What was already known
Nagata proved a plane square-number case; Harbourne obtained surface square-case estimates and asymptotic bounds. These did not show eventual algebraic maximality for every ample polarization and every large integer r.
AI involvement
OpenAI credits its internal model with the surface manuscript and proof artifacts. Staff organized the release; no named human checker or independent explanation of the interpolation argument is documented.
The institution credits model production of the surface manuscript and proof artifacts, with human selection and release work; prompt-level independence is not documented.
Importance
The result resolves qualitative eventual maximality for all smooth complex polarized surfaces.
Limitations
The threshold depends on (S,L) and is not explicit. The reported Lean scope is this surface theorem; higher-dimensional, positive-characteristic and sharp plane claims need separate assessment.
Technical verification
OpenAI's Lean scope page reports a formalized theorem for every smooth complex projective surface and ample L, with an (S,L)-dependent threshold, very general configurations and nef boundary class. The Main.lean proof and Comparator challenge match this surface claim. No corresponding machine check is established here for the broader higher-dimensional or positive-characteristic claims; the build was not rerun.
Formal checking
Source-reported Lean proof of maximalSeshadriConstants against the EventualMaximalSeshadri comparator statement
- Checker
- Lean kernel and Comparator in OpenAI's released Lean library
- Scope
- Eventual maximal multipoint Seshadri constants and nef boundary class for smooth integral complex projective surfaces with ample L
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Default for missing human explanation: the release supplies a proof overview but attributes the manuscripts to a model and names no person who explains or independently reviewed its central interpolation argument.
Correction and publication history
If correct, the result resolves qualitative eventual maximality for all smooth complex polarized surfaces.
Read this published revision