# Diluted spin-glass variational model library

Family 221: The Mézard–Parisi formula for diluted spin glasses. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Constraint-model researchers can organize hierarchical cavity free-energy approximations for admissible diluted even-arity systems.

## Applicability and commercial boundary

The exact limiting infimum over hierarchical trial laws need not have an efficient finite-depth optimizer or usable truncation error. Factorization, positivity and moment assumptions matter.

## Initial business decision

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

## Next verification action

Inspect a computable trial-law family and a convergence bound before claiming faster model fitting.

## 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

[The Mézard–Parisi formula for diluted spin glasses](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026/paper.pdf).