lean artifact · pending
Artifact ↗Source authenticated
The Mezard-Parisi formula for diluted spin glasses: the Panchenko-Talagrand equality conjecture
Main theorem: for Poisson-diluted even-arity Ising models in the Panchenko-Talagrand class (factorized interactions with the stated independence and positivity of moments of ), with only first moments of the interaction and field, the limiting pressure exists and equals of the infimum of the Mezard-Parisi hierarchical functional of depth . Covers Viana-Bray, symmetric diluted even-spin models and soft random even- SAT at positive temperature. Not covered: odd arity (for example K-SAT with odd K), models outside the positivity class, fixed-degree random regular graphs, identification of the optimal hierarchy depth, or zero temperature beyond the stated ground-state limits.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 23, 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 Mezard-Parisi formula for diluted spin glasses: the Panchenko-Talagrand equality conjecture · Mezard-Parisi diluted formula
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
Lean proof (OAI.DilutedSpinGlass.mezard_parisi) evidence for this event
This event attributed to Unreleased internal OpenAI model
Panchenko-Talagrand, Bounds for diluted mean-fields spin glass models (2004) evidence for this event
Main theorem: for Poisson-diluted even-arity Ising models in the Panchenko-Talagrand class (factorized interactions with the stated independence and positivity of moments of ), with only first moments of the interaction and field, the limiting pressure exists and equals of the infimum of the Mezard-Parisi hierarchical functional of depth . Covers Viana-Bray, symmetric diluted even-spin models and soft random even- SAT at positive temperature. Not covered: odd arity (for example K-SAT with odd K), models outside the positivity class, fixed-degree random regular graphs, identification of the optimal hierarchy depth, or zero temperature beyond the stated ground-state limits. parent of this event
VibeMathed record: The Mezard-Parisi formula for diluted spin glasses: the Panchenko-Talagrand equality conjecture evidence for this event
The Mezard-Parisi formula for diluted spin glasses: the Panchenko-Talagrand equality conjecture evidence for this event
The Mezard-Parisi formula for diluted spin glasses: the Panchenko-Talagrand equality conjecture parent of this event
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