{
  "abstract": "Within the full replica-symmetry-breaking (fullRSB) solution of dense hard spheres in infinite dimension, Charbonneau, Kurchan, Parisi, Urbani, and Zamponi (J. Stat. Mech. P10009, 2014) introduced three critical exponents a , b , c governing the matching region of the fullRSB profile near the jamming transition. These exponents satisfy two scaling relations. The first, b = ( 1 + c ) / 2 , was established analytically by the diffusion-drift balance in the scaling ansatz. The second, a + b = 1 , was observed numerically to arbitrary precision but could not be proven. The exponents a , b , c of the scaling fullRSB ansatz are related to the physical exponents α , θ , κ that control the gap, force, and overlap distributions by the relations α = a / b , θ = ( c − a ) / ( b − c ) , κ = c + 1 . Crucially, the relation a + b = 1 yields the scaling relations α = 1 / ( 2 + θ ) and κ = 2 − 2 / ( 3 + θ )",
  "abstract_shown": true,
  "affiliations": [
    "Beihang University",
    "Rome Unit",
    "Sapienza Università di Roma"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1,
        2
      ],
      "name": "Giorgio Parisi A",
      "orcid": "0000-0001-6500-5222"
    },
    {
      "affs": [
        2
      ],
      "name": "Francesco Zamponi",
      "orcid": "0000-0001-9260-1951"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86g224bj5dsqa.bib",
  "cited_by": 7,
  "doi": "10.1088/1742-5468/ae7bd7",
  "fulltext_url": null,
  "id": "86g224bj5dsqa",
  "issns": [
    "1742-5468"
  ],
  "landing_url": "https://doi.org/10.1088/1742-5468/ae7bd7",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2505|Material Dynamics and Properties"
    ]
  ],
  "openalex": "W7166874780",
  "pdf_url": "https://iopscience.iop.org/article/10.1088/1742-5468/ae7bd7/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "Institute of Physics",
  "ris": "https://research.draconitic.com/paper/86g224bj5dsqa.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:19Z",
      "native_id": "W7166874780",
      "source": "openalex",
      "url": "https://doi.org/10.1088/1742-5468/ae7bd7"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:2505|Material Dynamics and Properties",
      "subfield": "materials-polymers"
    }
  ],
  "title": "A proof of an identity for the critical exponents of jamming",
  "title_text": "A proof of an identity for the critical exponents of jamming",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T13:21:13Z",
  "url": "https://research.draconitic.com/paper/86g224bj5dsqa",
  "venue": "Journal of Statistical Mechanics Theory and Experiment",
  "versions": []
}