{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MXY622JIIQCANVMM7747GBLRUL","short_pith_number":"pith:MXY622JI","schema_version":"1.0","canonical_sha256":"65f1ed6928440406d58cfff9f30571a2d608968c83498f4c70de71be89444a91","source":{"kind":"arxiv","id":"1506.00724","version":3},"attestation_state":"computed","paper":{"title":"The Brownian web, the Brownian net, and their universality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer, Jan M. Swart, Rongfeng Sun","submitted_at":"2015-06-02T02:05:37Z","abstract_excerpt":"The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from everywhere in space and time, and the Brownian net is a generalization that also allows branching. They appear in the diffusive scaling limits of many one-dimensional interacting particle systems with branching and coalescence. This article gives an introduction to the Brownian web and net, and how they arise in the scaling limits of various one-dimensional models, focusing mainly on coalescing random walks and random walks in i.i.d. space-time random environments. We will also briefly survey models a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.00724","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-02T02:05:37Z","cross_cats_sorted":[],"title_canon_sha256":"ed81884f2e14360e7d5b65e34c98f91a4caa98eebe39f9c113ec43eb40f8cf54","abstract_canon_sha256":"8699291b3d95935535aafe8fa2c716e01b2f97b9b3f85cb76791e75d1221dc92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:17.813617Z","signature_b64":"yQqIiGmyLdahUYEavdxAog2NjpZsCEPuoKN5wU0G1FJXwMkf7wxHxmWG4xFEygf1Gk36u6XYgrs3of4wq4cNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65f1ed6928440406d58cfff9f30571a2d608968c83498f4c70de71be89444a91","last_reissued_at":"2026-05-18T00:53:17.813162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:17.813162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Brownian web, the Brownian net, and their universality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer, Jan M. Swart, Rongfeng Sun","submitted_at":"2015-06-02T02:05:37Z","abstract_excerpt":"The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from everywhere in space and time, and the Brownian net is a generalization that also allows branching. They appear in the diffusive scaling limits of many one-dimensional interacting particle systems with branching and coalescence. This article gives an introduction to the Brownian web and net, and how they arise in the scaling limits of various one-dimensional models, focusing mainly on coalescing random walks and random walks in i.i.d. space-time random environments. We will also briefly survey models a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00724","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.00724","created_at":"2026-05-18T00:53:17.813234+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00724v3","created_at":"2026-05-18T00:53:17.813234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00724","created_at":"2026-05-18T00:53:17.813234+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXY622JIIQCA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXY622JIIQCANVMM","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXY622JI","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL","json":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL.json","graph_json":"https://pith.science/api/pith-number/MXY622JIIQCANVMM7747GBLRUL/graph.json","events_json":"https://pith.science/api/pith-number/MXY622JIIQCANVMM7747GBLRUL/events.json","paper":"https://pith.science/paper/MXY622JI"},"agent_actions":{"view_html":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL","download_json":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL.json","view_paper":"https://pith.science/paper/MXY622JI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00724&json=true","fetch_graph":"https://pith.science/api/pith-number/MXY622JIIQCANVMM7747GBLRUL/graph.json","fetch_events":"https://pith.science/api/pith-number/MXY622JIIQCANVMM7747GBLRUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL/action/storage_attestation","attest_author":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL/action/author_attestation","sign_citation":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL/action/citation_signature","submit_replication":"https://pith.science/pith/MXY622JIIQCANVMM7747GBLRUL/action/replication_record"}},"created_at":"2026-05-18T00:53:17.813234+00:00","updated_at":"2026-05-18T00:53:17.813234+00:00"}