What was already known
Smale proved the inequality with constant 4 and asked whether 1 suffices. Restricted classes and low degrees had positive results.
AI involvement
GPT-6 Astra found the construction and Lean proof in an unsteered Epoch AI evaluation. Tom Adamczewski ran the evaluation; later human work explained and strengthened the result.
The evaluation record documents an unsteered Astra proof search and formal counterexample.
Importance
The formal witness answers the long-standing K=1 question negatively.
Limitations
The original witness has large unspecified degree and a small violation. Jatar and Ng’s later stronger numerical lower bound is separate human work; they explain but do not report checking Astra’s Lean proof line by line.
Technical verification
Lean and Comparator reportedly check the negated K=1 statement and its correspondence to the benchmark.
Formal checking
Kernel type checking, trusted-statement comparison and axiom audit
- Checker
- Lean 4 kernel and Comparator, reported by Adamczewski; VibeMathed audited the statement
- Scope
- Negation of MeanValueProblem.mean_value_problem, witnessed at z=0 with p′(0)=1
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Jatar and Ng explain the four main steps of Astra’s construction.
Correction and publication history
The AI-found K=1 counterexample is one claim across two catalog listings; later quantitative human bounds remain separate.
Read this published revision