{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:PTZBJDJVD2A7QNDMRRE3QTKCIE","short_pith_number":"pith:PTZBJDJV","schema_version":"1.0","canonical_sha256":"7cf2148d351e81f8346c8c49b84d42413b1005ecdcd36fcedec218be42a208b1","source":{"kind":"arxiv","id":"2010.08767","version":3},"attestation_state":"computed","paper":{"title":"Bounds on the running maximum of a random walk with small drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ofer Busani, Timo Sepp\\\"al\\\"ainen","submitted_at":"2020-10-17T11:19:17Z","abstract_excerpt":"We derive a lower bound for the probability that a random walk with i.i.d.\\ increments and small negative drift $\\mu$ exceeds the value $x>0$ by time $N$. When the moment generating functions are bounded in an interval around the origin, this probability can be bounded below by $1-O(x|\\mu| \\log N)$. The approach is elementary and does not use strong approximation theorems."},"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":"2010.08767","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-17T11:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"599e1e9238ce389ee7133b5e7d36b2a1ded976d1be36f32b1445f6cce326a0a2","abstract_canon_sha256":"5009e27749c00ddd93ccbaf29462c3c007f43a9dd905957f81b1974cd1f22404"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:50:59.261363Z","signature_b64":"pNCwjzAxGKxEvxHZFE5dAcDVMTEbMhpWxXLILCrpSUKOGG/mZKgKEZKlbo8ywgA5huj+NzEE6YIaIZ8n7BgvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cf2148d351e81f8346c8c49b84d42413b1005ecdcd36fcedec218be42a208b1","last_reissued_at":"2026-07-05T01:50:59.260857Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:50:59.260857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on the running maximum of a random walk with small drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ofer Busani, Timo Sepp\\\"al\\\"ainen","submitted_at":"2020-10-17T11:19:17Z","abstract_excerpt":"We derive a lower bound for the probability that a random walk with i.i.d.\\ increments and small negative drift $\\mu$ exceeds the value $x>0$ by time $N$. When the moment generating functions are bounded in an interval around the origin, this probability can be bounded below by $1-O(x|\\mu| \\log N)$. The approach is elementary and does not use strong approximation theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.08767","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.08767/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2010.08767","created_at":"2026-07-05T01:50:59.260916+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.08767v3","created_at":"2026-07-05T01:50:59.260916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.08767","created_at":"2026-07-05T01:50:59.260916+00:00"},{"alias_kind":"pith_short_12","alias_value":"PTZBJDJVD2A7","created_at":"2026-07-05T01:50:59.260916+00:00"},{"alias_kind":"pith_short_16","alias_value":"PTZBJDJVD2A7QNDM","created_at":"2026-07-05T01:50:59.260916+00:00"},{"alias_kind":"pith_short_8","alias_value":"PTZBJDJV","created_at":"2026-07-05T01:50:59.260916+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.03833","citing_title":"Computable Bounds for Strong Approximations with Applications","ref_index":11,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE","json":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE.json","graph_json":"https://pith.science/api/pith-number/PTZBJDJVD2A7QNDMRRE3QTKCIE/graph.json","events_json":"https://pith.science/api/pith-number/PTZBJDJVD2A7QNDMRRE3QTKCIE/events.json","paper":"https://pith.science/paper/PTZBJDJV"},"agent_actions":{"view_html":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE","download_json":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE.json","view_paper":"https://pith.science/paper/PTZBJDJV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.08767&json=true","fetch_graph":"https://pith.science/api/pith-number/PTZBJDJVD2A7QNDMRRE3QTKCIE/graph.json","fetch_events":"https://pith.science/api/pith-number/PTZBJDJVD2A7QNDMRRE3QTKCIE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE/action/storage_attestation","attest_author":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE/action/author_attestation","sign_citation":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE/action/citation_signature","submit_replication":"https://pith.science/pith/PTZBJDJVD2A7QNDMRRE3QTKCIE/action/replication_record"}},"created_at":"2026-07-05T01:50:59.260916+00:00","updated_at":"2026-07-05T01:50:59.260916+00:00"}