What was already known
Earlier classifications required additional pinching, symmetry, topological, or geometric hypotheses. The companion zero-plane and L²-gap results have different assumptions.
AI involvement
OpenAI attributes the manuscript to an internal model and is its named author. The release does not identify individual human mathematical steps or a completed human review.
OpenAI is credited as author and identifies the repository's manuscripts as internal-model products; no conflicting human-origin account was located.
Importance
This settles the unrestricted positive-sectional-curvature classification conjecture in dimension four.
Limitations
Exact arithmetic checks finite polynomial and integral steps, but the geometric and analytic reductions remain outside their stated coverage. No completed check of the full theorem or named human explanation is documented.
Technical verification
The paper's exact-arithmetic verifier checks finite polynomial, coefficient, and rational-integral claims used in the proof, but its coverage file explicitly excludes the geometric and analytic reductions. The public Lean catalogue does not list a formalized main result for this manuscript; the comparator challenge file contains sorry placeholders and is not a certificate of the full theorem.
Formal checking
Deterministic exact arithmetic with saved results comparison; 53 identities, 21 univariate rows, 12 triangle rows, and 24 additional assertions
- Checker
- OpenAI's verification/verify.py exact-arithmetic checker
- Scope
- Finite identities, univariate and triangle certificate rows, and rational-integral bounds used by the classification argument
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No identified human explanation of the weighted-Hessian and curvature-coupling mechanism was documented; Few is the evidence default, not a finding that humans cannot understand it.
Correction and publication history
If correct, this settles the unrestricted positive-sectional-curvature classification conjecture in dimension four.
Read this published revision