# Tree Ising distributed-sampling feasibility map

Family 236: The exact factor-of-IID threshold for free Ising spins on trees. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Distributed probability researchers can identify exactly when the free ferromagnetic Ising tree state has the specified factor-of-IID representation.

## Applicability and commercial boundary

An equivariant measurable construction, including at equality, does not automatically offer finite local communication, bounded random-bit cost or a practical finite-tree sampler.

## Initial business decision

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

## Next verification action

Inspect coding and implementation costs and distinguish the factor rule from finite rooted sampling.

## 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 sharp factor-of-IID threshold for the free Ising model on regular trees](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-sharp-factor-of-IID-threshold-for-the-free-Ising-model-on-regular-trees-September-26-2026/article.pdf).