{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:HY2GLRTQVWR5UPRZTEMOVCGAMI","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":"d4928546dc06ff20458fc2aab8e58ed6f595a906a0a0789ac077f8ac1f741142","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2005-07-26T01:32:39Z","title_canon_sha256":"ef49011f46c908e67bb3d46771eeaf8f5faa8a3fc4d0285bbb681d5cfab629ed"},"schema_version":"1.0","source":{"id":"math/0507522","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0507522","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0507522v3","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507522","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"HY2GLRTQVWR5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HY2GLRTQVWR5UPRZ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HY2GLRTQ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:e389053b78280264de7a90e238d7851d64216e3513ecc4a3533d3d75124c15ef","target":"graph","created_at":"2026-05-18T03:27:43Z","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 study a model of mass-bearing coagulating planar Brownian particles. Coagulation is prone to occur when two particles become within a distance of order $\\epsilon$. We assume that the initial number of particles is of the order of $| \\log \\epsilon |. Under suitable assumptions on the initial distribution of particles and the microscopic coagulation propensities, we show that the macroscopic particle densities satisfy a Smoluchowski-type equation.","authors_text":"Alan Hammond, Fraydoun Rezakhanlou","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2005-07-26T01:32:39Z","title":"The kinetic limit of a system of coagulating planar Brownian particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507522","kind":"arxiv","version":3},"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":"sha256:64b13d06151366275428ee6f51d2530f8292fe64b36072e998d26ce5aaf47221","target":"record","created_at":"2026-05-18T03:27:43Z","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":"d4928546dc06ff20458fc2aab8e58ed6f595a906a0a0789ac077f8ac1f741142","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2005-07-26T01:32:39Z","title_canon_sha256":"ef49011f46c908e67bb3d46771eeaf8f5faa8a3fc4d0285bbb681d5cfab629ed"},"schema_version":"1.0","source":{"id":"math/0507522","kind":"arxiv","version":3}},"canonical_sha256":"3e3465c670ada3da3e399918ea88c0622d4eabb7b6bc08085c6814758652d687","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e3465c670ada3da3e399918ea88c0622d4eabb7b6bc08085c6814758652d687","first_computed_at":"2026-05-18T03:27:43.153460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:43.153460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g1Y0U5DcGJINfzUZue9TOXWJdAmgt8sN/Z+/QijRybiYziduPblvMvg34o6mppXPXmgcu7+0TQON5Rd/eI0sBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:43.154264Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0507522","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64b13d06151366275428ee6f51d2530f8292fe64b36072e998d26ce5aaf47221","sha256:e389053b78280264de7a90e238d7851d64216e3513ecc4a3533d3d75124c15ef"],"state_sha256":"2d62c253ae8721129bbcd5df4666ebf3300fc64d96b52a37711ae1bf404de576"}