{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UGG4UI43MF3MQG5CWKG3MYHWFH","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":"7ffef0a96a2fab24892499dfbca28ed4d4f3ed7506849b7dc4b9b85f04e4592c","cross_cats_sorted":["cond-mat.mes-hall","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-06T02:44:08Z","title_canon_sha256":"ee606efa3c2240c852de120ca793dfd70ed6e18d58044785c48fb6ae5bf5a037"},"schema_version":"1.0","source":{"id":"1211.1093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1093","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1093v1","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1093","created_at":"2026-05-18T01:53:25Z"},{"alias_kind":"pith_short_12","alias_value":"UGG4UI43MF3M","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UGG4UI43MF3MQG5C","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UGG4UI43","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:5743c4f8974dd4f28b9a35f04e175b94e13996f8a0efe9e13362e1927b41c032","target":"graph","created_at":"2026-05-18T01:53:25Z","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":"Motivated by nucleation and molecular aggregation in physical, chemical and biological settings, we present a thorough analysis of the general problem of stochastic self-assembly of a fixed number of identical particles in a finite volume. We derive the Backward Kolmogorov equation (BKE) for the cluster probability distribution. From the BKE we study the distribution of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. In the limits of slow and fast self-assembly, we develop analytical approaches to calculate the mean cluster formati","authors_text":"Maria R. D'Orsogna, Romain Yvinec, Tom Chou","cross_cats":["cond-mat.mes-hall","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-06T02:44:08Z","title":"First passage times in homogeneous nucleation and self-assembly"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1093","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":"sha256:4df84f0f5eb9be6f8eff822d100fa8ab4d1eeae6b8669894504d231e4274b90c","target":"record","created_at":"2026-05-18T01:53:25Z","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":"7ffef0a96a2fab24892499dfbca28ed4d4f3ed7506849b7dc4b9b85f04e4592c","cross_cats_sorted":["cond-mat.mes-hall","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-11-06T02:44:08Z","title_canon_sha256":"ee606efa3c2240c852de120ca793dfd70ed6e18d58044785c48fb6ae5bf5a037"},"schema_version":"1.0","source":{"id":"1211.1093","kind":"arxiv","version":1}},"canonical_sha256":"a18dca239b6176c81ba2b28db660f629e8404944806b7d8050e2f183d969fc46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a18dca239b6176c81ba2b28db660f629e8404944806b7d8050e2f183d969fc46","first_computed_at":"2026-05-18T01:53:25.354949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:25.354949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k9GDRWkUFo3RiK3HNWNfu6j14hrpaXk7x9y/bBDtGIYD5nQB4yo2VcHx7ab07lSjQkheDGzQkO57m2UnWIU0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:25.355529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4df84f0f5eb9be6f8eff822d100fa8ab4d1eeae6b8669894504d231e4274b90c","sha256:5743c4f8974dd4f28b9a35f04e175b94e13996f8a0efe9e13362e1927b41c032"],"state_sha256":"4c90754227dcf69e7aeafecb238516035b7341ea135aa5294c3e57fd12cfe8bf"}