What was already known
Bogomolov and Tschinkel established reconstruction cases over algebraic closures of finite fields, and Pop obtained birational reconstruction results using additional decomposition or inertia data. The precise isomorphism formulation with scalar and Frobenius ambiguity was conjectural (companion manuscript, Previous work, p. 2).
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Identifies exactly the uniqueness ambiguity in the group-to-field reconstruction correspondence.
Limitations
The selected Lean-checked claim is injectivity or uniqueness only. It does not establish that every admissible Galois-data isomorphism comes from a field isomorphism; that existence direction is outside this record.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note identifies the injectivity of the reconstruction correspondence for the stated function fields and explicitly excludes existence.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Two field isomorphisms of perfect closures preserving constants that induce the same pro-ell abelian-by-central Galois-data isomorphism modulo ell-adic unit scaling agree modulo Frobenius.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary companion manuscript, attribution, prior-work, and exact Lean-scope review for non-notifying local inclusion.
Read this published revision