{"id":"openai-math/A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees","pdf":"https://github.com/openai/math/blob/main/preprints/A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees-October-5-2026/four-state-capacity.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Capacity-Criterion-for-Four-State-Potts-Reconstruction-on-Trees-October-5-2026","tags":["statistical-physics","reconstruction-problem","trees"],"score":0,"title":"A Capacity Criterion for Four-State Potts Reconstruction on Trees","domain":"Probability and statistical mechanics","family":"229","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"For the ferromagnetic four-state broadcast model with $`0\\lt \\lambda\\lt 1`$, we prove that reconstruction on a bounded-degree deterministic rooted tree occurs exactly when its L 3 capacity with edge resistances $`\\lambda^{-2|e|}`$ is positive. This gives an exact criterion without regularity or growth-rate assumptions on the tree, including at the exponential critical boundary.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Exact three- and four-state reconstruction thresholds and four-state tree capacity"}