{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UUJ6DNTZXXBE7ZJRLD6PGU6LRK","short_pith_number":"pith:UUJ6DNTZ","canonical_record":{"source":{"id":"1307.4313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T15:48:43Z","cross_cats_sorted":[],"title_canon_sha256":"c3f00074b9ab3cae07afcc37b217e39ba6e27f7d2b5f7c7a6b8feaa356c7baa6","abstract_canon_sha256":"682c7ce63526e2c2be5a9128817dfe3fb7d30899ed87b341d96222d9a4a7287b"},"schema_version":"1.0"},"canonical_sha256":"a513e1b679bdc24fe53158fcf353cb8a82f31cf243d554ff7bced2882d8875f9","source":{"kind":"arxiv","id":"1307.4313","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UUJ6DNTZXXBE7ZJRLD6PGU6LRK","target":"record","payload":{"canonical_record":{"source":{"id":"1307.4313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-16T15:48:43Z","cross_cats_sorted":[],"title_canon_sha256":"c3f00074b9ab3cae07afcc37b217e39ba6e27f7d2b5f7c7a6b8feaa356c7baa6","abstract_canon_sha256":"682c7ce63526e2c2be5a9128817dfe3fb7d30899ed87b341d96222d9a4a7287b"},"schema_version":"1.0"},"canonical_sha256":"a513e1b679bdc24fe53158fcf353cb8a82f31cf243d554ff7bced2882d8875f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:59.088752Z","signature_b64":"a8dQzTpSCrsSdDS7qzxUimOQgM1QOyQ6xhujJtbh9M+WcMLROQ6VaBhfrl211yd21mRVxLOtkRjL1kq4xO+fDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a513e1b679bdc24fe53158fcf353cb8a82f31cf243d554ff7bced2882d8875f9","last_reissued_at":"2026-05-18T01:23:59.087930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:59.087930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.4313","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPAfJfp4H0JcNtH+a7rJwiJ13+lP4zXBWGdj6nWzWUhhGAWl/zQhXrrO3+sQgGhBS7BwpMsHKNPEjm57tPvECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:38:12.909054Z"},"content_sha256":"ba974cd38e92aaea687ec4e6945e3e27abcbbc656dadd4de077069230fc4e17a","schema_version":"1.0","event_id":"sha256:ba974cd38e92aaea687ec4e6945e3e27abcbbc656dadd4de077069230fc4e17a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UUJ6DNTZXXBE7ZJRLD6PGU6LRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coalescing Brownian flows: A new approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arnab Sen, Christophe Garban, Nathana\\\"el Berestycki","submitted_at":"2013-07-16T15:48:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4313","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"du7t0k2O31toHB6VQTDz9Yyvj1xSXFOzPSbi1+zqi4rLWyn5dwK0ylhd57EhJ9AJryutsdyYwFxB3FGEVnh6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:38:12.909473Z"},"content_sha256":"33820e6621de411b196b766f9096e5d62eab57a251eaaa8c98e3e1cf51cc76b3","schema_version":"1.0","event_id":"sha256:33820e6621de411b196b766f9096e5d62eab57a251eaaa8c98e3e1cf51cc76b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUJ6DNTZXXBE7ZJRLD6PGU6LRK/bundle.json","state_url":"https://pith.science/pith/UUJ6DNTZXXBE7ZJRLD6PGU6LRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUJ6DNTZXXBE7ZJRLD6PGU6LRK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T16:38:12Z","links":{"resolver":"https://pith.science/pith/UUJ6DNTZXXBE7ZJRLD6PGU6LRK","bundle":"https://pith.science/pith/UUJ6DNTZXXBE7ZJRLD6PGU6LRK/bundle.json","state":"https://pith.science/pith/UUJ6DNTZXXBE7ZJRLD6PGU6LRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUJ6DNTZXXBE7ZJRLD6PGU6LRK/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5wVHvFWF/Qy0CEwLFrenwm5UHb3yv3jp2ibrGIOlco73L3PmgIngKe6qW1Q8fNyOrXXrqpTdkRBFrygGLeYTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:38:12.911389Z","bundle_sha256":"ac698ea057220c0fd2ea97b661c16b12f56e6f3881f94f2585ce008ec85314f6"}}