{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LGWAJR67764QWPWFWQNTHY7YOU","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":"c54b8156e6b76fb36de77fc1e4dd753379c5f5cfec8414f55bfb247ef063bb36","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-07-20T20:10:03Z","title_canon_sha256":"bbf051c88b4263c8d09d40f9c7f8b4d39dd7282f4250f88b510525328be34233"},"schema_version":"1.0","source":{"id":"1207.5054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5054","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5054v1","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5054","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"LGWAJR67764Q","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LGWAJR67764QWPWF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LGWAJR67","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:2f73928c5a9a2efda7d558b97c7bf47d00b9bdd838eafc8746f99d235481e59a","target":"graph","created_at":"2026-05-18T00:31:00Z","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 introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of three-dimensional microstructures that are often regarded as close analogues in the literature: one resulting from normal grain growth (mean curvature flow) and another resulting from a random Poisson-Voronoi tessellation of space. Grain growth strongly favors particular grain topologies, compared with the Poisson-Voronoi model. Moreover, the frequencies of h","authors_text":"David J. Srolovitz, Emanuel A. Lazar, Jeremy K. Mason, Robert D. MacPherson","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-07-20T20:10:03Z","title":"Complete topology of cells, grains, and bubbles in three-dimensional microstructures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5054","kind":"arxiv","version":1},"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":"sha256:6438ca9168940cdf9a90cdaf916287511ea6e8793b780be3059b52381b9a9905","target":"record","created_at":"2026-05-18T00:31:00Z","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":"c54b8156e6b76fb36de77fc1e4dd753379c5f5cfec8414f55bfb247ef063bb36","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2012-07-20T20:10:03Z","title_canon_sha256":"bbf051c88b4263c8d09d40f9c7f8b4d39dd7282f4250f88b510525328be34233"},"schema_version":"1.0","source":{"id":"1207.5054","kind":"arxiv","version":1}},"canonical_sha256":"59ac04c7dfffb90b3ec5b41b33e3f8752eeeeea615ca1b59c4de652aa023e9f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59ac04c7dfffb90b3ec5b41b33e3f8752eeeeea615ca1b59c4de652aa023e9f5","first_computed_at":"2026-05-18T00:31:00.790015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:00.790015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B80LDoTk5m7Eqvj8orCoYUQvUR24dkFcsI/JvNWwK70j91m8yZ+OAWOgxiv5BLtTUiCWYAdyLxARWzCV9Zf+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:00.790694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6438ca9168940cdf9a90cdaf916287511ea6e8793b780be3059b52381b9a9905","sha256:2f73928c5a9a2efda7d558b97c7bf47d00b9bdd838eafc8746f99d235481e59a"],"state_sha256":"1990068512432f04a56b96954dc8a84ed013d098c26ba617eeca7b052e2216cc"}