{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:EM22CYQ5BAQZV623FLNXW73JJZ","short_pith_number":"pith:EM22CYQ5","schema_version":"1.0","canonical_sha256":"2335a1621d08219afb5b2adb7b7f694e5d0366177aefed617839792845c7987d","source":{"kind":"arxiv","id":"2404.11167","version":3},"attestation_state":"computed","paper":{"title":"Ito's formula for flows of conditional measures on semimartingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jiacheng Zhang, Xin Guo","submitted_at":"2024-04-17T08:32:08Z","abstract_excerpt":"Motivated by recent development of mean-field systems with common noise, this paper establishes Ito's formula for flows of conditional probability measures under a common filtration associated with general semimartingales. This generalizes existing works on flows of conditional measures on Ito processes and flows of deterministic measure on general semimartingales. The key technical components involve constructing conditional independent copies and establishing the equivalence between stochastic integrals with respect to the conditional law of semimartingales and the conditional expectation of"},"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":"2404.11167","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-04-17T08:32:08Z","cross_cats_sorted":[],"title_canon_sha256":"bc951eaef52616bdef4fb9f7cf85ee083e6bf07d632433356d3cd0e8e87276e3","abstract_canon_sha256":"605df611818c7f9a421b71609d1fccf2849999e61db7e4dbfda071451642971c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:51:59.801532Z","signature_b64":"sEOD63mDSq2tL/K7UJ4HY4v4TzikFW+oPeZE5196EPPURKIicKBqxQstgiWKUyKVMZcVh88T87ZaHuWEzlKSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2335a1621d08219afb5b2adb7b7f694e5d0366177aefed617839792845c7987d","last_reissued_at":"2026-07-05T11:51:59.801047Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:51:59.801047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ito's formula for flows of conditional measures on semimartingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jiacheng Zhang, Xin Guo","submitted_at":"2024-04-17T08:32:08Z","abstract_excerpt":"Motivated by recent development of mean-field systems with common noise, this paper establishes Ito's formula for flows of conditional probability measures under a common filtration associated with general semimartingales. This generalizes existing works on flows of conditional measures on Ito processes and flows of deterministic measure on general semimartingales. The key technical components involve constructing conditional independent copies and establishing the equivalence between stochastic integrals with respect to the conditional law of semimartingales and the conditional expectation of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.11167","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.11167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2404.11167","created_at":"2026-07-05T11:51:59.801102+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.11167v3","created_at":"2026-07-05T11:51:59.801102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.11167","created_at":"2026-07-05T11:51:59.801102+00:00"},{"alias_kind":"pith_short_12","alias_value":"EM22CYQ5BAQZ","created_at":"2026-07-05T11:51:59.801102+00:00"},{"alias_kind":"pith_short_16","alias_value":"EM22CYQ5BAQZV623","created_at":"2026-07-05T11:51:59.801102+00:00"},{"alias_kind":"pith_short_8","alias_value":"EM22CYQ5","created_at":"2026-07-05T11:51:59.801102+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2407.05356","citing_title":"Extended mean-field control problems with Poissonian common noise: Stochastic maximum principle and Hamiltonian-Jacobi-Bellman equation","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ","json":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ.json","graph_json":"https://pith.science/api/pith-number/EM22CYQ5BAQZV623FLNXW73JJZ/graph.json","events_json":"https://pith.science/api/pith-number/EM22CYQ5BAQZV623FLNXW73JJZ/events.json","paper":"https://pith.science/paper/EM22CYQ5"},"agent_actions":{"view_html":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ","download_json":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ.json","view_paper":"https://pith.science/paper/EM22CYQ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.11167&json=true","fetch_graph":"https://pith.science/api/pith-number/EM22CYQ5BAQZV623FLNXW73JJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EM22CYQ5BAQZV623FLNXW73JJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ/action/storage_attestation","attest_author":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ/action/author_attestation","sign_citation":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ/action/citation_signature","submit_replication":"https://pith.science/pith/EM22CYQ5BAQZV623FLNXW73JJZ/action/replication_record"}},"created_at":"2026-07-05T11:51:59.801102+00:00","updated_at":"2026-07-05T11:51:59.801102+00:00"}