Document SODA 2026 cycle-only repairs

README.md

@@ -777,4 +777,70 @@ The `num_cycle_repair_rounds` field counts every structural repair round, includ
 - **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>
+
+### 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`](https://huggingface.co/datasets/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. Some source graphs have unrelated legacy structural issues (for example, missing or multiple primary parents or no overview node); those issues may remain. 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.
+
+<details>
+<summary>SODA 2026 legacy v1.6: 53 of 142 DAGs repaired</summary>
+
+- **#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
+
+</details>
+
 <!-- cycle-repair-note:end -->