{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RK5XJ3H25KTHA3XFN4W443UQA3","short_pith_number":"pith:RK5XJ3H2","schema_version":"1.0","canonical_sha256":"8abb74ecfaeaa6706ee56f2dce6e9006d1af169c40941fcd26e115d0a99816fa","source":{"kind":"arxiv","id":"1108.2210","version":1},"attestation_state":"computed","paper":{"title":"Phase diagram and structural diversity of the densest binary sphere packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","physics.atm-clus"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato, Yang Jiao","submitted_at":"2011-08-10T15:50:04Z","abstract_excerpt":"The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the alpha-x plane of sphere radius ratio alpha and relative concentration x are at the Kepler limit alpha = 1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (alpha,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.2210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-08-10T15:50:04Z","cross_cats_sorted":["cond-mat.soft","physics.atm-clus"],"title_canon_sha256":"a4822864febe7ce80d2f2a2b6634bfbcd360760d32d3907393ad9afcf151e27c","abstract_canon_sha256":"27c617cc157ca6090bd173dcd50822b3d8f2fe3ac0c34a6c8c24aa0ef2b4d332"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:55.623733Z","signature_b64":"mh7dNcxxRmLlscs9yJKnan1VEhWacLzybs5bpPqfiRsI2V0hrx9gcHuqud0GrBJFR4ZVq20SYJtBwE2FnaFwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8abb74ecfaeaa6706ee56f2dce6e9006d1af169c40941fcd26e115d0a99816fa","last_reissued_at":"2026-05-18T02:00:55.623192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:55.623192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase diagram and structural diversity of the densest binary sphere packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","physics.atm-clus"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato, Yang Jiao","submitted_at":"2011-08-10T15:50:04Z","abstract_excerpt":"The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the alpha-x plane of sphere radius ratio alpha and relative concentration x are at the Kepler limit alpha = 1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (alpha,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2210","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.2210","created_at":"2026-05-18T02:00:55.623276+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2210v1","created_at":"2026-05-18T02:00:55.623276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2210","created_at":"2026-05-18T02:00:55.623276+00:00"},{"alias_kind":"pith_short_12","alias_value":"RK5XJ3H25KTH","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RK5XJ3H25KTHA3XF","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RK5XJ3H2","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3","json":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3.json","graph_json":"https://pith.science/api/pith-number/RK5XJ3H25KTHA3XFN4W443UQA3/graph.json","events_json":"https://pith.science/api/pith-number/RK5XJ3H25KTHA3XFN4W443UQA3/events.json","paper":"https://pith.science/paper/RK5XJ3H2"},"agent_actions":{"view_html":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3","download_json":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3.json","view_paper":"https://pith.science/paper/RK5XJ3H2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2210&json=true","fetch_graph":"https://pith.science/api/pith-number/RK5XJ3H25KTHA3XFN4W443UQA3/graph.json","fetch_events":"https://pith.science/api/pith-number/RK5XJ3H25KTHA3XFN4W443UQA3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3/action/storage_attestation","attest_author":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3/action/author_attestation","sign_citation":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3/action/citation_signature","submit_replication":"https://pith.science/pith/RK5XJ3H25KTHA3XFN4W443UQA3/action/replication_record"}},"created_at":"2026-05-18T02:00:55.623276+00:00","updated_at":"2026-05-18T02:00:55.623276+00:00"}