Krauth-Mezard Storage Capacity of the Ising Perceptron
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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 . 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 in probability with .
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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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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