Parisi and Zamponi give an analytic proof of a+b=1 from the scaling full replica-symmetry-breaking equations for infinite-dimensional hard-sphere jamming.
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Parisi and Zamponi give an analytic proof of a+b=1 from the scaling full replica-symmetry-breaking equations for infinite-dimensional hard-sphere jamming. Together with the earlier relation b=(1+c)/2, it yields the scaling identities linking force, gap and overlap exponents.
Read original source Parisi–Zamponi: precise identity, assumptions and AI disclosurearxiv.org
Original report: 2026-06-02Parisi and Zamponi give an analytic proof of a+b=1 from the scaling full replica-symmetry-breaking equations for infinite-dimensional hard-sphere jamming. Together with the earlier relation b=(1+c)/2, it yields the scaling identities linking force, gap and overlap exponents.
The 2014 fullRSB calculation established one scaling relation analytically, while a+b=1 was observed numerically without an analytic proof. Independent mechanical-marginal-stability arguments predicted the resulting physical exponent relations.
If correct, replaces a longstanding numerical observation with an analytic derivation and connects two notions of marginal stability within the specified mathematical model.
A sourced advance or substantial formalization with the exact target, hypotheses, baseline and AI role stated. Importance and verification are assessed separately.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
Parisi–Zamponi–Claude: an analytic proof of the jamming exponent identity
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