OpenAI · 217-02 · 2026-09-24 · Probability and statistical mechanics

The low-temperature Sherrington–Kirkpatrick fluctuation scale

preprints/The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026

Family 217. The low-temperature Sherrington–Kirkpatrick fluctuation law.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

For every fixed inverse temperature $β > 1$ , determines the fluctuation scale and limiting law of the zero-field Gaussian Sherrington–Kirkpatrick log partition function. Its variance is asymptotic to $c_{β} n^{1/3}$ , with $c_{β} > 0$ , confirming the predicted $n^{1/6}$ standard-deviation scale. Exact centering and standardization give full-sequence convergence to a uniquely characterized nondegenerate law.

For the zero-field Gaussian Sherrington–Kirkpatrick model at every fixed inverse temperature β > 1, we prove that the standard deviation of the log partition function is $n^{1/6 + o (1)}$ . The same exponent describes its typical centered absolute fluctuations, establishing the predicted one-sixth exponent in this regime.

Preprint source and Lean scope

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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.