{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UUJ6DNTZXXBE7ZJRLD6PGU6LRK","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":"682c7ce63526e2c2be5a9128817dfe3fb7d30899ed87b341d96222d9a4a7287b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T15:48:43Z","title_canon_sha256":"c3f00074b9ab3cae07afcc37b217e39ba6e27f7d2b5f7c7a6b8feaa356c7baa6"},"schema_version":"1.0","source":{"id":"1307.4313","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4313","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4313v3","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4313","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"UUJ6DNTZXXBE","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UUJ6DNTZXXBE7ZJR","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UUJ6DNTZ","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:33820e6621de411b196b766f9096e5d62eab57a251eaaa8c98e3e1cf51cc76b3","target":"graph","created_at":"2026-05-18T01:23:59Z","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":"The coalescing Brownian flow on $\\mathbb{R}$ is a process which was introduced by Arratia [Coalescing Brownian motions on the line (1979) Univ. Wisconsin, Madison] and T\\'{o}th and Werner [Probab. Theory Related Fields 111 (1998) 375-452], and which formally corresponds to starting coalescing Brownian motions from every space-time point. We provide a new state space and topology for this process and obtain an invariance principle for coalescing random walks. This result holds under a finite variance assumption and is thus optimal. In previous works by Fontes et al. [Ann. Probab. 32 (2004) 2857","authors_text":"Arnab Sen, Christophe Garban, Nathana\\\"el Berestycki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T15:48:43Z","title":"Coalescing Brownian flows: A new approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4313","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:ba974cd38e92aaea687ec4e6945e3e27abcbbc656dadd4de077069230fc4e17a","target":"record","created_at":"2026-05-18T01:23:59Z","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":"682c7ce63526e2c2be5a9128817dfe3fb7d30899ed87b341d96222d9a4a7287b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T15:48:43Z","title_canon_sha256":"c3f00074b9ab3cae07afcc37b217e39ba6e27f7d2b5f7c7a6b8feaa356c7baa6"},"schema_version":"1.0","source":{"id":"1307.4313","kind":"arxiv","version":3}},"canonical_sha256":"a513e1b679bdc24fe53158fcf353cb8a82f31cf243d554ff7bced2882d8875f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a513e1b679bdc24fe53158fcf353cb8a82f31cf243d554ff7bced2882d8875f9","first_computed_at":"2026-05-18T01:23:59.087930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:59.087930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a8dQzTpSCrsSdDS7qzxUimOQgM1QOyQ6xhujJtbh9M+WcMLROQ6VaBhfrl211yd21mRVxLOtkRjL1kq4xO+fDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:59.088752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4313","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba974cd38e92aaea687ec4e6945e3e27abcbbc656dadd4de077069230fc4e17a","sha256:33820e6621de411b196b766f9096e5d62eab57a251eaaa8c98e3e1cf51cc76b3"],"state_sha256":"4f3faa3c8ee2aade5ef9e8bbf1f8926d19729e629e8637130366bb2711de76ea"}