Structure-First Automated Reasoning for Equational Theories: 197/200 Cumulative Lean-Verified Coverage on the SAIR Stage-2 Public Sample
Year: 2026
Type: preprint
Abstract: Structure-First Automated Reasoning for Equational Theories This preprint reports cumulative Lean-verified coverage of 197/200 (98.5%) problems on the public SAIR Mathematics Distillation Challenge — Equational Theories Stage-2 sample_200 development set. The result was obtained through a sequence of independently frozen solver branches combining structure-first automated reasoning, critical-pair reasoning, completion-based search, finite-model search, and exact constraint-satisfaction methods. The verified progression was: 175/200 → 178/200 → 187/200 → 195/200 → 196/200 → 197/200. The transition from 175/200 to 178/200 corresponds to the addition of the critical-pair module to the encoding-safe baseline. Completion-based reasoning subsequently increased verified coverage to 187/200. A frozen homogeneous V8 run reached 195/200. Two additional residual problems were independently verified in later experiments, including an exact finite-magma CSP countermodel accepted by the Lean Judge. Important interpretation: the reported 197/200 is cumulative Lean-verified coverage across independently frozen solver branches. It is not a single homogeneous full-200 benchmark score, not an official hidden-test or leaderboard result, and not a quantitative prediction of private-set generalization. The public sample was repeatedly inspected during system development and should therefore be interpreted as a development set. No quantitative claim is made regarding performance on the private Stage-2 evaluation. At the time of publication, the Stage-2 competition remained under evaluation. No official same-setting leaderboard or other-team result was available for a controlled external comparison. The accompanying evidence package contains the complete 200-problem verification ledger, branch-by-branch unique-solve differences, cryptographic hashes, evidence manifest, and the Judge-accepted finite countermodel certificate used to audit the reported cumulative coverage. Private solver coefficients and unpublished experimental branch source code are intentionally withheld while the competition remains under evaluation.
Author: Kim, Min Gi
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213756509
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