What was already known
Hilbert–Smith was known in dimensions one through three and for stronger regularity classes. An earlier OpenAI manuscript reports a different proof in every finite dimension.
AI involvement
A. Dabrowski guided the project. The paper credits Opus 5.5 and GPT 6.1 with critical construction steps and Opus 5.5 with the Lean formalization; the later repository migration also involved human direction.
AI agents receive paper authorship and the disclosure assigns critical mathematical constructions to Opus 5.5 and GPT 6.1, with human research guidance.
Importance
This gives a new integral-signature route to the remaining finite-dimensional Hilbert–Smith problem.
Limitations
The paper states broader versions; the selected formal statements retain second countability and the boundaryless manifold condition. Comparator and SafeVerify logs cover an earlier development; a fresh check of the later migrated revision is not documented.
Technical verification
Comparator and SafeVerify logs document machine checks of the second-countable Formal Conjectures variants at the earlier c51a2d5 development. The cited b75523f revision migrated the modules, and its own README and metadata say those historical runs do not validate the migration. The local structural audit checks theorem signatures, imports and absence of sorry, but no fresh Lean build or Comparator result for this selected revision is documented. The informal paper's broader boundary and countability scope is outside the historical formal check.
Independent checking
Fresh-clone Lean build inside the reported Comparator sandbox, kernel/NanoDa check and SafeVerify replay
- Checker
- Lean kernel, Comparator and SafeVerify in the repository's historical verification run
- Scope
- The second-countable Hilbert–Smith and p-adic Formal Conjectures variants in FCSolution.lean at c51a2d5, not the migrated b75523f source
- Basis
- Reported by the linked checker
Human understanding
Human guidance is disclosed, but the reviewed sources do not identify a person who explains the central signature-tail divisibility and realization argument. Few is the evidence default here, not a report that people cannot understand it.
Correction and publication history
If correct, this gives a new integral-signature route to the remaining finite-dimensional Hilbert–Smith problem.
Read this published revision