{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NZAG4GK74H4HVE77SLYZ6RTIVK","short_pith_number":"pith:NZAG4GK7","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"},"canonical_sha256":"6e406e195fe1f87a93ff92f19f4668aaa7e897366edf68ef5feda5ba4872acc4","source":{"kind":"arxiv","id":"1006.5834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5834","created_at":"2026-05-18T02:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5834v1","created_at":"2026-05-18T02:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5834","created_at":"2026-05-18T02:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"NZAG4GK74H4H","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"NZAG4GK74H4HVE77","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"NZAG4GK7","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NZAG4GK74H4HVE77SLYZ6RTIVK","target":"record","payload":{"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"},"canonical_sha256":"6e406e195fe1f87a93ff92f19f4668aaa7e897366edf68ef5feda5ba4872acc4","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"},"source_kind":"arxiv","source_id":"1006.5834","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+/EpQAbHtKkJumGagqxqD13So3P8sl35A7kZOh1goUkTgt/V3snI3TE5zkILfhahDOExQmZxYYeezIpdPqsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:13:30.445212Z"},"content_sha256":"4de075dfc1fc37271088e5cfe311023e8ed2d61e683ad8963add94a6cb658718","schema_version":"1.0","event_id":"sha256:4de075dfc1fc37271088e5cfe311023e8ed2d61e683ad8963add94a6cb658718"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NZAG4GK74H4HVE77SLYZ6RTIVK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gK6dSFrzAcyJcrV/ur1WhSl8/LWOAIJQ6tKek47p8tbAdKZusi1LttYl/Y70AbLB5TjXlk6IYh+Kv0xyrAzDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:13:30.445688Z"},"content_sha256":"ad69da642ed92a23a18a47367b03cd2bc3580816bdbbdcd10192c3d5b005f04b","schema_version":"1.0","event_id":"sha256:ad69da642ed92a23a18a47367b03cd2bc3580816bdbbdcd10192c3d5b005f04b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/bundle.json","state_url":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/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":"2026-06-04T14:13:30Z","links":{"resolver":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK","bundle":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/bundle.json","state":"https://pith.science/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZAG4GK74H4HVE77SLYZ6RTIVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NZAG4GK74H4HVE77SLYZ6RTIVK","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":"45fe9866c9deb1bff32a559dec41099af88d65c2b29608ac3ef64d7bf6865098","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-06-30T11:56:33Z","title_canon_sha256":"625bbfcda342ba488b1ee68b8c9464bf58517919693f8d9a75c859f17fc6d6ae"},"schema_version":"1.0","source":{"id":"1006.5834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5834","created_at":"2026-05-18T02:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5834v1","created_at":"2026-05-18T02:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5834","created_at":"2026-05-18T02:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"NZAG4GK74H4H","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"NZAG4GK74H4HVE77","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"NZAG4GK7","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:ad69da642ed92a23a18a47367b03cd2bc3580816bdbbdcd10192c3d5b005f04b","target":"graph","created_at":"2026-05-18T02:06:33Z","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":"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^{-\\","authors_text":"Alan J. Bray, Satya N. Majumdar","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-06-30T11:56:33Z","title":"Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5834","kind":"arxiv","version":1},"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":"sha256:4de075dfc1fc37271088e5cfe311023e8ed2d61e683ad8963add94a6cb658718","target":"record","created_at":"2026-05-18T02:06:33Z","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":"45fe9866c9deb1bff32a559dec41099af88d65c2b29608ac3ef64d7bf6865098","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-06-30T11:56:33Z","title_canon_sha256":"625bbfcda342ba488b1ee68b8c9464bf58517919693f8d9a75c859f17fc6d6ae"},"schema_version":"1.0","source":{"id":"1006.5834","kind":"arxiv","version":1}},"canonical_sha256":"6e406e195fe1f87a93ff92f19f4668aaa7e897366edf68ef5feda5ba4872acc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e406e195fe1f87a93ff92f19f4668aaa7e897366edf68ef5feda5ba4872acc4","first_computed_at":"2026-05-18T02:06:33.961465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:33.961465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2dgK2uJ1MaYur6Sy16YKYdFMU9ouPJBbo2fDHF1pNBazWLSbaGD/B7o3tVTNPJWKb2ewhq6G51CvdxTz7BnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:33.962227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4de075dfc1fc37271088e5cfe311023e8ed2d61e683ad8963add94a6cb658718","sha256:ad69da642ed92a23a18a47367b03cd2bc3580816bdbbdcd10192c3d5b005f04b"],"state_sha256":"aadfffef3c9d54e519e94876840799f70008415865e03ed061cac35245999bdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SaZdB7aiAxgndq+wb11Mbf2GjpVbcXnfh+CGXrxdSyLz6CbgtWK9rLyouJMkgQ+P2g77rSxJtn/qV2oNRHLJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:13:30.447670Z","bundle_sha256":"0dde23dac27912cd039218120cc42a854f542a37fb3bc8f414dd142bba188166"}}