# Graph reconstruction feasibility audit

Family 229: Exact three- and four-state reconstruction thresholds and four-state tree capacity. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Community-detection teams can compare a model-fitted three-state symmetric network or tree-broadcast problem to an exact asymptotic reconstruction threshold.

## Applicability and commercial boundary

The new four-state ferromagnetic claims and nonreconstruction direction are outside the selected formal scope, which proves only three-state supercritical reconstruction. Tree survival averaging and equal-community model assumptions matter; real graph labels and finite sizes need separate validation.

## Initial business decision

Conditional evidence workflow. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Extract the exact three-community parameter mapping and compare finite recovery above, at and below threshold with existing algorithms.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstract passages and available family scope notes were also inspected; paper-level theorem and algorithm details still require deeper review. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Reconstruction-Threshold-for-the-Ferromagnetic-Four-State-Potts-Model-October-5-2026/four-state-potts.pdf).