# Perceptron capacity and jamming regime planner

Family 222: Perceptron free energies and microscopic jamming exponents. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Learning-theory researchers can compare Gaussian or invariant spherical perceptron simulations with stated limiting feasibility and force/gap laws.

## Applicability and commercial boundary

These particular random models, potentials and ordered limits do not give capacity estimates for arbitrary neural networks or real data. No efficient training algorithm follows from a free-energy formula.

## Initial business decision

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

## Next verification action

Extract effective model parameters and test a finite synthetic benchmark distinct from general ML performance.

## 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 free energy of the Ising random perceptron](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-free-energy-of-the-Ising-random-perceptron-September-24-2026/The-free-energy-of-the-Ising-random-perceptron-September-24-2026.pdf).