{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7LPLSBKCVHFOJ6SGUT3XAUSW5J","short_pith_number":"pith:7LPLSBKC","schema_version":"1.0","canonical_sha256":"fadeb90542a9cae4fa46a4f7705256ea5468ff01197c08de005333aef78d0531","source":{"kind":"arxiv","id":"1105.1662","version":1},"attestation_state":"computed","paper":{"title":"On progressive filtration expansion with a process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip Protter, Younes Kchia","submitted_at":"2011-05-09T13:06:32Z","abstract_excerpt":"In this paper we study progressive filtration expansions with cadlag processes. Using results from the weak convergence of sigma fields theory, we first establish a semimartingale convergence theorem. Then we apply it in a filtration expansion with a process setting and provide sufficient conditions for a semimartingale of the base filtration to remain a semimartingale in the expanded filtration. Finally, an application to the expansion of a Brownian filtration with a time reversed diffusion is given through a detailed study."},"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":"1105.1662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-09T13:06:32Z","cross_cats_sorted":[],"title_canon_sha256":"63051493fbb358123579829159391b5266dd257f0cab70a34d06e53022ef7326","abstract_canon_sha256":"526d5f0ccf9a8b7e05f77bf9fb19de6811e20f89103a40b16ce4667cd85fcf41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:32.715860Z","signature_b64":"0Wk+wc18vpWoWqfgRrivbey5WSAXCd9/vIQ+WwbZepiCBUzZDJvJ12iHwmY+9QRoH/tofls0C/ffS+75T7OMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fadeb90542a9cae4fa46a4f7705256ea5468ff01197c08de005333aef78d0531","last_reissued_at":"2026-05-18T04:22:32.715428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:32.715428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On progressive filtration expansion with a process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip Protter, Younes Kchia","submitted_at":"2011-05-09T13:06:32Z","abstract_excerpt":"In this paper we study progressive filtration expansions with cadlag processes. Using results from the weak convergence of sigma fields theory, we first establish a semimartingale convergence theorem. Then we apply it in a filtration expansion with a process setting and provide sufficient conditions for a semimartingale of the base filtration to remain a semimartingale in the expanded filtration. Finally, an application to the expansion of a Brownian filtration with a time reversed diffusion is given through a detailed study."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1662","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":"1105.1662","created_at":"2026-05-18T04:22:32.715501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1662v1","created_at":"2026-05-18T04:22:32.715501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1662","created_at":"2026-05-18T04:22:32.715501+00:00"},{"alias_kind":"pith_short_12","alias_value":"7LPLSBKCVHFO","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7LPLSBKCVHFOJ6SG","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7LPLSBKC","created_at":"2026-05-18T12:26:22.705136+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/7LPLSBKCVHFOJ6SGUT3XAUSW5J","json":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J.json","graph_json":"https://pith.science/api/pith-number/7LPLSBKCVHFOJ6SGUT3XAUSW5J/graph.json","events_json":"https://pith.science/api/pith-number/7LPLSBKCVHFOJ6SGUT3XAUSW5J/events.json","paper":"https://pith.science/paper/7LPLSBKC"},"agent_actions":{"view_html":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J","download_json":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J.json","view_paper":"https://pith.science/paper/7LPLSBKC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1662&json=true","fetch_graph":"https://pith.science/api/pith-number/7LPLSBKCVHFOJ6SGUT3XAUSW5J/graph.json","fetch_events":"https://pith.science/api/pith-number/7LPLSBKCVHFOJ6SGUT3XAUSW5J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J/action/storage_attestation","attest_author":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J/action/author_attestation","sign_citation":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J/action/citation_signature","submit_replication":"https://pith.science/pith/7LPLSBKCVHFOJ6SGUT3XAUSW5J/action/replication_record"}},"created_at":"2026-05-18T04:22:32.715501+00:00","updated_at":"2026-05-18T04:22:32.715501+00:00"}