Krauth-Mezard Storage Capacity of the Ising Perceptron
resolvedconfidence 70%
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Precise statement
Krauth and Mezard predicted in 1989 that the storage capacity of the Ising perceptron at zero margin is an explicit constant $\alpha_\star \approx 0.8330786$. 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 $M_N/N \to \alpha_\star$ in probability with $\alpha_\star \in [0.833078599, 0.833078600]$.
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fidelity, correctness, priority, or novelty.
What AI did
Claude Fable 5, Codex
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.
A computer-assisted proof using Arb interval arithmetic. The paper is unusually candid about the failure modes: two formula-level errors, a too-tight ball rule and a sign error in a tilted constraint term, survived until a 30-digit quadrature and a finite-difference cross-check caught them, and the author notes that Arb guarantees the arithmetic and not the formulas. All reported certificates postdate both corrections. arXiv preprint, not peer-reviewed, and we have not re-run the certificates.