What was already known
Yan had proved the single-point sufficiency direction, and earlier work covered restricted two-point cases; the higher-multiplicity multipoint case remained open.
AI involvement
Yan prompted GPT-5.6 to extend his earlier method; it found the example. Yan wrote the proof and independently derived the decisive coefficient.
The model found the retained counterexample within Yan's directed extension of his prior result.
Importance
The explicit mixed-resonance example resolves the unrestricted direction while leaving restricted cases and a corrected criterion open.
Limitations
Yan independently checks the key mixed sextic coefficient 32/41 and boundary terms, but no complete separate check of the full counterexample proof was documented.
Technical verification
Yan independently recomputes the decisive 32/41 coefficient from a finite-unitary GGT matrix and checks boundary/sign terms in the paper. This is a documented human consistency check of key components, not an explicit independent complete proof review.
Independent checking
independent finite-unitary GGT Taylor-coefficient derivation and boundary/sign analysis
- Checker
- Jun Yan, author
- Scope
- Decisive mixed sextic coefficient and its normalization in the proposed counterexample
- Basis
- Reported by the linked checker
Human understanding
Yan explains the mixed-phase resonance and why exponent 3/20 satisfies the decomposition ℓ⁸ threshold while leaving a nonsummable sextic term.
Correction and publication history
The explicit mixed-resonance example resolves the unrestricted direction while leaving restricted cases and a corrected criterion open.
Read this published revision