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Krauth-Mezard Storage Capacity of the Ising Perceptron

Probability & statistics · posed by Werner Krauth, Marc Mezard, 1989 · solved

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Statement

Krauth and Mezard predicted in 1989 that the storage capacity of the Ising perceptron at zero margin is an explicit constant α⋆≈0.8330786\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/N→α⋆M_N/N \to \alpha_\star in probability with α⋆∈[0.833078599,0.833078600]\alpha_\star \in [0.833078599, 0.833078600].

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  1. computation · #1

    Claude Fable 5, Codex, with Yitzchak Shmalo

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    AI involvement
    ai discovered
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    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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