What was already known
Annealed free-energy limits and Hamiltonian linear-statistics fluctuation results did not establish this thermodynamic fluctuation statement.
AI involvement
Humans proposed the partition-function route and refined ChatGPT-generated arguments; the authors report AI-generated, human-reviewed Lean code.
ChatGPT supplied retained analytic proof arguments after humans proposed the partition-function route and refined them. Human direction does not erase the central proof contribution.
Importance
Identifies the fluctuation law in a quantum-disorder model studied in statistical physics and holography.
Limitations
High-temperature asymptotics through even N; no low-temperature claim. The reported Lean development assumes Proposition 4.2, which is unformalized. AIProofWatch has not audited the proof or compiled the code.
Technical verification
Only the stated computational, numerical, conditional or component checks are documented for this scope; the full claimed endpoint has not received a documented complete rigorous check in the reviewed evidence. High-temperature asymptotics through even N; no low-temperature claim. The reported Lean development assumes Proposition 4.2, which is unformalized. AIProofWatch has not audited the proof or compiled the code.
Human understanding
Named human researchers explain or reconstruct the scoped central mechanism in the cited paper/account; credit for that explanation is separate from technical checking. Humans proposed the partition-function route and refined ChatGPT-generated arguments; the authors report AI-generated, human-reviewed Lean code.
Correction and publication history
Primary-source statement, baseline, AI role and limitations reviewed on 14 October 2026. Complete current catalog checked for equivalent records. New recent paper; ordinary notifying publication.
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