{"paper":{"title":"Random close packing fraction of bidisperse discs: theoretical derivation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A disorder-guaranteeing theory using cell order distributions derives the highest possible random close packing fraction for bidisperse discs along with exact bounds.","cross_cats":["cond-mat.dis-nn","math-ph","math.MP"],"primary_cat":"cond-mat.soft","authors_text":"Raphael Blumenfeld","submitted_at":"2025-09-24T13:59:10Z","abstract_excerpt":"Predicting theoretically the highest density, which a disordered packing of discs can achieve, has been a long-standing unresolved problem. Such predictions are hindered by two difficulties - the dependence of the density on the packing procedure and ensuring disorder. A theory that overcomes these difficulties has been developed recently for mono-disperse disc packing~\\cite{Bl21}. However, to minimise order, experiments and numerical simulations often use two-size discs and a prediction of the highest possible packing fraction, $\\phi_{RCP}$, for these packings is arguably more useful. This pr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A disorder-guaranteeing theory is formulated here to derive the highest mathematically possible value of φ_RCP(p,D), using the concept of the cell order distribution. I also derive exact upper and lower bounds on this densest disordered packing fraction.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The cell order distribution can be defined and used in a way that mathematically guarantees the packing remains fully disordered while still achieving the highest possible density.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives the maximum random close packing fraction φ_RCP(p,D) for bidisperse discs via cell order distribution and supplies exact bounds.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A disorder-guaranteeing theory using cell order distributions derives the highest possible random close packing fraction for bidisperse discs along with exact bounds.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f6de793cc05482a4c578d1e90f24bd59e997ea69752496b2f5c2fc9747962b5e"},"source":{"id":"2509.20132","kind":"arxiv","version":4},"verdict":{"id":"afb0e12a-e527-4a64-8dbd-5e83160233a5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T14:09:15.000811Z","strongest_claim":"A disorder-guaranteeing theory is formulated here to derive the highest mathematically possible value of φ_RCP(p,D), using the concept of the cell order distribution. I also derive exact upper and lower bounds on this densest disordered packing fraction.","one_line_summary":"Derives the maximum random close packing fraction φ_RCP(p,D) for bidisperse discs via cell order distribution and supplies exact bounds.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The cell order distribution can be defined and used in a way that mathematically guarantees the packing remains fully disordered while still achieving the highest possible density.","pith_extraction_headline":"A disorder-guaranteeing theory using cell order distributions derives the highest possible random close packing fraction for bidisperse discs along with exact bounds."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.20132/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"619430416aa0d78925a19e4a1f7383b9089fa4dc49dcb9455e2723105b4b2857"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}