FullRSB Jamming Identity a + b = 1

Precise statement

Can the critical-exponent relation $a + b = 1$ 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?

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

Claude Sonnet 4.6, Claude Opus 4.7

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.

Provider: Anthropic · Prompt public: unknown · Independence: unknown

Verification boundary

independent expert verified

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

Correctness: supported · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-06-02

   arXiv:2606.03300 - A proof of an identity for the critical exponents of jamming

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.