Research-math reasoning, judged beyond raw solved counts.

Strengths: highest-yield full run, excellent at decisive obstructions, exact formulas, and literal counterexamples. Weaknesses: many isolated strong claims are conditional, wording-dependent, or partial-mislabeled. Post-training: our audited rows can train stronger verdict calibration: require theorem dependencies, literal-vs-natural statement tags, and a final “what remains unproved?” check before a solved label is allowed.

Strengths: most creative challenger, strong on compact constructions and counterexamples. Weaknesses: solved labels sometimes hide proof gaps, false uniformity assumptions, or theorem-scope drift. Post-training: our accepted-vs-rejected Kimi pairs are ideal for DPO and process-reward training focused on quantifier discipline, uniformity checks, and “creative idea but not yet proof” downgrades.

Strengths: best reviewer profile, strong gap accounting, and many well-scoped partials. Weaknesses: underclaims short decisive obstructions and sometimes keeps a solved subproblem in “partial” mode. Post-training: our data can teach partial-to-theorem extraction: when a divisor bound, coloring invariant, or literal obstruction already closes the statement, promote it confidently while preserving caveats.

Strengths: strong entrant with many real A/B partials and good theorem-aware reductions. Weaknesses: theorem importation is uneven; some partials cite stronger-than-available results or make local-to-global jumps. Post-training: our full partial audit can train theorem-scope verification: state the exact theorem used, check hypotheses, and classify each row as strong partial, useful partial, heuristic, or invalid.

Strengths: useful full-coverage corroborator with many reasonable theorem-family suggestions. Weaknesses: fewer decisive accepted results and a tendency to phrase plausible programs as if they were complete proofs. Post-training: our judge labels can train missing-lemma detection: separate proved statement, conjectural extension, and required external lemma before producing a final answer.

Strengths: full coverage and a few good compact obstructions, literal counterexamples, and underclaimed A-level partials. Weaknesses: C-heavy partial profile and unreliable solved labels, with many D/F strong claims caused by wrong theorem scope, wrong recurrence, or wrong problem interpretation. Post-training: our data can train solved-label discipline: demote bad proofs, preserve useful subclaims, and reward explicit statement parsing before invoking a theorem.