{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GATI42SQA4JORVOZJC2CJSXZ2F","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":"6e39da736fb5e3ffd767743c7f3a9811de146ab13da7d6a1062f5b667e043bcc","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-18T09:17:04Z","title_canon_sha256":"499501cf06d4cee0671103ce42ea4036afffd5787ddbbd2edb183b9a204bb0b8"},"schema_version":"1.0","source":{"id":"1501.04274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04274","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04274v2","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04274","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"GATI42SQA4JO","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GATI42SQA4JORVOZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GATI42SQ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:7a135a7e0249ec811c4b3f5d852a46b7b1ca0e5b5e25cb248c03f1db5a111c37","target":"graph","created_at":"2026-05-18T02:27:58Z","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":"We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).","authors_text":"Constantinos Kardaras, Ioannis Karatzas","cross_cats":["q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-18T09:17:04Z","title":"Optional Decomposition for continuous semimartingales under arbitrary filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04274","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":"sha256:2d1e4b89f20275b911235bcc3785591a178d9642a3e073612a0e304ad8f85c3a","target":"record","created_at":"2026-05-18T02:27:58Z","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":"6e39da736fb5e3ffd767743c7f3a9811de146ab13da7d6a1062f5b667e043bcc","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-18T09:17:04Z","title_canon_sha256":"499501cf06d4cee0671103ce42ea4036afffd5787ddbbd2edb183b9a204bb0b8"},"schema_version":"1.0","source":{"id":"1501.04274","kind":"arxiv","version":2}},"canonical_sha256":"30268e6a500712e8d5d948b424caf9d17a11bb777e068d16cc9f7eacca5ff687","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30268e6a500712e8d5d948b424caf9d17a11bb777e068d16cc9f7eacca5ff687","first_computed_at":"2026-05-18T02:27:58.293498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:58.293498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V4qCQc0dJAgBL1l1zGFxdaaJo4DvqpUfPDZvgWKkSdP0yyscBB6zyVTd7GZ1lHINa4YYntuyO4Hi6fmqSUL1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:58.294005Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d1e4b89f20275b911235bcc3785591a178d9642a3e073612a0e304ad8f85c3a","sha256:7a135a7e0249ec811c4b3f5d852a46b7b1ca0e5b5e25cb248c03f1db5a111c37"],"state_sha256":"3a2f65da090224a823131fffe38a9bddead0d6605526fadf290b90ad4e0d35ea"}