# Invariant spin-glass pressure reference

Family 234: All-temperature pressure of orthogonally invariant Ising spin glasses. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Optimization researchers can compare orthogonally invariant Ising experiments with the all-temperature limiting variational pressure.

## Applicability and commercial boundary

Haar rotations, compact limiting spectrum and edge convergence are essential. A variational formula is not an efficient optimizer for general Ising or business allocation instances.

## Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Inspect a finite trial family and convergence controls before proposing a benchmarking calculator.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[All-temperature pressure for orthogonally invariant Ising spin glasses](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/All-temperature-pressure-for-orthogonally-invariant-Ising-spin-glasses-September-25-2026/paper.pdf).