{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IWEQLLNPRRRZAKQSGGQB37RUNC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a7c459f99eddaa1a6d04ee3734f2cd06a140f8395b278181f2460da960599de0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-25T12:34:37Z","title_canon_sha256":"fc4af29d1f20a0b18a4ce7fbedbc8efac623ca5510869406397cc028f780732b"},"schema_version":"1.0","source":{"id":"1403.6323","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6323","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6323v2","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6323","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"IWEQLLNPRRRZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IWEQLLNPRRRZAKQS","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IWEQLLNP","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:1067f70bb757e14f01352a0e90baf4fa6274d0d47bfff64999478b98ac08e0ee","target":"graph","created_at":"2026-05-18T02:42:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study progressive filtration expansions with c\\`adl\\`ag processes. Using results from the theory of the weak convergence of $\\sigma$-fields, 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. Applications to the expansion of a Brownian filtration are given. The paper concludes with applications to models of insider trading in financial mathematics.","authors_text":"Philip Protter, Younes Kchia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-25T12:34:37Z","title":"On Progressive Filtration Expansions with a Process; Applications to Insider Trading"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6323","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a8f1c30f04150906631a71072e5dc663d0988c06be63deb6446889591b773233","target":"record","created_at":"2026-05-18T02:42:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a7c459f99eddaa1a6d04ee3734f2cd06a140f8395b278181f2460da960599de0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-25T12:34:37Z","title_canon_sha256":"fc4af29d1f20a0b18a4ce7fbedbc8efac623ca5510869406397cc028f780732b"},"schema_version":"1.0","source":{"id":"1403.6323","kind":"arxiv","version":2}},"canonical_sha256":"458905adaf8c63902a1231a01dfe3468a01a92132f143cf23351111b923c38df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"458905adaf8c63902a1231a01dfe3468a01a92132f143cf23351111b923c38df","first_computed_at":"2026-05-18T02:42:39.347695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:39.347695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"czBfYhSG+f1OyT9EiW5+ymZTaP790BhVBkWrKa47kQM1Qiboxv4W5sQy29njCmTj2o4CnNr3ZP/dOXG01/IxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:39.348349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6323","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8f1c30f04150906631a71072e5dc663d0988c06be63deb6446889591b773233","sha256:1067f70bb757e14f01352a0e90baf4fa6274d0d47bfff64999478b98ac08e0ee"],"state_sha256":"91ada5f2f5c64bb0563eb871ead9078431b3bf8560e194e96de5743fb706a813"}