{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZDVYYF2PAFZI46BWVZZVRUDKAA","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":"e4ec481930aa7e02128b53ac12e0c4c9f4486f15a8ea82e73e1edd84fe29d3b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-03T20:11:13Z","title_canon_sha256":"007793ac8ada2b7f219f25012d6f9f2c97f598c49a2ff76f59f46dd83d14d6de"},"schema_version":"1.0","source":{"id":"1908.01225","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01225","created_at":"2026-07-05T01:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01225v2","created_at":"2026-07-05T01:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01225","created_at":"2026-07-05T01:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZDVYYF2PAFZI","created_at":"2026-07-05T01:13:23Z"},{"alias_kind":"pith_short_16","alias_value":"ZDVYYF2PAFZI46BW","created_at":"2026-07-05T01:13:23Z"},{"alias_kind":"pith_short_8","alias_value":"ZDVYYF2P","created_at":"2026-07-05T01:13:23Z"}],"graph_snapshots":[{"event_id":"sha256:a658c1259f5ae388811fa314085cb2b6e8d7a730c36649e345d1aaa1e2fd8efc","target":"graph","created_at":"2026-07-05T01:13:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.01225/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a product formula for the multiple stochastic integrals with respect to Levy process. The idea is to use exponential vectors and the polarization technique which greatly simplify the argument.","authors_text":"Neha Sharma, Nishant Agrawal, Yaozhong Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-03T20:11:13Z","title":"Product Formula of Multiple Integrals of Levy Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01225","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:e0716205152d4938d89fbf6b32bb31117daa92369f015ef17aa3819b5a500873","target":"record","created_at":"2026-07-05T01:13:23Z","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":"e4ec481930aa7e02128b53ac12e0c4c9f4486f15a8ea82e73e1edd84fe29d3b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-03T20:11:13Z","title_canon_sha256":"007793ac8ada2b7f219f25012d6f9f2c97f598c49a2ff76f59f46dd83d14d6de"},"schema_version":"1.0","source":{"id":"1908.01225","kind":"arxiv","version":2}},"canonical_sha256":"c8eb8c174f01728e7836ae7358d06a0027107487e550bf25a408370834902807","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8eb8c174f01728e7836ae7358d06a0027107487e550bf25a408370834902807","first_computed_at":"2026-07-05T01:13:23.288873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:13:23.288873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mIsDN14sXBC50xUmAcDSx5lIXDVyMOKtbpg8Twv7nKt6nzgISU8Tn+uy7oSwtYH8FqVQsjLreD/lRHY24gR4Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T01:13:23.289270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01225","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0716205152d4938d89fbf6b32bb31117daa92369f015ef17aa3819b5a500873","sha256:a658c1259f5ae388811fa314085cb2b6e8d7a730c36649e345d1aaa1e2fd8efc"],"state_sha256":"8348cce258f2fbc72e347cb1901a1f7450ae973f7275abf9144889bd45c77ae1"}