What was already known
The supercritical Kesten–Stigum reconstruction direction was known. Earlier critical nonreconstruction for four states covered sufficiently large branching degree or mean, leaving the all-degree threshold open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Settles the all-degree four-state ferromagnetic tree-reconstruction threshold in both regular and Poisson models.
Limitations
The channel has λ∈[0,1]. Poisson advantage averages over the full observed tree without conditioning on survival. The manuscript reports exact-arithmetic verification of polynomial inequalities in its appendix, but the linked Lean scope checks only three-state supercritical reconstruction and does not verify this four-state claim.
Technical verification
The manuscript appendix reports reproducible exact-arithmetic checks of polynomial inequalities used in the four-state threshold argument. The full theorem is not documented as completely checked, and the linked Lean note concerns a different three-state result.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and precise partial or mismatched Lean-scope review for non-notifying local inclusion.
Read this published revision