{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QARS3ZASFKRMBMLCXFKW7BTZ7D","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":"1d83a08a26747feae30f991ab214737c4519504c1da628083484293bc71ebcea","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.BM","submitted_at":"2015-10-15T22:27:10Z","title_canon_sha256":"4ed609ca5d1a453a31a462610fbd0bc908a9c9eaf8721acdae07a9c97186f325"},"schema_version":"1.0","source":{"id":"1510.04730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04730","created_at":"2026-05-18T01:20:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04730v1","created_at":"2026-05-18T01:20:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04730","created_at":"2026-05-18T01:20:42Z"},{"alias_kind":"pith_short_12","alias_value":"QARS3ZASFKRM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QARS3ZASFKRMBMLC","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QARS3ZAS","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:ba2fac56d8498b528d01999d0d865e79c04b3f75a6ba791a6526972d26a68f14","target":"graph","created_at":"2026-05-18T01:20:42Z","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 an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistic of times it requires for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volume, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volume, we develop a scaling framework to study the behavior of the fi","authors_text":"Erwan Hingant, Laurent Pujo-Menjouet, Romain Yvinec, Samuel Bernard","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.BM","submitted_at":"2015-10-15T22:27:10Z","title":"First passage times in homogeneous nucleation: dependence on the total number of particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04730","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:ea0c4504e6c5011249e99c130c6cff874c0bcad5fac65aa1e23f1d960f221367","target":"record","created_at":"2026-05-18T01:20:42Z","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":"1d83a08a26747feae30f991ab214737c4519504c1da628083484293bc71ebcea","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.BM","submitted_at":"2015-10-15T22:27:10Z","title_canon_sha256":"4ed609ca5d1a453a31a462610fbd0bc908a9c9eaf8721acdae07a9c97186f325"},"schema_version":"1.0","source":{"id":"1510.04730","kind":"arxiv","version":1}},"canonical_sha256":"80232de4122aa2c0b162b9556f8679f8e17ca5be5869af69ef12a236b6fdca6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80232de4122aa2c0b162b9556f8679f8e17ca5be5869af69ef12a236b6fdca6e","first_computed_at":"2026-05-18T01:20:42.327379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:42.327379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMiflTeUenQ0tZbIjYBlsOiN8jn/c7fJLjcm81OuE2kG427Z/W7VvuL5jlT4JEdGkOWU1eH+KFs/MQMQq6E7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:42.327870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea0c4504e6c5011249e99c130c6cff874c0bcad5fac65aa1e23f1d960f221367","sha256:ba2fac56d8498b528d01999d0d865e79c04b3f75a6ba791a6526972d26a68f14"],"state_sha256":"a7461566234f27a0454289e583195ab40fdb7d100246fed4be4d8edcf084697c"}