FullRSB Jamming Identity a + b = 1
Can the critical-exponent relation 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?
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Statistical physics
- Posed by
- —
- Year posed
- 2014
- Years open
- 12y
- Solved
- 2026-06-02
- Model
- Claude Sonnet 4.6, Claude Opus 4.7
- Vendor
- Anthropic
- Collaborators
- Giorgio Parisi, Francesco Zamponi
- Verification
- Independently expert-verified
- Publication
- Peer-reviewed
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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.
Verification
Peer-reviewed and published in the Journal of Statistical Mechanics (2026); also public as an arXiv preprint.
Source
arXiv:2606.03300 - A proof of an identity for the critical exponents of jamming