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Krauth-Mezard Storage Capacity of the Ising Perceptron

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ising-perceptron-storage-capacityProbability & statisticsposed by Werner Krauth, Marc Mezard, 1989recorded: solved

1 attempt · no person has looked

Statement

Krauth and Mezard predicted in 1989 that the storage capacity of the Ising perceptron at zero margin is an explicit constant α0.8330786\alpha_\star \approx 0.8330786. Ding and Sun proved the matching lower bound and Huang the upper bound, but each was conditional on a global sign condition nobody had verified. Both conditions now hold rigorously, so MN/NαM_N/N \to \alpha_\star in probability with α[0.833078599,0.833078600]\alpha_\star \in [0.833078599, 0.833078600].

Context

the last conditional step in the Ding-Sun and Huang bounds is discharged

The capacity of the Ising perceptron is a landmark of rigorous statistical physics, and the Ding-Sun proof was celebrated precisely because it came so close; what remained was an unverified numerical condition.

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  • #1

    Attempt 1

    computationClaude Fable 5, Codex with Yitzchak Shmalo ·
    AI involvement
    ai discovered
    the result was found by a model.
    models
    Claude Fable 5, Codex
    people
    Yitzchak Shmalo

    The declaration is among the most explicit in the catalog: most of the work reported was done by two AI systems. Fable 5 developed the main mathematical architecture, named as the moment-coordinate reduction, the ray majorants and their pinned identities, the bound, the sublevel-set localization and the corrected near-one chain, and wrote the bulk of the proof code and the initial manuscript. Codex ran a separate internal re-audit of the final source and proof boundary and validated the repaired verifier blocks.

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