lean artifact · pending
Artifact ↗Source authenticated
The Nam-Sly-Zhang conjecture: the free Ising state on the d-regular tree is a factor of IID up to the reconstruction threshold
Theorem 1.1: for every and , is a factor of IID if and only if ; the new part is the positive implication including equality, and the factor can be chosen to commute with every automorphism on every input. The converse is Sly's, as given by Lyons, with the Backhausz-Szegedy-Virag bound. The construction inverts the innovations of the Nam-Sly-Zhang stochastic-localization observation process. It does not treat antiferromagnetic or nonzero-field states, other Gibbs measures, or finitary factors.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 26, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Nam-Sly-Zhang conjecture: the free Ising state on the d-regular tree is a factor of IID up to the reconstruction threshold · Free Ising on trees as a factor of IID
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
Compute record
No linked compute attempts recorded.
Lineage and corrections
Nam, Sly and Zhang, Ising model on trees and factors of IID (arXiv 2012.09484) evidence for this event
This event attributed to Unreleased internal OpenAI model
The Nam-Sly-Zhang conjecture: the free Ising state on the d-regular tree is a factor of IID up to the reconstruction threshold evidence for this event
Lean: OAI/Probability/FreeIsing/Main.lean evidence for this event
Lyons, Factors of IID on trees (arXiv 1401.4197) evidence for this event
Theorem 1.1: for every and , is a factor of IID if and only if ; the new part is the positive implication including equality, and the factor can be chosen to commute with every automorphism on every input. The converse is Sly's, as given by Lyons, with the Backhausz-Szegedy-Virag bound. The construction inverts the innovations of the Nam-Sly-Zhang stochastic-localization observation process. It does not treat antiferromagnetic or nonzero-field states, other Gibbs measures, or finitary factors. parent of this event
The Nam-Sly-Zhang conjecture: the free Ising state on the d-regular tree is a factor of IID up to the reconstruction threshold parent of this event
VibeMathed record: The Nam-Sly-Zhang conjecture: the free Ising state on the d-regular tree is a factor of IID up to the reconstruction threshold evidence for this event
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