OpenAI reports the exact ferromagnetic four-state Potts reconstruction threshold

For the ferromagnetic four-state Potts broadcast model on every regular d-ary tree with d≥2 and every observed Poisson Galton–Watson tree of mean d>0, reconstruction occurs exactly when dλ²>1, including nonreconstruction at equality.

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Understanding the problem

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For the ferromagnetic four-state Potts broadcast model on every regular d-ary tree with d≥2 and every observed Poisson Galton–Watson tree of mean d>0, reconstruction occurs exactly when dλ²>1, including nonreconstruction at equality.

Why it matters

If correct, settles the all-degree four-state ferromagnetic tree-reconstruction threshold in both regular and Poisson models.

What counts as progress

Is the Kesten–Stigum threshold exact for ferromagnetic four-state broadcasting on all regular and Poisson trees?

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