{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2BGW3PKED4CPAOJD446IDLRWGY","short_pith_number":"pith:2BGW3PKE","schema_version":"1.0","canonical_sha256":"d04d6dbd441f04f03923e73c81ae3636038f802e8b90d1f9c9ee1e1c174997e7","source":{"kind":"arxiv","id":"1610.07430","version":2},"attestation_state":"computed","paper":{"title":"Coalescence on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"B\\'ela Bollob\\'as, Bhargav Narayanan, Jonathan Lee, Paul Balister","submitted_at":"2016-10-24T14:34:03Z","abstract_excerpt":"We study a geometrically constrained coalescence model derived from spin systems. Given two probability distributions $\\mathbb{P}_R$ and $\\mathbb{P}_B$ on the positive reals with finite means, colour the real line alternately with red and blue intervals so that the lengths of the red intervals have distribution $\\mathbb{P}_R$, the lengths of the blue intervals have distribution $\\mathbb{P}_B$, and distinct intervals have independent lengths. Now, iteratively update this colouring of the line by coalescing intervals: change the colour of any interval that is surrounded by longer intervals so th"},"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":"1610.07430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-24T14:34:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f176e3e2fbd45cdd2e7f6e8d24a23d59c7af2d12618447cf3be2452fd0b56ce2","abstract_canon_sha256":"147dd2117c1daf17414bed4011ffc1f1b0f3b98ad75a2dc3dbc05117c67874da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.505489Z","signature_b64":"T8oMipDvHY11qKir+n+V3wkUDBXV3GyVDImlBHdSJ/I8LpP66yEejR68L8WdQQEgoXa6N+CnLwSTStNN+gfSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d04d6dbd441f04f03923e73c81ae3636038f802e8b90d1f9c9ee1e1c174997e7","last_reissued_at":"2026-05-18T00:35:55.504968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.504968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coalescence on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"B\\'ela Bollob\\'as, Bhargav Narayanan, Jonathan Lee, Paul Balister","submitted_at":"2016-10-24T14:34:03Z","abstract_excerpt":"We study a geometrically constrained coalescence model derived from spin systems. Given two probability distributions $\\mathbb{P}_R$ and $\\mathbb{P}_B$ on the positive reals with finite means, colour the real line alternately with red and blue intervals so that the lengths of the red intervals have distribution $\\mathbb{P}_R$, the lengths of the blue intervals have distribution $\\mathbb{P}_B$, and distinct intervals have independent lengths. Now, iteratively update this colouring of the line by coalescing intervals: change the colour of any interval that is surrounded by longer intervals so th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07430","kind":"arxiv","version":2},"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":"1610.07430","created_at":"2026-05-18T00:35:55.505042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07430v2","created_at":"2026-05-18T00:35:55.505042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07430","created_at":"2026-05-18T00:35:55.505042+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BGW3PKED4CP","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BGW3PKED4CPAOJD","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BGW3PKE","created_at":"2026-05-18T12:29:52.810259+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/2BGW3PKED4CPAOJD446IDLRWGY","json":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY.json","graph_json":"https://pith.science/api/pith-number/2BGW3PKED4CPAOJD446IDLRWGY/graph.json","events_json":"https://pith.science/api/pith-number/2BGW3PKED4CPAOJD446IDLRWGY/events.json","paper":"https://pith.science/paper/2BGW3PKE"},"agent_actions":{"view_html":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY","download_json":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY.json","view_paper":"https://pith.science/paper/2BGW3PKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07430&json=true","fetch_graph":"https://pith.science/api/pith-number/2BGW3PKED4CPAOJD446IDLRWGY/graph.json","fetch_events":"https://pith.science/api/pith-number/2BGW3PKED4CPAOJD446IDLRWGY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY/action/storage_attestation","attest_author":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY/action/author_attestation","sign_citation":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY/action/citation_signature","submit_replication":"https://pith.science/pith/2BGW3PKED4CPAOJD446IDLRWGY/action/replication_record"}},"created_at":"2026-05-18T00:35:55.505042+00:00","updated_at":"2026-05-18T00:35:55.505042+00:00"}