{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:I4GWY4DACDH26EEV4V3ZVATJ3E","short_pith_number":"pith:I4GWY4DA","schema_version":"1.0","canonical_sha256":"470d6c706010cfaf1095e5779a8269d910331aebde8fcccac111c41cf4c5999e","source":{"kind":"arxiv","id":"1009.3003","version":1},"attestation_state":"computed","paper":{"title":"Densest local packing diversity. II. Application to three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.MG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato","submitted_at":"2010-09-15T19:27:28Z","abstract_excerpt":"The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper [A.B. Hopkins, F.H. Stillinger and S. Torquato, Phys. Rev. E 81 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space Rd and presented those packings in R2 for values of N up to N = 348. We analyze the properties and characteristics of the densest local packings in R3 and employ knowledge"},"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":"1009.3003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-15T19:27:28Z","cross_cats_sorted":["cond-mat.soft","math.MG"],"title_canon_sha256":"c740dbe14eb68ea2696950eebadf33a11f7d3b30abd9ebf187edf969a8b58c32","abstract_canon_sha256":"556551b043e85b375b0a989d5d0a47aec220988199204242ebff65da1ad082d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:37.083605Z","signature_b64":"f5PlIaq8eLRYNcnFoTVsEu1evbJL/hVya/NCdCMI9dI76C0/gdNybkQMVPm7rftBVSoyzk3U177XcOLGWcRsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"470d6c706010cfaf1095e5779a8269d910331aebde8fcccac111c41cf4c5999e","last_reissued_at":"2026-05-18T03:23:37.082919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:37.082919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Densest local packing diversity. II. Application to three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.MG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato","submitted_at":"2010-09-15T19:27:28Z","abstract_excerpt":"The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper [A.B. Hopkins, F.H. Stillinger and S. Torquato, Phys. Rev. E 81 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space Rd and presented those packings in R2 for values of N up to N = 348. We analyze the properties and characteristics of the densest local packings in R3 and employ knowledge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3003","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":"1009.3003","created_at":"2026-05-18T03:23:37.083032+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3003v1","created_at":"2026-05-18T03:23:37.083032+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3003","created_at":"2026-05-18T03:23:37.083032+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4GWY4DACDH2","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4GWY4DACDH26EEV","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4GWY4DA","created_at":"2026-05-18T12:26:07.630475+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/I4GWY4DACDH26EEV4V3ZVATJ3E","json":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E.json","graph_json":"https://pith.science/api/pith-number/I4GWY4DACDH26EEV4V3ZVATJ3E/graph.json","events_json":"https://pith.science/api/pith-number/I4GWY4DACDH26EEV4V3ZVATJ3E/events.json","paper":"https://pith.science/paper/I4GWY4DA"},"agent_actions":{"view_html":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E","download_json":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E.json","view_paper":"https://pith.science/paper/I4GWY4DA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3003&json=true","fetch_graph":"https://pith.science/api/pith-number/I4GWY4DACDH26EEV4V3ZVATJ3E/graph.json","fetch_events":"https://pith.science/api/pith-number/I4GWY4DACDH26EEV4V3ZVATJ3E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E/action/storage_attestation","attest_author":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E/action/author_attestation","sign_citation":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E/action/citation_signature","submit_replication":"https://pith.science/pith/I4GWY4DACDH26EEV4V3ZVATJ3E/action/replication_record"}},"created_at":"2026-05-18T03:23:37.083032+00:00","updated_at":"2026-05-18T03:23:37.083032+00:00"}