What was already known
The log version with nonzero boundary, lower-dimensional cases, and non-effective threefold results were known. The effective non-algebraically-integrable threefold cases were the main gap.
AI involvement
Rethlas proposed a dimension-three reduction and Lie-theoretic strategy for difficult cases. Liu and Qin supplied essential repairs and the rigorous final argument.
Rethlas supplied a central Lie-theoretic strategy for the difficult non-algebraically-integrable cases, while human additions were essential to the final theorem.
Importance
The repaired route supports a threefold resolution of the stated global-index question.
Limitations
Rethlas missed references and necessary details. Liu and Qin supplied the log-canonical reduction, references, finite-cover and equivariance steps needed for the final theorem.
Technical verification
The named human authors report verification and replaced model gaps with a rigorous proof; the source identifies missing references and case-specific repairs. The completed human check is author-reported.
Formal checking
Human verification and rigorous reorganization of generated argument, supplying missing references and finite-cover/equivariance steps
- Checker
- Jihao Liu and Sheng Qin, paper authors
- Scope
- Final dimension-at-most-three global-index Theorems 1.1 and 1.2, including repaired Rethlas-origin cases
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the rank and algebraic-rank split, the Lie-theoretic mechanism, the missing references and the precise human repairs.
Correction and publication history
The repaired route supports a threefold resolution of the stated global-index question.
Read this published revision