scheduling problem in quasipolynomial time",
+      "num_questions": 3,
+      "source_dag_sha256": "bf876eb0802a3e273c941fcd2ec2c8a08e83a62c795cd17c862d02db1a723b85"
+    },
+    {
+      "paper_id": "algebraic_closure_matrix",
+      "title": "Algebraic Closure of Matrix Sets Recognized by 1-VASS",
+      "num_questions": 0,
+      "source_dag_sha256": "5c80f4bb8cd457556e40e30188fe2e89df73ccd916ec08fef7fcf8d901eb95a7"
+    },
+    {
+      "paper_id": "algorithmic_improvements_list",
+      "title": "Algorithmic Improvements to List Decoding of Folded Reed-Solomon Codes",
+      "num_questions": 2,
+      "source_dag_sha256": "d215f4ecc399ad6f533947dbc0695fbf10c633066638e1214aaabfcf0e8afccf"
+    },
+    {
+      "paper_id": "algorithms_lower_bounds",
+      "title": "Algorithms and Lower Bounds for the Maximum Overlap of Two Polygons Under Translation",
+      "num_questions": 2,
+      "source_dag_sha256": "7cb8a7874f853bc7d065e063f3653449eeed8065b1aa6fe80328af4b75c331d3"
+    },
+    {
+      "paper_id": "almost_perfect_discrete",
+      "title": "(Almost) Perfect Discrete Iterative Load Balancing",
+      "num_questions": 1,
+      "source_dag_sha256": "72315c15bd3cc777b17451b24128ab7ed34c4049bb38f6adad8fee34a47cd77b"
+    },
+    {
+      "paper_id": "approaching_optimality_solving",
+      "title": "Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure",
+      "num_questions": 3,
+      "source_dag_sha256": "daa65fdc195d1fa686167c0a75af3413e621d4e8a3f6e7d82eab966e19d08cdf"
+    },
+    {
+      "paper_id": "approximate_counting_permutation",
+      "title": "Approximate Counting of Permutation Patterns",
+      "num_questions": 1,
+      "source_dag_sha256": "ff33c620e64e58514abbac48e636874fdc16a3d745dd2f4bb2673e02e08c0502"
+    },
+    {
+      "paper_id": "approximate_light_spanners",
+      "title": "Approximate Light Spanners in Planar Graphs",
+      "num_questions": 2,
+      "source_dag_sha256": "2adb952c328af79b999d89fb417058697990dacc9a448f60f1b983dde8896ac8"
+    },
+    {
+      "paper_id": "approximately_dominating_sets",
+      "title": "Approximately Dominating Sets in Elections",
+      "num_questions": 1,
+      "source_dag_sha256": "9a4fda9ea00b3f26581b0f9ab55eb9ec84226c58ffb67219212ec95180a8f0cd"
+    },
+    {
+      "paper_id": "approximating_matroid_basis",
+      "title": "Approximating Matroid Basis Testing for Partition Matroids using Budget-In-Expectation",
+      "num_questions": 2,
+      "source_dag_sha256": "f25017eb0c0cc5e5fcea865253916bfa8c53a034787b0963d75967311c7bbb3e"
+    },
+    {
+      "paper_id": "balls_bins_infinite",
+      "title": "Balls and Bins and the Infinite Process with Random Deletions",
+      "num_questions": 2,
+      "source_dag_sha256": "baafa772032fe7197a4284f5a9d3063aba3c5c3cfba1addb0dcd57f3e1ae78cc"
+    },
+    {
+      "paper_id": "better-than-2_approximation_directed",
+      "title": "A Better-Than-2 Approximation for the Directed Tree Augmentation Problem",
+      "num_questions": 3,
+      "source_dag_sha256": "f8695354a0ba703f6a6b2aa4a80db6b8153221714ec33fa925109693f078cfc5"
+    },
+    {
+      "paper_id": "block_size_matter",
+      "title": "Does block size matter in randomized block Krylov low-rank approximation?",
+      "num_questions": 3,
+      "source_dag_sha256": "76c94b133e39458cdf811f5376dc90b2ce6aaad04bb83119378f2082d2ce923b"
+    },
+    {
+      "paper_id": "braiding_vineyards",
+      "title": "Braiding Vineyards",
+      "num_questions": 2,
+      "source_dag_sha256": "6473f734d2a07d3207e4c1f61b6581d346a5e9afd907901c81add8fac29f92a0"
+    },
+    {
+      "paper_id": "broader_view_clustering",
+      "title": "A Broader View on Clustering under Cluster-Aware Norm Objectives",
+      "num_questions": 2,
+      "source_dag_sha256": "f3cf4ff8034023fab019339f5b8add8f02aea066c3cef975579dcd73e3e3dca7"
+    },
+    {
+      "paper_id": "burling_graphs_graphs",
+      "title": "BURLING GRAPHS IN GRAPHS WITH LARGE CHROMATIC NUMBER",
+      "num_questions": 0,
+      "source_dag_sha256": "eaddae67ef4009938c95b99913296b4afe2d94df37959045e403b8013583c03e"
+    },
+    {
+      "paper_id": "catching_rats_h-minor-free",
+      "title": "Catching Rats in $H$-minor-free Graphs",
+      "num_questions": 3,
+      "source_dag_sha256": "c6529fa5affdc94ee243889d3f5622f46f10773fc6b213fd0a9302ed848a92fc"
+    },
+    {
+      "paper_id": "cell-probe_lower_bounds",
+      "title": "Cell-Probe Lower Bounds via Semi-Random CSP Refutation: Simplified and the Odd-Locality Case",
+      "num_questions": 3,
+      "source_dag_sha256": "f8ff06c892e922f73cd1d4c39282bbc02edc8fb4df76107d47769ab8c79b5361"
+    },
+    {
+      "paper_id": "centered_colorings_minor-closed",
+      "title": "CENTERED COLORINGS IN MINOR-CLOSED GRAPH CLASSES",
+      "num_questions": 3,
+      "source_dag_sha256": "9e3ff907b7e173415536e3bd6aa05d49fdb35155d837f5748002e75c646aa8c8"
+    },
+    {
+      "paper_id": "cfg_dnnf_admit",
+      "title": "#CFG and #DNNF admit FPRAS",
+      "num_questions": 2,
+      "source_dag_sha256": "f78a33ee44c305fe1fc40726de26191bb1a2c83ebe9a22a9b313cc547de3085f"
+    },
+    {
+      "paper_id": "classification_long-refinement_graphs",
+      "title": "A Classification of Long-Refinement Graphs for Colour Refinement",
+      "num_questions": 2,
+      "source_dag_sha256": "a0712b2fd749ad3eb85ec2e50d01fd1774f65eba1634664c5574d8284d078fc1"
+    },
+    {
+      "paper_id": "coloring_3-colorable_graphs",
+      "title": "Coloring 3-Colorable Graphs with Low Threshold Rank",
+      "num_questions": 2,
+      "source_dag_sha256": "9df9ba0aeb0bf22512b197834d8d1033db8a09748727424619eb3b2ed65070f5"
+    },
+    {
+      "paper_id": "combinatorial_philosopher_inequalities",
+      "title": "Combinatorial Philosopher Inequalities",
+      "num_questions": 3,
+      "source_dag_sha256": "1430bc6e034667456d21954d76eecee560dbbe3447834ef783818854722926c8"
+    },
+    {
+      "paper_id": "communication_complexity_combinatorial",
+      "title": "The Communication Complexity of Combinatorial Auctions with Additional Succinct Bidders",
+      "num_questions": 3,
+      "source_dag_sha256": "ca6db54df37b817988e0b2029c30df11503d3a6696f9638d9494f6b33df7ba5f"
+    },
+    {
+      "paper_id": "comparison_theorems_mixing",
+      "title": "Comparison Theorems for the Mixing Times of Systematic and Random Scan Dynamics",
+      "num_questions": 3,
+      "source_dag_sha256": "e200123c6aa8b1d9000c2d2ac28d06cef5f0ef208d7fd91467c462290989f1d6"
+    },
+    {
+      "paper_id": "compatibility_fairness_nash",
+      "title": "Compatibility of Fairness and Nash Welfare under Subadditive Valuations",
+      "num_questions": 3,
+      "source_dag_sha256": "7f470f6922ce777f28ee0e11eb67387ec5e8385c8b31b7cdda09a6568bf532a0"
+    },
+    {
+      "paper_id": "complexity_skolem_problem",
+      "title": "On the Complexity of the Skolem Problem at Low Orders",
+      "num_questions": 3,
+      "source_dag_sha256": "6bc655ea355511bc15b7e3ed73c7b47d0fa380d32d5974f32a32688a41ef8e3c"
+    },
+    {
+      "paper_id": "computation_schrijver_kernels",
+      "title": "On the Computation of Schrijver’s Kernels",
+      "num_questions": 0,
+      "source_dag_sha256": "eadd06809cc3c425be64c347ea04935bfd633b0cbdd6da6348fc4dc359f6b6e6"
+    },
+    {
+      "paper_id": "computational_complexity_property",
+      "title": "Computational Complexity in Property Testing",
+      "num_questions": 1,
+      "source_dag_sha256": "14519e018e882973cd83d448f9dcf956151aa41e449375678652a9865b19a774"
+    },
+    {
+      "paper_id": "contract_design_sequential",
+      "title": "Contract Design for Sequential Actions",
+      "num_questions": 1,
+      "source_dag_sha256": "90a413de2146cf59bb26019ddb9a883a9660f1591c30b9bded1729281e61f0a8"
+    },
+    {
+      "paper_id": "covering_euclidean_plane",
+      "title": "Covering the Euclidean Plane by a Pair of Trees",
+      "num_questions": 3,
+      "source_dag_sha256": "12c4f546c4a6dedb42bb712a05bfddef92ac0a70aae7015ec11da16b7487d5de"
+    },
+    {
+      "paper_id": "csp_approach_graph",
+      "title": "A CSP approach to Graph Sandwich Problems",
+      "num_questions": 0,
+      "source_dag_sha256": "07a6f9d48b0a9747a0a6cdf464d1e6124bc6b5a98eff1b747ee9005842638d1f"
+    },
+    {
+      "paper_id": "derandomizing_pseudopolynomial_algorithms",
+      "title": "Derandomizing Pseudopolynomial Algorithms for Subset Sum",
+      "num_questions": 2,
+      "source_dag_sha256": "fec1591d67ea657262d1dc59f295a9800820cfb6c51c7bf91d128a679ff3c679"
+    },
+    {
+      "paper_id": "deterministic_dynamic_edge",
+      "title": "Deterministic Dynamic Edge Colouring",
+      "num_questions": 1,
+      "source_dag_sha256": "380769133dbd6a1c2ebd333e88d2056e50ca7e8dd3044e864b54668ab6f1e361"
+    },
+    {
+      "paper_id": "deterministic_polylogarithmic_competitive",
+      "title": "A Deterministic Polylogarithmic Competitive Algorithm for Matching with Delays",
+      "num_questions": 3,
+      "source_dag_sha256": "98cf7d22157ae375cf17dc31087c5f862d9c5419c6f01d8ba8882d5a10f4fa64"
+    },
+    {
+      "paper_id": "deterministically_finding_element",
+      "title": "ON DETERMINISTICALLY FINDING AN ELEMENT OF HIGH ORDER MODULO A COMPOSITE",
+      "num_questions": 3,
+      "source_dag_sha256": "cadfb791c01cab6fea3343ea08b3d431d9bfe3984e778a42653c5e7d1ac932ef"
+    },
+    {
+      "paper_id": "dichotomy_orderings",
+      "title": "Dichotomy for orderings?",
+      "num_questions": 0,
+      "source_dag_sha256": "79cb192fbe8f942b6a5fdc48aabdce335f83210910d41ed51df542923bf969ab"
+    },
+    {
+      "paper_id": "differentially_private_algorithms",
+      "title": "Differentially Private Algorithms for Graph Cuts: A Shifting Mechanism Approach and More",
+      "num_questions": 3,
+      "source_dag_sha256": "bca94265671587627a433f4b68f7459d2fb08f4bd81f009effeb0f2d3d29e67e"
+    },
+    {
+      "paper_id": "differentially_private_quasi-concave",
+      "title": "Differentially Private Quasi-Concave Optimization: Bypassing the Lower Bound and Application to Geometric Problems",
+      "num_questions": 3,
+      "source_dag_sha256": "35eab707c39e9d48400219a53478cb7d06896a52e950f716ab9ddf75237bb5fc"
+    },
+    {
+      "paper_id": "directed_disjoint_paths",
+      "title": "The Directed Disjoint Paths Problem with Congestion",
+      "num_questions": 2,
+      "source_dag_sha256": "01849c7af9004a598e6d7fa8be2aed914bd1dc85412083ef398634f38e5128d6"
+    },
+    {
+      "paper_id": "disjoint_paths_expanders",
+      "title": "Disjoint Paths in Expanders in Deterministic Almost-Linear Time via Hypergraph Perfect Matching",
+      "num_questions": 1,
+      "source_dag_sha256": "011494752958c77234a2a5a85fc00127a5de5190049c23eb1b39719f6e67c208"
+    },
+    {
+      "paper_id": "distributed_interactive_proofs",
+      "title": "Distributed Interactive Proofs for Planarity with Log-Star Communication",
+      "num_questions": 2,
+      "source_dag_sha256": "e02cd2d29b6370b4ddec860c832e2269c9efcb11f09168c9c8659f8a7e1f940d"
+    },
+    {
+      "paper_id": "downward_self-reducibility_total",
+      "title": "Downward self-reducibility in the total function polynomial hierarchy",
+      "num_questions": 1,
+      "source_dag_sha256": "035a4515f05dc0bda3c5f57f11f3a4e35a405054d3b97890809216c59c488daf"
+    },
+    {
+      "paper_id": "dynamic_3d_convex",
+      "title": "Dynamic 3D Convex Hulls Revisited and Applications",
+      "num_questions": 0,
+      "source_dag_sha256": "569e3c4d1604dca34ccf30f323b674176d6150798b1bfc04f7a780f3a3747d19"
+    },
+    {
+      "paper_id": "dynamic_connectivity_expected",
+      "title": "Dynamic Connectivity with Expected Polylogarithmic Worst-Case Update Time",
+      "num_questions": 2,
+      "source_dag_sha256": "f05e56d7051ab06a0bda011a7b70ae8cccdf464bc9f1c9b0932789ad49712f7d"
+    },
+    {
+      "paper_id": "edge_expansion_random",
+      "title": "ON THE EDGE EXPANSION OF RANDOM POLYTOPES",
+      "num_questions": 3,
+      "source_dag_sha256": "1b4df151ad06a414ae1d312a3763e0d59d2607c0e26281c32af6cca35fae3762"
+    },
+    {
+      "paper_id": "efficient_online_random",
+      "title": "Efficient Online Random Sampling via Randomness Recycling",
+      "num_questions": 3,
+      "source_dag_sha256": "fcb28c2654d0acc0a48b8df91d7e47abf183ae811ea5e780a049f815254731ea"
+    },
+    {
+      "paper_id": "efficiently_constructing_sparse",
+      "title": "Efficiently Constructing Sparse Navigable Graphs",
+      "num_questions": 3,
+      "source_dag_sha256": "fec0c7cd8bf1678d0f2d50f710b23311ce8fc7f371bf94ae077494fa33f5ad46"
+    },
+    {
+      "paper_id": "erd_s-p_sa",
+      "title": "The Erdős-Pósa property for circle graphs as vertex-minors",
+      "num_questions": 3,
+      "source_dag_sha256": "0062d55c721b3897e71289dd5b3caa264b03c9c9f4a00049e5eff44f75e23c63"
+    },
+    {
+      "paper_id": "evasive_sets_twisted",
+      "title": "Evasive sets, twisted varieties, and container-clique trees",
+      "num_questions": 3,
+      "source_dag_sha256": "c56369c9ec36da99818c2a2a12ac1a2ee0b9c9ff91b76977055c81eccc9870b9"
+    },
+    {
+      "paper_id": "excluding_line_minor",
+      "title": "Excluding a Line Minor via Design Matrices and Column Number Bounds for the Circuit Imbalance Measure",
+      "num_questions": 3,
+      "source_dag_sha256": "a65a96dc8d50dc4e11ba5b57ddfa700cfb3f6a73348a5acf5d6e07a4c0dc4226"
+    },
+    {
+      "paper_id": "existence_fair_efficient",
+      "title": "Existence of Fair and Efficient Allocation of Indivisible Chores",
+      "num_questions": 0,
+      "source_dag_sha256": "f8db068dd0b11556e91a88782f2fa23204fb376dafb0e3b834a7afc2fd31451e"
+    },
+    {
+      "paper_id": "expander_pruning_polylogarithmic",
+      "title": "Expander Pruning with Polylogarithmic Worst-Case Recourse and Update Time",
+      "num_questions": 3,
+      "source_dag_sha256": "cfb2303f2df9120895a5ccf4134801595176b5ec1efedac7922a28f3b12fe3c2"
+    },
+    {
+      "paper_id": "explicit_min-wise_hash",
+      "title": "Explicit Min-wise Hash Families with Optimal Size",
+      "num_questions": 1,
+      "source_dag_sha256": "2385fd2ab3dc8d5f58ddb604987f8a8165bf5d024c351d6c2827888147536116"
+    },
+    {
+      "paper_id": "extended_vc-dimension_radon",
+      "title": "Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets",
+      "num_questions": 2,
+      "source_dag_sha256": "ac3a348d4823b83f090fda7f4ccd8fcec689ffaa5e0a4ff1bc218d7858352061"
+    },
+    {
+      "paper_id": "faster_algorithms_packing",
+      "title": "Faster algorithms for packing forests in graphs and related problems",
+      "num_questions": 3,
+      "source_dag_sha256": "3e72bdf9dafaa7c64a95c4e5705accec37bf6bc9bec6f0a034018d5d03bee7e6"
+    },
+    {
+      "paper_id": "faster_estimation_average",
+      "title": "Faster Estimation of the Average Degree of a Graph Using Random Edges and Structural Queries",
+      "num_questions": 3,
+      "source_dag_sha256": "44116dda9f643a3a11d86a3bea881a3afce09c3f0f497091d3534386a941135f"
+    },
+    {
+      "paper_id": "faster_negative-weight_shortest",
+      "title": "Faster Negative-Weight Shortest Paths and Directed Low-Diameter Decompositions",
+      "num_questions": 2,
+      "source_dag_sha256": "b314130ab569e44ba80540067af914a381e3bb4513e1e6c8251330d35db1202c"
+    },
+    {
+      "paper_id": "faster_negative_length",
+      "title": "Faster negative length shortest paths by bootstrapping hop reducers",
+      "num_questions": 3,
+      "source_dag_sha256": "e0ec2ce4316794505059f43381988b4ea50e1508e0ea2337f22365a1cb3351bb"
+    },
+    {
+      "paper_id": "feature_selection_junta",
+      "title": "Feature Selection and Junta Testing are Statistically Equivalent",
+      "num_questions": 3,
+      "source_dag_sha256": "1dc73df0d12074751ede7866564be0a78c24ccb140431c42f3960fa0ade8f0ac"
+    },
+    {
+      "paper_id": "few_good_choices",
+      "title": "A FEW GOOD CHOICES",
+      "num_questions": 3,
+      "source_dag_sha256": "355c7f4ee506db667a09c959251c229fa235f38361d6e091cc926e61dfaffd6a"
+    },
+    {
+      "paper_id": "finding_sparse_induced",
+      "title": "Finding sparse induced subgraphs on graphs of bounded induced matching treewidth",
+      "num_questions": 2,
+      "source_dag_sha256": "c8f34a00d5b0a97832041bf9adfb9ccc58347f2ea46c5ed3f45ebc487b4b8224"
+    },
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+}