{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PYA23CY562LDA6USBYTEONH5PZ","short_pith_number":"pith:PYA23CY5","schema_version":"1.0","canonical_sha256":"7e01ad8b1df696307a920e264734fd7e777511b1e192448ee5dda896ae7382c2","source":{"kind":"arxiv","id":"1505.01184","version":2},"attestation_state":"computed","paper":{"title":"Intermediate-Level Crossings of a First-Passage Path","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR"],"primary_cat":"physics.data-an","authors_text":"S. Redner, Uttam Bhat","submitted_at":"2015-05-05T20:59:49Z","abstract_excerpt":"We investigate some simple and surprising properties of a one-dimensional Brownian trajectory with diffusion coefficient $D$ that starts at the origin and reaches $X$ either: (i) at time $T$ or (ii) for the first time at time $T$. We determine the most likely location of the first-passage trajectory from $(0,0)$ to $(X,T)$ and its distribution at any intermediate time $t<T$. A first-passage path typically starts out by being repelled from its final location when $X^2/DT\\ll 1$. We also determine the distribution of times when the trajectory first crosses and last crosses an arbitrary intermedia"},"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":"1505.01184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2015-05-05T20:59:49Z","cross_cats_sorted":["cond-mat.stat-mech","math.PR"],"title_canon_sha256":"0fccc31ec8713835335a2d20bc4c0b27e542ddd55a151a004e7c8678a0bff507","abstract_canon_sha256":"7dae81e3034a27584eaacd57f0e2cb1df2dec864e4fb99e047c929954f9ad578"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.347709Z","signature_b64":"DxVlIxsIvMsWdu/YbgFIvh3YL69IYYFRmQm1Aduk2Hu2fLHophNdPPk0w/3wnBmY+AWNvZ4E/EMMI1xvrdIcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e01ad8b1df696307a920e264734fd7e777511b1e192448ee5dda896ae7382c2","last_reissued_at":"2026-05-18T00:57:38.347141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.347141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intermediate-Level Crossings of a First-Passage Path","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR"],"primary_cat":"physics.data-an","authors_text":"S. Redner, Uttam Bhat","submitted_at":"2015-05-05T20:59:49Z","abstract_excerpt":"We investigate some simple and surprising properties of a one-dimensional Brownian trajectory with diffusion coefficient $D$ that starts at the origin and reaches $X$ either: (i) at time $T$ or (ii) for the first time at time $T$. We determine the most likely location of the first-passage trajectory from $(0,0)$ to $(X,T)$ and its distribution at any intermediate time $t<T$. A first-passage path typically starts out by being repelled from its final location when $X^2/DT\\ll 1$. We also determine the distribution of times when the trajectory first crosses and last crosses an arbitrary intermedia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01184","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":"1505.01184","created_at":"2026-05-18T00:57:38.347221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.01184v2","created_at":"2026-05-18T00:57:38.347221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01184","created_at":"2026-05-18T00:57:38.347221+00:00"},{"alias_kind":"pith_short_12","alias_value":"PYA23CY562LD","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PYA23CY562LDA6US","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PYA23CY5","created_at":"2026-05-18T12:29:37.295048+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/PYA23CY562LDA6USBYTEONH5PZ","json":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ.json","graph_json":"https://pith.science/api/pith-number/PYA23CY562LDA6USBYTEONH5PZ/graph.json","events_json":"https://pith.science/api/pith-number/PYA23CY562LDA6USBYTEONH5PZ/events.json","paper":"https://pith.science/paper/PYA23CY5"},"agent_actions":{"view_html":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ","download_json":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ.json","view_paper":"https://pith.science/paper/PYA23CY5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.01184&json=true","fetch_graph":"https://pith.science/api/pith-number/PYA23CY562LDA6USBYTEONH5PZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PYA23CY562LDA6USBYTEONH5PZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ/action/storage_attestation","attest_author":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ/action/author_attestation","sign_citation":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ/action/citation_signature","submit_replication":"https://pith.science/pith/PYA23CY562LDA6USBYTEONH5PZ/action/replication_record"}},"created_at":"2026-05-18T00:57:38.347221+00:00","updated_at":"2026-05-18T00:57:38.347221+00:00"}