What was already known
Grechuk’s question concerns integer solutions of the cubic equation. The reviewed source identifies no earlier theorem excluding these rational polynomial families, but its literature search is incomplete.
AI involvement
Brandon Yates chose and directed the problem. Claude agents devised the exclusions and the degree-three reduction to Fermat’s Last Theorem for exponent three.
Agents supplied the central exclusion argument and decisive degree-three reduction while Yates selected and directed the question.
Importance
Closes one bounded-degree polynomial-family route to the cubic equation.
Limitations
The result does not decide sporadic integer solutions or families with deg g≥5. The formal proof has no documented human expert mathematical review, and priority for this narrow exclusion is unresolved.
Technical verification
The cited project reports a clean Lean build of the exact degree-one-to-four rational-polynomial theorem, standard-axiom audit, and independent statement-diff/bridge checks. These do not address sporadic integer solutions or degree at least five. Source-reported; this review did not replay Lean.
Independent checking
Clean rebuild, per-theorem axiom audit, challenge/library statement diff and definitional bridge
- Checker
- Lean 4 kernel and independent Claude Fable re-verification pass
- Scope
- No rational-polynomial family with nonconstant g of degree at most four for the specified cubic identity
- Basis
- Reported by the linked checker
Human understanding
Default for undocumented human explanation: Yates says agents devised the proof steps and no human expert reviewed the mathematics.
Correction and publication history
Closes one bounded-degree polynomial-family route to the cubic equation.
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