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FullRSB Jamming Identity a + b = 1

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fullrsb-jamming-identityMathematical physicsposed by 2014recorded: solved

1 attempt · 1 machine check · no person has looked

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?

Context

A central identity of replica theory and jamming physics (Parisi school).

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptClaude Sonnet 4.6, Claude Opus 4.7 with Giorgio Parisi, Francesco Zamponi ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    Claude Sonnet 4.6, Claude Opus 4.7
    people
    Giorgio Parisi, Francesco Zamponi

    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.

    Reviews

    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: correct

      Recorded from VibeMathed 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.

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Discussion

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