What was already known
The best cited lower-limit coefficient for every genus was 2/9; coefficient one was known only along a sequence of genera.
AI involvement
Yifei Cai supplied the constant-twist pants-decomposition framework. He credits GPT-5.6 Sol with the first complete proof, then checked, simplified and reorganized it.
The model is expressly credited with the first complete proof; the author supplied the approach and subsequently checked and simplified it.
Importance
Raises the every-genus asymptotic lower-limit coefficient from 2/9 to one.
Limitations
This improves the every-genus lower bound, not the sequence upper limit or the general asymptotic upper bound. Cai’s complete check is source-reported.
Technical verification
The author explicitly reports checking the full proof in the manuscript. No machine formalization or independent replay is documented.
Independent checking
author check of the complete GPT-developed proof, followed by simplification and reorganization
- Checker
- Yifei Cai
- Scope
- Theorem 1 every-sufficiently-large-genus systole bound
- Basis
- Reported by the linked checker
Human understanding
Cai gives and simplifies the central geometric coding, probability, and local-lemma mechanism; no central unexplained step is reported.
Correction and publication history
Cai’s theorem improves the systole lower bound in every sufficiently large genus.
Read this published revision