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FullRSB Jamming Identity a + b = 1

Mathematical physics · posed by 2014 · solved

2 comments

Statement

Can the critical-exponent relation a+b=1a + b = 1 at the jamming transition, observed numerically to high precision in the full replica-symmetry-breaking solution of hard spheres, be derived analytically from the scaling equations?

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Giorgio Parisi and Francesco Zamponi, using Claude Sonnet 4.6, Claude Opus 4.7

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    Parisi and Zamponi asked Claude for help; it quickly proposed the essentially correct idea - integration-by-parts identities combined with a maximum principle - whose first formal write-up contained errors the authors then fixed and verified.

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed expert verification (imported)

    scope Expert review reported upstream; the reviewer has no probXiv account and is not credited here

    Peer-reviewed and published in the Journal of Statistical Mechanics (2026); also public as an arXiv preprint.

    Repeated from the source; nothing was checked here.

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