What was already known
Earlier rigorous formulas for orthogonally invariant Ising interactions imposed high-temperature conditions; this manuscript extends the variational limit to every fixed temperature under spectral-edge control.
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
Gives an all-temperature variational pressure limit for this invariant spin-glass class.
Limitations
The eigenvectors have Haar law and the spectrum has no asymptotic outliers. The main claim is not an all-temperature formula for arbitrary Ising interaction matrices.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For Ising interactions with Haar orthogonal eigenvectors, empirical eigenvalues converging to a compactly supported law, and extreme eigenvalues converging to the support edges, the normalized pressure converges in expectation and almost surely at every fixed positive temperature to the paper’s overlap-hierarchy variational functional.
- Basis
- Reported by the linked checker
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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.
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