Document cycle repairs for FOCS and STOC 2026 DAGs

README.md

@@ -659,3 +659,68 @@ configs:
   - split: gemini_3_8_flash
     path: STOC_2026/gemini_3_8_flash-*
 ---
+
+# tcs_dags
+
+Structured theorem-dependency graphs extracted from theoretical computer science papers. Configs identify the conference and year; splits identify the model used to construct the graph.
+
+<!-- cycle-repair-note:start -->
+## Cycle-repair provenance
+
+Every FOCS/STOC 2026 graph in the `gemini_3_8_flash` split was checked procedurally for directed cycles during DAG construction and again after validation. When a cycle was detected, the repair model proposed an explicit edge patch; the patched graph was accepted only after it passed the acyclicity and structural checks.
+
+**39 published DAGs required cycle-edge removal:** 16 from FOCS 2026 and 23 from STOC 2026. The published graphs are the repaired, acyclic versions. Questions associated with these papers were generated from those repaired DAGs.
+
+The `num_cycle_repair_rounds` field counts every structural repair round, including repairs unrelated to cycles. The lists below are narrower: they include only papers whose `cycle_repair_log` records at least one nonempty `before.cyclic_components` value. Each DAG row retains the full log, including the affected nodes and edges, the proposed patch, and the post-repair validation result.
+
+<details>
+<summary>FOCS 2026: 16 of 67 published DAGs</summary>
+
+- **A Polynomial Coreset for Furthest Neighbor in Planar Metrics** (`A_Polynomial_Coreset_for_Furthest_Neighbor_in_Planar_Metrics`) — 3 cyclic components; 3 edges removed
+- **Almost Optimal Multiple Source Shortest Paths and Reachability** (`Almost_Optimal_Multiple_Source_Shortest_Paths_and_Reachability`) — 1 cyclic component; 1 edge removed
+- **Approximately Efficient Multidimensional Bilateral Trade** (`Approximately_Efficient_Multidimensional_Bilateral_Trade`) — 1 cyclic component; 1 edge removed
+- **Approximating the Permanent of a Random Matrix with Polynomially Small Mean: Zeros and Universality** (`Approximating_the_Permanent_of_a_Random_Matrix_with_Polynomially_Small_Mean_Zeros_and_Universality`) — 1 cyclic component; 3 edges removed
+- **Approximation Algorithms for Matroid-Intersection Coloring with Applications to Rota’s Basis Conjecture** (`Approximation_Algorithms_for_Matroid-Intersection_Coloring_with_Applications_to_Rotas_Basis_Conjecture`) — 1 cyclic component; 1 edge removed
+- **Bellman-Ford in Almost-Linear Time for Dense Graphs** (`Bellman-Ford_in_Almost-Linear_Time_for_Dense_Graphs`) — 1 cyclic component; 1 edge removed
+- **Branch-width of connectivity functions is fixed-parameter tractable** (`Branch-width_of_connectivity_functions_is_fixed-parameter_tractable`) — 2 cyclic components; 3 edges removed
+- **Distances in Planar Graphs are Almost for Free!** (`Distances_in_Planar_Graphs_are_Almost_for_Free`) — 1 cyclic component; 1 edge removed
+- **Faster Approximate Fixed Points of $\ell_\infty$-Contractions** (`Faster_Approximate_Fixed_Points_of_ell_infty-Contractions`) — 1 cyclic component; 6 edges removed
+- **Hard CNF Instances for Ideal Proof Systems: The ROABP Case** (`Hard_CNF_Instances_for_Ideal_Proof_Systems_The_ROABP_Case`) — 3 cyclic components; 5 edges removed
+- **Instance-Optimality of Bidirectional PageRank Estimation** (`Instance-Optimality_of_Bidirectional_PageRank_Estimation`) — 1 cyclic component; 1 edge removed
+- **Non-existence probabilities and lower tails in the critical regime via Belief Propagation** (`Non-existence_probabilities_and_lower_tails_in_the_critical_regime_via_Belief_Propagation`) — 2 cyclic components; 2 edges removed
+- **NP-Hardness and a PTAS for the Pinwheel Problem** (`NP-Hardness_and_a_PTAS_for_the_Pinwheel_Problem`) — 2 cyclic components; 5 edges removed
+- **Online Algorithms via Minimax and Posterior Matching** (`Online_Algorithms_via_Minimax_and_Posterior_Matching`) — 2 cyclic components; 4 edges removed
+- **Stronger Memory-Query Tradeoffs for Convex Optimization: The Limitations of Subquadratic Memory** (`Stronger_Memory-Query_Tradeoffs_for_Convex_Optimization_The_Limitations_of_Subquadratic_Memory`) — 1 cyclic component; 1 edge removed
+- **Strongly Refuting Random CSP without Literals** (`Strongly_Refuting_Random_CSP_without_Literals`) — 2 cyclic components; 4 edges removed
+
+</details>
+
+<details>
+<summary>STOC 2026: 23 of 59 published DAGs</summary>
+
+- **Determination of the fifth Busy Beaver value** (`Determination_of_the_fifth_Busy_Beaver_value`) — 1 cyclic component; 1 edge removed
+- **Efficient Quantum Hermite Transform** (`Efficient_Quantum_Hermite_Transform`) — 1 cyclic component; 1 edge removed
+- **Fast Mixing of Quantum Spin Chains at All Temperatures** (`Fast_Mixing_of_Quantum_Spin_Chains_at_All_Temperatures`) — 1 cyclic component; 2 edges removed
+- **Faster All-Pairs Minimum Cut: Bypassing Exact Max-Flow** (`Faster_All-Pairs_Minimum_Cut_Bypassing_Exact_Max-Flow`) — 2 cyclic components; 2 edges removed
+- **Few Single-Qubit Measurements Suffice to Certify Any Quantum State** (`Few_Single-Qubit_Measurements_Suffice_to_Certify_Any_Quantum_State`) — 2 cyclic components; 3 edges removed
+- **Hesse’s Redemption: Efficient Convex Polynomial Programming** (`Hesses_Redemption_Efficient_Convex_Polynomial_Programming`) — 2 cyclic components; 2 edges removed
+- **Ideals, Macaulay Bases, and PCPs** (`Ideals_Macaulay_Bases_and_PCPs`) — 2 cyclic components; 9 edges removed
+- **Improved Bounds for Coin Flipping, Leader Election, and Random Selection** (`Improved_Bounds_for_Coin_Flipping_Leader_Election_and_Random_Selection`) — 1 cyclic component; 2 edges removed
+- **Learning CNF formulas from uniform random solutions in the local lemma regime** (`Learning_CNF_formulas_from_uniform_random_solutions_in_the_local_lemma_regime`) — 1 cyclic component; 1 edge removed
+- **Lower Bounds against the Ideal Proof System in Finite Fields** (`Lower_Bounds_against_the_Ideal_Proof_System_in_Finite_Fields`) — 1 cyclic component; 1 edge removed
+- **MIPco=coRE** (`MIPcocoRE`) — 1 cyclic component; 1 edge removed
+- **Near Optimal Hardness of Approximating k-CSP** (`Near_Optimal_Hardness_of_Approximating_k-CSP`) — 2 cyclic components; 3 edges removed
+- **No exponential quantum speedup for SIS∞ anymore** (`No_exponential_quantum_speedup_for_SIS_anymore`) — 1 cyclic component; 2 edges removed
+- **Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations** (`Non-Adaptive_Cryptanalytic_Time-Space_Lower_Bounds_via_a_Shearer-like_Inequality_for_Permutations`) — 1 cyclic component; 1 edge removed
+- **Perfect Network Resilience in Polynomial Time** (`Perfect_Network_Resilience_in_Polynomial_Time`) — 2 cyclic components; 2 edges removed
+- **Reviving Thorup's Shortcut Conjecture** (`Reviving_Thorups_Shortcut_Conjecture`) — 1 cyclic component; 1 edge removed
+- **S-unit equations in modules and linear-exponential Diophantine equations** (`S-unit_equations_in_modules_and_linear-exponential_Diophantine_equations`) — 1 cyclic component; 3 edges removed
+- **Sample Complexity of Agnostic Multiclass Classification: Natarajan Dimension Strikes Back** (`Sample_Complexity_of_Agnostic_Multiclass_Classification_Natarajan_Dimension_Strikes_Back`) — 1 cyclic component; 2 edges removed
+- **Semi-Streaming Matching in a Single Pass: A New Framework for Lower Bounds via Blueprints** (`Semi-Streaming_Matching_in_a_Single_Pass_A_New_Framework_for_Lower_Bounds_via_Blueprints`) — 1 cyclic component; 1 edge removed
+- **Sparsifying Suprema of Gaussian Processes** (`Sparsifying_Suprema_of_Gaussian_Processes`) — 2 cyclic components; 2 edges removed
+- **Testing noisy low-degree polynomials for sparsity** (`Testing_noisy_low-degree_polynomials_for_sparsity`) — 1 cyclic component; 1 edge removed
+- **The Skolem Problem in rings of positive characteristic** (`The_Skolem_Problem_in_rings_of_positive_characteristic`) — 1 cyclic component; 1 edge removed
+- **What Can Be Computed Locally Revisited - First-Order Logic on Sparse Graphs in Distributed Computing -** (`What_Can_Be_Computed_Locally_Revisited_-_First-Order_Logic_on_Sparse_Graphs_in_Distributed_Computing_-`) — 1 cyclic component; 1 edge removed
+
+</details>
+<!-- cycle-repair-note:end -->