{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CTV63H6AW4UOPXZ2ZW7L5E37BB","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":"60ddaa24debe10d32edb408b9a48b212cce482e90de6b42de788f220c91e40ac","cross_cats_sorted":["cond-mat.soft","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-17T06:02:00Z","title_canon_sha256":"8928768c07441058fa6fbffe279a5bf5e9e8eea76a9f635420076ebd7362310c"},"schema_version":"1.0","source":{"id":"1003.3301","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3301","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3301v2","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3301","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"CTV63H6AW4UO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CTV63H6AW4UOPXZ2","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CTV63H6A","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:e026871097d049a77f0c3d29a4c184b6cf81d5fd7277a89373215dda94f8a394","target":"graph","created_at":"2026-05-18T03:38:24Z","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":"The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting \\textit{de novo} (from-scratch) searches for dense packings becomes crucial. In this paper, we use the \\textit{divide and concur} framework to develop a general search method for the solution of periodic constraint problems, and we apply it to the discovery of dense perio","authors_text":"Simon Gravel, Veit Elser, Yoav Kallus","cross_cats":["cond-mat.soft","cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-17T06:02:00Z","title":"A method for dense packing discovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3301","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":"sha256:36bbac2b9ebb8ba94f54477e613a693224acb4c8f498f22135bf9af30fef67d9","target":"record","created_at":"2026-05-18T03:38:24Z","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":"60ddaa24debe10d32edb408b9a48b212cce482e90de6b42de788f220c91e40ac","cross_cats_sorted":["cond-mat.soft","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-17T06:02:00Z","title_canon_sha256":"8928768c07441058fa6fbffe279a5bf5e9e8eea76a9f635420076ebd7362310c"},"schema_version":"1.0","source":{"id":"1003.3301","kind":"arxiv","version":2}},"canonical_sha256":"14ebed9fc0b728e7df3acdbebe937f085bbdacc848842456121b5420c2aac164","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14ebed9fc0b728e7df3acdbebe937f085bbdacc848842456121b5420c2aac164","first_computed_at":"2026-05-18T03:38:24.085002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:24.085002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhFNezD0MKONFzixjKFGya7FAvXLQ9UjL8I2Arm2SMe/x4jayWN6+FhE9oLenk0LPWI8hKk1gWW4hsbkf1cSDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:24.085584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3301","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36bbac2b9ebb8ba94f54477e613a693224acb4c8f498f22135bf9af30fef67d9","sha256:e026871097d049a77f0c3d29a4c184b6cf81d5fd7277a89373215dda94f8a394"],"state_sha256":"d6ee126b2a4e2ef54e04ffb11c92f32c047b5ada3478936bbd5696454c4cb2d6"}