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 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.

FOCS 2026: 16 of 67 published DAGs

• 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

STOC 2026: 23 of 59 published DAGs

• 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

SODA 2026 legacy v1.6 de-cycling

The SODA_2026/legacy_v1_6_decycled_gemini_3_8_flash split contains all 142 SODA 2026 DAGs from AI-Math-TCS/tcs_dataset_v1_6_dags, pinned to source revision d73772c60fd1770939fef4ed7d6db0b9b81e788b. Procedural cycle detection found cycles in 53; Gemini 3.8 Flash (medium) proposed edge-only patches for those 53. All 142 published graphs passed a final acyclicity check, and node content was preserved. The other 89 graphs had no cycles and received no model repair call.

This was cycle-only remediation, not a full re-validation or re-DAGification. After cycle removal, 86 of 142 graphs still fail the current non-cycle structural gate (for example, missing or multiple primary parents or unknown endpoints); 11 have no overview node. These were not repaired in this pass. The original v1.6 dataset is unchanged. had_cycles, num_original_cyclic_components, num_cycle_repair_rounds, cycle_repair_log, legacy_structural_issues, and the source revision/hash columns document each row. The split name identifies the source and repair model; it does not imply Gemini generated the original DAG nodes.

SODA 2026 legacy v1.6: 53 of 142 DAGs repaired

• #CFG and #DNNF admit FPRAS (cfg_dnnf_admit) — 1 cyclic component(s); 20 edges removed
• (Almost) Perfect Discrete Iterative Load Balancing (almost_perfect_discrete) — 1 cyclic component(s); 17 edges removed
• A $(2 + \epsilon)$-approximation algorithm for the general scheduling problem in quasipolynomial time (-approximation_algorithm_general) — 1 cyclic component(s); 14 edges removed
• A FEW GOOD CHOICES (few_good_choices) — 1 cyclic component(s); 1 edges removed
• A Post-Quantum Lower Bound for the Distributed Lovász Local Lemma (post-quantum_lower_bound) — 1 cyclic component(s); 2 edges removed
• A Simple and Fast Reduction from Gomory-Hu Trees to Polylog Maxflows (simple_fast_reduction) — 1 cyclic component(s); 4 edges removed
• Algorithmic Improvements to List Decoding of Folded Reed-Solomon Codes (algorithmic_improvements_list) — 1 cyclic component(s); 6 edges removed
• Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure (approaching_optimality_solving) — 2 cyclic component(s); 4 edges removed
• Approximately Dominating Sets in Elections (approximately_dominating_sets) — 3 cyclic component(s); 6 edges removed
• Braiding Vineyards (braiding_vineyards) — 1 cyclic component(s); 2 edges removed
• BURLING GRAPHS IN GRAPHS WITH LARGE CHROMATIC NUMBER (burling_graphs_graphs) — 1 cyclic component(s); 18 edges removed
• Catching Rats in $H$-minor-free Graphs (catching_rats_h-minor-free) — 1 cyclic component(s); 12 edges removed
• Cell-Probe Lower Bounds via Semi-Random CSP Refutation: Simplified and the Odd-Locality Case (cell-probe_lower_bounds) — 2 cyclic component(s); 2 edges removed
• CENTERED COLORINGS IN MINOR-CLOSED GRAPH CLASSES (centered_colorings_minor-closed) — 4 cyclic component(s); 4 edges removed
• Computational Complexity in Property Testing (computational_complexity_property) — 2 cyclic component(s); 2 edges removed
• Derandomizing Pseudopolynomial Algorithms for Subset Sum (derandomizing_pseudopolynomial_algorithms) — 1 cyclic component(s); 9 edges removed
• Deterministic Dynamic Edge Colouring (deterministic_dynamic_edge) — 1 cyclic component(s); 5 edges removed
• Disjoint Paths in Expanders in Deterministic Almost-Linear Time via Hypergraph Perfect Matching (disjoint_paths_expanders) — 1 cyclic component(s); 1 edges removed
• Does block size matter in randomized block Krylov low-rank approximation? (block_size_matter) — 2 cyclic component(s); 6 edges removed
• Dynamic 3D Convex Hulls Revisited and Applications (dynamic_3d_convex) — 1 cyclic component(s); 3 edges removed
• Evasive sets, twisted varieties, and container-clique trees (evasive_sets_twisted) — 1 cyclic component(s); 1 edges removed
• Existence of Fair and Efficient Allocation of Indivisible Chores (existence_fair_efficient) — 4 cyclic component(s); 8 edges removed; 1 replacement edge
• Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets (extended_vc-dimension_radon) — 1 cyclic component(s); 15 edges removed
• Faster algorithms for packing forests in graphs and related problems (faster_algorithms_packing) — 1 cyclic component(s); 1 edges removed
• Halfspaces are hard to test with relative error (halfspaces_hard_test) — 1 cyclic component(s); 1 edges removed
• Interaction between skew-representability, tensor products, extension properties, and rank inequalities (interaction_between_skew-representability) — 1 cyclic component(s); 11 edges removed
• LISTING FACES OF POLYTOPES (listing_faces_polytopes) — 1 cyclic component(s); 1 edges removed; 1 replacement edge
• LOCAL GIBBS SAMPLING BEYOND LOCAL UNIFORMITY (local_gibbs_sampling) — 2 cyclic component(s); 2 edges removed
• Low-Sensitivity Matching via Sampling from Gibbs Distributions (low-sensitivity_matching_sampling) — 4 cyclic component(s); 9 edges removed
• Matroids are Equitable* (matroids_equitable) — 3 cyclic component(s); 7 edges removed
• MAX BISECTION might be harder to approximate than MAX CUT (max_bisection_harder) — 1 cyclic component(s); 5 edges removed
• Near-linear time subhypergraph counting in bounded degeneracy hypergraphs (near-linear_time_subhypergraph) — 2 cyclic component(s); 2 edges removed
• Networked Information Aggregation via Machine Learning (networked_information_aggregation) — 1 cyclic component(s); 7 edges removed
• On the quantum chromatic gap (quantum_chromatic_gap) — 2 cyclic component(s); 3 edges removed
• Online Conformal Prediction with Efficiency Guarantees (online_conformal_prediction) — 1 cyclic component(s); 20 edges removed
• Online Joint Replenishment Problem with Arbitrary Holding and Backlog Costs (online_joint_replenishment) — 1 cyclic component(s); 1 edges removed
• Online Orthogonal Vectors Revisited (online_orthogonal_vectors) — 1 cyclic component(s); 1 edges removed
• Optimal Type-Dependent Liquid Welfare Guarantees for Autobidding Agents with Budgets (optimal_type-dependent_liquid) — 1 cyclic component(s); 2 edges removed; 2 replacement edges
• PERFECT MATCHINGS IN RANDOM SPARSIFICATIONS OF DENSE HYPERGRAPHS (perfect_matchings_random) — 1 cyclic component(s); 7 edges removed
• PROBLEMS FROM OPTIMIZATION AND COMPUTATIONAL ALGEBRA EQUIVALENT TO HILBERT’S NULLSTELLENSATZ (problems_optimization_computational) — 4 cyclic component(s); 4 edges removed
• Quantum Advantage via Solving Multivariate Polynomials (quantum_advantage_solving) — 1 cyclic component(s); 1 edges removed
• Recognizing Leaf Powers and Pairwise Compatibility Graphs is NP-Complete (recognizing_leaf_powers) — 1 cyclic component(s); 6 edges removed
• RUMOUR SPREADING DEPENDS ON THE LATENT GEOMETRY AND DEGREE DISTRIBUTION IN SOCIAL NETWORK MODELS (rumour_spreading_depends) — 1 cyclic component(s); 9 edges removed
• Short circuit walks in fixed dimension (short_circuit_walks) — 1 cyclic component(s); 1 edges removed
• Shortcuts and Transitive-Closure Spanners Approximation (shortcuts_transitive-closure_spanners) — 1 cyclic component(s); 1 edges removed
• Smooth Trade-off for Tensor PCA via Sharp Bounds for Kikuchi Matrices (smooth_trade-off_tensor) — 1 cyclic component(s); 6 edges removed
• Sublinear Metric Steiner Forest via Maximal Independent Set (sublinear_metric_steiner) — 1 cyclic component(s); 1 edges removed
• The Power of Matching for Online Fractional Hedonic Games (power_matching_online) — 2 cyclic component(s); 3 edges removed
• Tight Differentially Private PCA via Matrix Coherence (tight_differentially_private) — 1 cyclic component(s); 1 edges removed
• Tree covers of size 2 for the Euclidean plane (tree_covers_size) — 1 cyclic component(s); 2 edges removed; 1 replacement edge
• Tree Embedding in High Dimensions: Dynamic and Massively Parallel (tree_embedding_high) — 1 cyclic component(s); 16 edges removed
• Unbounded Error Correcting Codes (unbounded_error_correcting) — 1 cyclic component(s); 1 edges removed
• Weighted $k$-Server Admits an Exponentially Competitive Algorithm (weighted_k-server_admits) — 2 cyclic component(s); 2 edges removed

SODA 2026 structurally validated DAGs

The SODA_2026 split legacy_v1_6_structurally_repaired_gemini_3_8_flash contains 142 DAGs derived from the earlier cycle-only split. Of these, 56 needed no further structural change, 75 received bounded edge-only repairs by Gemini 3.8 Flash (medium effort), and 11 with missing overview roots were regenerated from the corresponding paper PDFs using the full parsing and DAG pipeline. Every row passes deterministic checks for unique node IDs, one overview root, valid edge endpoints, no directed cycles, exactly one primary parent per non-root node, and primary-path reachability to the root.

The was_structurally_repaired and was_regenerated columns distinguish the two interventions. original_structural_issues, structural_repair_log, regeneration_reason, regeneration_source_paper_id, and regeneration_cycle_repair_log provide per-paper provenance. The existing had_cycles column describes cycles in the original legacy graph before the earlier de-cycling pass; it is historical and does not mean that the new DAG contains cycles. The original cycle-only split remains available, and its DAG payloads are unchanged.

11 regenerated papers

• approximately_dominating_sets
• approximating_matroid_basis
• better-than-2_approximation_directed
• centered_colorings_minor-closed
• erd_s-p_sa
• expander_pruning_polylogarithmic
• lower_bounds_universal
• online_3-taxi_general
• quantum_state_preparation
• vizing_theorem_deterministic
• weighted_k-server_admits