What was already known
The exact asymptotic strength of the Cohn–Elkies program and related sign-uncertainty constant was unknown. The linear-programming bound itself was earlier human work.
AI involvement
OpenAI attributes the mathematical argument and Lean formalization to Astra. Humans chose the problem and prepared the manuscript; later reviewers examined selected calculations.
OpenAI’s original disclosure assigns the argument and subsequent Lean formalization to Astra; human manuscript preparation is separately credited.
Importance
The result fixes the high-dimensional limit of a major packing bound and related Fourier threshold.
Limitations
It bounds true packing density but does not determine its actual asymptotic exponent. A Lean certificate is reported; human reviewers checked the constant and parts of the Fourier argument without rederiving every analytic estimate.
Technical verification
The project reports a complete Lean certificate for the stated formal theorem. Human assessments have narrower scope; semantic matching and any manuscript gaps remain separately noted.
Independent checking
chapter-specific mathematical review of the published argument, with the limited coverage summarized in the audit
- Checker
- Chapter 1 human reviewers in the Sienicki et al. review corpus
- Scope
- asymptotic constant, normalization and selected Fourier/Mellin structure
- Basis
- Reported by the linked checker
Formal checking
Lean 4.32.0 formal certificate in SpherePacking.lean; comparator target for PackingBounds.sharpFullCohnElkiesManuscriptConclusions; manifest reports zero sorry and only standard axioms
- Checker
- OpenAI ten-proofs project, Lean kernel and Comparator configuration
- Scope
- exact Cohn–Elkies LP asymptotic and stated packing bridge
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Human reviewers recomputed the central asymptotic constant and inspected Fourier/Mellin structure, while explicitly not reconstructing the dense analytic estimates from first principles.
Correction and publication history
The asymptotic strength of the Cohn–Elkies program is a distinct high-dimensional result.
Read this published revision