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.

Main source

The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model.