What was already known
Nielsen and Okamura posed Conjecture 9.1 and supplied the midpoint-expansion framework and constant-cubic sufficiency. This project supplies the planar necessity direction; it does not address arbitrary dimension.
AI involvement
JD Jones maintained the project. Its disclosure credits GPT-6 Astra with the geometric and algebraic arguments, exact certificates and Lean formalization under his direction.
The disclosure credits GPT-6 Astra agents with the geometric proof, exact polynomial certificates and Lean formalization while JD Jones set project scope.
Importance
Resolves a nontrivial dimension-two case of a stated geometric conjecture with a direct local-geodesic proof.
Limitations
The main theorem is planar, local and assumes a smooth tensor field and the stated midpoint complementarity. It does not settle higher dimensions. No independent human specialist review is claimed.
Technical verification
The source reports three compared lean declarations with constructed local geodesic branches, definition checks and standard-axiom audit. This applies to the selected claim and is not an independent reproduction by AIProofWatch.
Formal checking
The source reports three compared Lean declarations, only standard axioms, exact-commit build and statement checks, plus Lean/NanoDa/con-ron proof replay. The Challenge placeholders are not imported by Solution.
- Checker
- Lean 4 kernel and documented Comparator or independent-kernel replay run by repository authors
- Scope
- On a connected open subset of the Euclidean plane, if the canonical local geodesic midpoint maps of the dual torsion-free connections D+KC and D−KC are complementary near every diagonal point, then their totally symmetric cubic tensor field C is constant. The formal proof constructs the short geodesic branches and also proves a differential obstruction criterion and a five-direction test.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The source reports internal agent checks of scope and statement fidelity, but no independent human mathematical review or explanation of the planar obstruction argument. Few is the evidence default.
Correction and publication history
Claim-level primary-source review of exact theorem, prior baseline, AI contribution and documented checking scope.
Read this published revision