What was already known
Short arguments covered the stable-curve compactification and principally polarized abelian varieties. Patel describes the corresponding smooth-curve question as open in the moduli community since about 2015.
AI involvement
Patel reports that Aletheia supplied the mathematical content after one proof request with no further hints. He revised the exposition, added mathematical comments and a supporting lemma, and corrected the displayed equation.
The disclosure says Aletheia supplied the proof's mathematical content from one prompt without further mathematical hints; Patel's later exposition and correction do not erase that origin.
Importance
The proof resolves the smooth-curve version of a recurring Hodge-bundle question.
Limitations
The revised paper corrects a missing factor of four in one displayed equation, and Patel says the remainder is unaffected. No complete human or machine proof check is documented; claims in other characteristics are outside this theorem.
Technical verification
Patel's v3 Human Comment 2.8 identifies and repairs his omitted factor 4 in the involution-eigenspace equation and states the remaining proof is unaffected. That is documented checking of a specific proof step, but no complete human or machine check of the whole theorem is stated.
Independent checking
Correction during rewriting of the model output and inspection of the downstream proof
- Checker
- Anand Patel, human author
- Scope
- The factor 4 in the second equality of Lemma 2.7 and its use in the final rank-divisibility step
- Basis
- Reported by the linked checker
Human understanding
Patel explains the role of automorphisms and involution traces, proposes an alternative algebraic route for a central lemma, adds a supporting proof, and explains the final divisibility mechanism. These are person-specific explanations beyond model prose.
Correction and publication history
Initial publication of this result.
Read this published revision