{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VOD4ZYJ4UNDSVAORKAQSFWPRZG","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":"f7dcafad2abfab584b4efe063872689bfe85c7016b05e92ce02d3ed4e24ecb7f","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-20T10:18:40Z","title_canon_sha256":"2d665ddc88b8c52c8538c11411e8b74453360b142e2f1aace5047db4cf25fd21"},"schema_version":"1.0","source":{"id":"1611.06493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06493","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06493v1","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06493","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"VOD4ZYJ4UNDS","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VOD4ZYJ4UNDSVAOR","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VOD4ZYJ4","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:a1f90a6765105f5bbf022ac14cf372bbf7baa78ebba9e0a653547551c95c8cd2","target":"graph","created_at":"2026-05-18T00:57:36Z","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":"Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention especially in stochastic analysis and statistical physics of cellular biology, as novel experimental data is now available, but their interpretation remains challenging.} We derive here probability distribution functions for clusters that can either aggregate upon binding to form clusters of arbitrary sizes or a single cluster can dissociate into two sub-clusters. U","authors_text":"David Holcman, Nathanael Hoze","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-20T10:18:40Z","title":"Stochastic coagulation-fragmentation processes with a finite number of particles and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06493","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":"sha256:996714fba05b4cb459abdfbb1069ee7d33d755c9a3bb47141de73bd7ce6b37b7","target":"record","created_at":"2026-05-18T00:57:36Z","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":"f7dcafad2abfab584b4efe063872689bfe85c7016b05e92ce02d3ed4e24ecb7f","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-20T10:18:40Z","title_canon_sha256":"2d665ddc88b8c52c8538c11411e8b74453360b142e2f1aace5047db4cf25fd21"},"schema_version":"1.0","source":{"id":"1611.06493","kind":"arxiv","version":1}},"canonical_sha256":"ab87cce13ca3472a81d1502122d9f1c9a5e8a8fa3f9a2f2a0edf6b5c641c17d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab87cce13ca3472a81d1502122d9f1c9a5e8a8fa3f9a2f2a0edf6b5c641c17d8","first_computed_at":"2026-05-18T00:57:36.659426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:36.659426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aJ2sLGx7tOPLyTsapGal+/p54/28/SQ2++Ty15dhwE7Y236hFK4SXk6o+4J2USk1l3LeIXylpbrNjjYf/0kuBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:36.660141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:996714fba05b4cb459abdfbb1069ee7d33d755c9a3bb47141de73bd7ce6b37b7","sha256:a1f90a6765105f5bbf022ac14cf372bbf7baa78ebba9e0a653547551c95c8cd2"],"state_sha256":"0856ca85a7b535875f4a7acde4505530ef9ebd1d13a55787d6d0ed818e75d5d7"}