{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:NZAG4GK74H4HVE77SLYZ6RTIVK","short_pith_number":"pith:NZAG4GK7","schema_version":"1.0","canonical_sha256":"6e406e195fe1f87a93ff92f19f4668aaa7e897366edf68ef5feda5ba4872acc4","source":{"kind":"arxiv","id":"1006.5834","version":1},"attestation_state":"computed","paper":{"title":"Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alan J. Bray, Satya N. Majumdar","submitted_at":"2010-06-30T11:56:33Z","abstract_excerpt":"We consider three independent Brownian walkers moving on a line. The process terminates when the left-most walker (the `Leader') meets either of the other two walkers. For arbitrary values of the diffusion constants D_1 (the Leader), D_2 and D_3 of the three walkers, we compute the probability distribution P(m|y_2,y_3) of the maximum distance m between the Leader and the current right-most particle (the `Laggard') during the process, where y_2 and y_3 are the initial distances between the leader and the other two walkers. The result has, for large m, the form P(m|y_2,y_3) \\sim A(y_2,y_3) m^{-\\"},"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":"1006.5834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-06-30T11:56:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"625bbfcda342ba488b1ee68b8c9464bf58517919693f8d9a75c859f17fc6d6ae","abstract_canon_sha256":"45fe9866c9deb1bff32a559dec41099af88d65c2b29608ac3ef64d7bf6865098"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:33.962227Z","signature_b64":"z2dgK2uJ1MaYur6Sy16YKYdFMU9ouPJBbo2fDHF1pNBazWLSbaGD/B7o3tVTNPJWKb2ewhq6G51CvdxTz7BnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e406e195fe1f87a93ff92f19f4668aaa7e897366edf68ef5feda5ba4872acc4","last_reissued_at":"2026-05-18T02:06:33.961465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:33.961465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alan J. Bray, Satya N. Majumdar","submitted_at":"2010-06-30T11:56:33Z","abstract_excerpt":"We consider three independent Brownian walkers moving on a line. The process terminates when the left-most walker (the `Leader') meets either of the other two walkers. For arbitrary values of the diffusion constants D_1 (the Leader), D_2 and D_3 of the three walkers, we compute the probability distribution P(m|y_2,y_3) of the maximum distance m between the Leader and the current right-most particle (the `Laggard') during the process, where y_2 and y_3 are the initial distances between the leader and the other two walkers. The result has, for large m, the form P(m|y_2,y_3) \\sim A(y_2,y_3) m^{-\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5834","kind":"arxiv","version":1},"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":"1006.5834","created_at":"2026-05-18T02:06:33.961592+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.5834v1","created_at":"2026-05-18T02:06:33.961592+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5834","created_at":"2026-05-18T02:06:33.961592+00:00"},{"alias_kind":"pith_short_12","alias_value":"NZAG4GK74H4H","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"NZAG4GK74H4HVE77","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"NZAG4GK7","created_at":"2026-05-18T12:26:12.377268+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/NZAG4GK74H4HVE77SLYZ6RTIVK","json":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK.json","graph_json":"https://pith.science/api/pith-number/NZAG4GK74H4HVE77SLYZ6RTIVK/graph.json","events_json":"https://pith.science/api/pith-number/NZAG4GK74H4HVE77SLYZ6RTIVK/events.json","paper":"https://pith.science/paper/NZAG4GK7"},"agent_actions":{"view_html":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK","download_json":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK.json","view_paper":"https://pith.science/paper/NZAG4GK7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.5834&json=true","fetch_graph":"https://pith.science/api/pith-number/NZAG4GK74H4HVE77SLYZ6RTIVK/graph.json","fetch_events":"https://pith.science/api/pith-number/NZAG4GK74H4HVE77SLYZ6RTIVK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/action/storage_attestation","attest_author":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/action/author_attestation","sign_citation":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/action/citation_signature","submit_replication":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/action/replication_record"}},"created_at":"2026-05-18T02:06:33.961592+00:00","updated_at":"2026-05-18T02:06:33.961592+00:00"}