Identity for the critical exponents of jamming derived analytically
The relation a + b = 1 between critical exponents at the jamming transition, previously seen only numerically in the full replica-symmetry-breaking solution of hard spheres, is derived from the scaling equations and published after peer review.
- Lab
- Independent
- Model
- Claude Sonnet 4.6, Claude Opus 4.7
- Field
- Physics
- Date
- 2026-06-02
- Human collaborators
- Giorgio Parisi, Francesco Zamponi
- Problem posed
- 2014 · open 12 yrs
Sources
Original work
Independent commentary
What was found
In the full replica-symmetry-breaking solution for hard spheres, the critical exponents a and b at the jamming transition had been observed numerically to high precision to satisfy a + b = 1, without an analytic derivation from the scaling equations. Parisi and Zamponi asked Claude for help; the model quickly proposed what proved to be essentially the correct idea, combining integration-by-parts identities with a maximum principle. Its first formal write-up contained errors, which the authors then fixed and verified before publication in the Journal of Statistical Mechanics.
Novelty check
The numerical observation that a + b = 1 in the FullRSB jamming solution dates to the 2014 work of Charbonneau, Kurchan, Parisi, Urbani and Zamponi on the exact mean-field theory of hard-sphere glasses, where the relation was reported as observed but unexplained. It remained without analytic derivation in the subsequent literature. The derivation is new.
Caveats and known objections
Peer-reviewed and published, which is the appropriate grade for a physics result of this kind, but this is an analytic derivation within an established mean-field framework rather than an independently replicated calculation. Autonomy graded collaborative: the model supplied the key idea, but its first formal write-up contained errors that the human authors fixed and verified, and the authors framed the exchange as asking for help on a problem they posed.
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Entry history (1 event)
- AddedEntered the registry graded Peer reviewed and Collaborative.
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Graded peer reviewed for verification and collaborative for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). Identity for the critical exponents of jamming derived analytically. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-06-02-jamming-exponent-identityBibTeX
@misc{whataifound-independent-2026-identity,
title = {Identity for the critical exponents of jamming derived analytically},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Peer reviewed. Autonomy: Collaborative.},
url = {https://whataifound.org/finding/2026-06-02-jamming-exponent-identity}
}