{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BBWLRTSA7YTP7D5Z5Q47WFQQJ6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"95e4953542f641fdd3c66cbd255f2c62c9c498b182dfb24441321135f92752f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2012-02-23T15:32:20Z","title_canon_sha256":"db57de837062c0b9b149caaee4373c4433732b29ad16baa5c6fe5c182210c333"},"schema_version":"1.0","source":{"id":"1202.5208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5208","created_at":"2026-05-18T01:58:20Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5208v2","created_at":"2026-05-18T01:58:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5208","created_at":"2026-05-18T01:58:20Z"},{"alias_kind":"pith_short_12","alias_value":"BBWLRTSA7YTP","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BBWLRTSA7YTP7D5Z","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BBWLRTSA","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:7ec65f6a60a8cdc2a4226d5f58348189241ce75772b2578cb5561490d24e4a68","target":"graph","created_at":"2026-05-18T01:58:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and their diversity of structure and symmetry increases with increasing $N$ and decreases with increasing hyperstaticity $H \\equiv N_c - N_{ISO}$, where $N_c$ is the number of pair contacts and $N_{ISO} = 3N-6$. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fra","authors_text":"Corey S. O'Hern, Jared Harwayne-Gidansky, Robert S. Hoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2012-02-23T15:32:20Z","title":"Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5208","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e164e919012aac85e5f707c1137ee23a2b55ea75d3f81a8f5d09cb67ac2a2eb8","target":"record","created_at":"2026-05-18T01:58:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"95e4953542f641fdd3c66cbd255f2c62c9c498b182dfb24441321135f92752f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2012-02-23T15:32:20Z","title_canon_sha256":"db57de837062c0b9b149caaee4373c4433732b29ad16baa5c6fe5c182210c333"},"schema_version":"1.0","source":{"id":"1202.5208","kind":"arxiv","version":2}},"canonical_sha256":"086cb8ce40fe26ff8fb9ec39fb16104f8114171ccf15dac2793027b881fee410","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"086cb8ce40fe26ff8fb9ec39fb16104f8114171ccf15dac2793027b881fee410","first_computed_at":"2026-05-18T01:58:20.368706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:20.368706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bG1In0hthoCd5jIRRxpawan/8egm53Mnt0MsoNtTIrJSmSJHGDUlu92BgskJGUQUeSMpPhg2VWLgV+hi55pZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:20.369392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e164e919012aac85e5f707c1137ee23a2b55ea75d3f81a8f5d09cb67ac2a2eb8","sha256:7ec65f6a60a8cdc2a4226d5f58348189241ce75772b2578cb5561490d24e4a68"],"state_sha256":"03438a67d0a1b1f352eadc115bff3558117c9049164cde18a737c2159d5035bf"}