{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:B3EDJOPFKRJLKURRXUMAWT7MIB","short_pith_number":"pith:B3EDJOPF","schema_version":"1.0","canonical_sha256":"0ec834b9e55452b55231bd180b4fec405825a7611cb0ba877262790363081cea","source":{"kind":"arxiv","id":"1203.2587","version":2},"attestation_state":"computed","paper":{"title":"Conditioned Martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johannes Ruf, Nicolas Perkowski","submitted_at":"2012-03-12T18:55:57Z","abstract_excerpt":"It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous local martingale and clarifies the role of finite versus infinite time in this setting. As a consequence, we can describe the law of regular diffusions that are conditioned upward or downward."},"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":"1203.2587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-12T18:55:57Z","cross_cats_sorted":[],"title_canon_sha256":"bcd9bb7c38574cbc79aa8242aa0bae47eb89f1a7cc6afdc446d4b5d9e235dcce","abstract_canon_sha256":"81bd2d533c293c3247445064f5492331a5743d1860f27c0bf376ca6c9df58388"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:42.250050Z","signature_b64":"ShaKeoa56kbqeU3dxamIgBq3/EHI0CoVs4orDvfSNnIwg+zBcio+qVZeHRR2cARA1011FyfM8y8lgsDa84+jAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec834b9e55452b55231bd180b4fec405825a7611cb0ba877262790363081cea","last_reissued_at":"2026-05-18T03:43:42.249324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:42.249324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditioned Martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johannes Ruf, Nicolas Perkowski","submitted_at":"2012-03-12T18:55:57Z","abstract_excerpt":"It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous local martingale and clarifies the role of finite versus infinite time in this setting. As a consequence, we can describe the law of regular diffusions that are conditioned upward or downward."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2587","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":"1203.2587","created_at":"2026-05-18T03:43:42.249460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.2587v2","created_at":"2026-05-18T03:43:42.249460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2587","created_at":"2026-05-18T03:43:42.249460+00:00"},{"alias_kind":"pith_short_12","alias_value":"B3EDJOPFKRJL","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"B3EDJOPFKRJLKURR","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"B3EDJOPF","created_at":"2026-05-18T12:26:58.693483+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/B3EDJOPFKRJLKURRXUMAWT7MIB","json":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB.json","graph_json":"https://pith.science/api/pith-number/B3EDJOPFKRJLKURRXUMAWT7MIB/graph.json","events_json":"https://pith.science/api/pith-number/B3EDJOPFKRJLKURRXUMAWT7MIB/events.json","paper":"https://pith.science/paper/B3EDJOPF"},"agent_actions":{"view_html":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB","download_json":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB.json","view_paper":"https://pith.science/paper/B3EDJOPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.2587&json=true","fetch_graph":"https://pith.science/api/pith-number/B3EDJOPFKRJLKURRXUMAWT7MIB/graph.json","fetch_events":"https://pith.science/api/pith-number/B3EDJOPFKRJLKURRXUMAWT7MIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB/action/storage_attestation","attest_author":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB/action/author_attestation","sign_citation":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB/action/citation_signature","submit_replication":"https://pith.science/pith/B3EDJOPFKRJLKURRXUMAWT7MIB/action/replication_record"}},"created_at":"2026-05-18T03:43:42.249460+00:00","updated_at":"2026-05-18T03:43:42.249460+00:00"}