What was already known
The manuscript places its result after Cohn–Kumar’s universal-optimality program and sharp E8 and Leech-lattice results; earlier planar comparisons restricted the competitor class or potential family.
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
Establishes universal optimality in the plane against nonperiodic configurations under a density condition.
Limitations
The density condition is centered-disk density one, and the potential is nonnegative completely monotone in squared distance. The claim does not compare arbitrary finite point sets.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves the lower-energy comparison and identifies sharp Gaussian Fourier minorants used as an atomic certificate.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- The density-one triangular lattice minimizes lower energy per particle among all locally finite planar configurations of centered-disk density one for every nonnegative completely monotone function of squared distance, including infinite-energy comparisons.
- 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 manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision