{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DQKMXMKCTX27COLG3PLMK3O62Z","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":"b40cba213ad8f8dff8e2a8d7a3f3bf32302b8a6906388fc5be35f0b73f84701a","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-28T01:54:22Z","title_canon_sha256":"dc3b3195c5beb1b551e30c120ab658946972506673a5e2b2b48679c9b583b6f5"},"schema_version":"1.0","source":{"id":"1212.6451","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6451","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6451v3","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6451","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"DQKMXMKCTX27","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DQKMXMKCTX27COLG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DQKMXMKC","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:f53314f708d9f6e679e17d8767f9e5fec8a58ef767f9eab1ee9b22393e027bd1","target":"graph","created_at":"2026-05-18T02:22:30Z","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 investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuous-state branching theory. In particular, this equation governs the evolution of the L\\'{e}vy measure of a critical continuous-state branching process which becomes extinct (i.e., is absorbed at zero) almost surely. We show that a nondegenerate scaling limit of the L\\'{e}vy measure (and the process) exists if and only if the branching mechanism is regularly varying at 0. When the branching mechanism","authors_text":"Gautam Iyer, Nicholas Leger, Robert L. Pego","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-28T01:54:22Z","title":"Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6451","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":"sha256:006b9f3130bd7b0e068f125e1e98cd2d61a6f2f6d73ab599a9c1f4bf8d21a2f3","target":"record","created_at":"2026-05-18T02:22:30Z","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":"b40cba213ad8f8dff8e2a8d7a3f3bf32302b8a6906388fc5be35f0b73f84701a","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-28T01:54:22Z","title_canon_sha256":"dc3b3195c5beb1b551e30c120ab658946972506673a5e2b2b48679c9b583b6f5"},"schema_version":"1.0","source":{"id":"1212.6451","kind":"arxiv","version":3}},"canonical_sha256":"1c14cbb1429df5f13966dbd6c56dded643785170b79348099e924bb8bdfe3b0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c14cbb1429df5f13966dbd6c56dded643785170b79348099e924bb8bdfe3b0d","first_computed_at":"2026-05-18T02:22:30.235931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:30.235931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5kIedNzXnGFDvHWBWChb+/C6/vuucRY9hJDt5lLBqbXwMLJyj/n84DR0BpdEPjXMpIDPP2wQ8zTshpAUrePTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:30.236376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6451","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:006b9f3130bd7b0e068f125e1e98cd2d61a6f2f6d73ab599a9c1f4bf8d21a2f3","sha256:f53314f708d9f6e679e17d8767f9e5fec8a58ef767f9eab1ee9b22393e027bd1"],"state_sha256":"0918fdf93bfba71629fce335791823bb6d3882678e5d1a953f37a6945161a98c"}