{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:ZFIAL4UXGYYWLPQCDC2TVVHYN2","short_pith_number":"pith:ZFIAL4UX","schema_version":"1.0","canonical_sha256":"c95005f297363165be0218b53ad4f86ebe51410e5b69a7bd52abb8f4a1365287","source":{"kind":"arxiv","id":"math/0103033","version":1},"attestation_state":"computed","paper":{"title":"Filtered stochastic calculus","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Romuald Lenczewski","submitted_at":"2001-03-06T10:31:16Z","abstract_excerpt":"By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. In this new notion of adaptedness,``classical'' time filtration makes the integrands similar to adapted processes, whereas ``quantum'' color filtration produces their deviations from adaptedness. An important feature of this calculus, which we call filtered stochastic calculus, is that it provides an explicit interpolation between the main types of calculi, regardless of the type of independence, including freeness, B"},"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":"math/0103033","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-03-06T10:31:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4f85ddf741f756ab46508130ff89907f34c4e104511e32f37f36fd35cf8fc155","abstract_canon_sha256":"2942fa3d032cbc752b4c3ba9b472c5ef86b74c01c8d177ea1b27c4fc821495cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:38.147919Z","signature_b64":"wurzG66ZaxY0nZK3/Vcqxyr7mvHYRIWqML3/IIFmZ3OAXlAgOZDGoRJPMj+cZCI9tMknNcAW8v3X4k0VhDbpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c95005f297363165be0218b53ad4f86ebe51410e5b69a7bd52abb8f4a1365287","last_reissued_at":"2026-05-18T02:46:38.147386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:38.147386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Filtered stochastic calculus","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Romuald Lenczewski","submitted_at":"2001-03-06T10:31:16Z","abstract_excerpt":"By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. In this new notion of adaptedness,``classical'' time filtration makes the integrands similar to adapted processes, whereas ``quantum'' color filtration produces their deviations from adaptedness. An important feature of this calculus, which we call filtered stochastic calculus, is that it provides an explicit interpolation between the main types of calculi, regardless of the type of independence, including freeness, B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103033","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":"math/0103033","created_at":"2026-05-18T02:46:38.147464+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0103033v1","created_at":"2026-05-18T02:46:38.147464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103033","created_at":"2026-05-18T02:46:38.147464+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZFIAL4UXGYYW","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZFIAL4UXGYYWLPQC","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZFIAL4UX","created_at":"2026-05-18T12:25:50.845339+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/ZFIAL4UXGYYWLPQCDC2TVVHYN2","json":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2.json","graph_json":"https://pith.science/api/pith-number/ZFIAL4UXGYYWLPQCDC2TVVHYN2/graph.json","events_json":"https://pith.science/api/pith-number/ZFIAL4UXGYYWLPQCDC2TVVHYN2/events.json","paper":"https://pith.science/paper/ZFIAL4UX"},"agent_actions":{"view_html":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2","download_json":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2.json","view_paper":"https://pith.science/paper/ZFIAL4UX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0103033&json=true","fetch_graph":"https://pith.science/api/pith-number/ZFIAL4UXGYYWLPQCDC2TVVHYN2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZFIAL4UXGYYWLPQCDC2TVVHYN2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2/action/storage_attestation","attest_author":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2/action/author_attestation","sign_citation":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2/action/citation_signature","submit_replication":"https://pith.science/pith/ZFIAL4UXGYYWLPQCDC2TVVHYN2/action/replication_record"}},"created_at":"2026-05-18T02:46:38.147464+00:00","updated_at":"2026-05-18T02:46:38.147464+00:00"}