{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QZNOSSAVPWPV2J5OFD4PZ7WNTP","short_pith_number":"pith:QZNOSSAV","canonical_record":{"source":{"id":"1304.7510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","cross_cats_sorted":[],"title_canon_sha256":"1fdf1790ad408cc97f24d076e4173f76bdf34faee1f7795c01cddad29c042c8a","abstract_canon_sha256":"399d276dc4f25ab272e4d091fea391b282d5fa86fcfd806d22898fc02d8e9c86"},"schema_version":"1.0"},"canonical_sha256":"865ae948157d9f5d27ae28f8fcfecd9bc9c5bbdea88328de19b521e78089698b","source":{"kind":"arxiv","id":"1304.7510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7510","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7510v2","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7510","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"QZNOSSAVPWPV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QZNOSSAVPWPV2J5O","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QZNOSSAV","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QZNOSSAVPWPV2J5OFD4PZ7WNTP","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","cross_cats_sorted":[],"title_canon_sha256":"1fdf1790ad408cc97f24d076e4173f76bdf34faee1f7795c01cddad29c042c8a","abstract_canon_sha256":"399d276dc4f25ab272e4d091fea391b282d5fa86fcfd806d22898fc02d8e9c86"},"schema_version":"1.0"},"canonical_sha256":"865ae948157d9f5d27ae28f8fcfecd9bc9c5bbdea88328de19b521e78089698b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:09.448634Z","signature_b64":"FxMv+b2yj3eevX7PMK6ZCjDMCzP5bUTugd05voOF8CqNARp9deCiS6qw30TUMmbWdmUkyMWVYqxSuE0J6Bp0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"865ae948157d9f5d27ae28f8fcfecd9bc9c5bbdea88328de19b521e78089698b","last_reissued_at":"2026-05-18T02:43:09.448142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:09.448142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7510","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2KKdZC7W68tve5EeLX/d9tGBax8Yy0rde7iHmj54FiB9dl+MuVeU8jjunCSSCFrlZFUotsFZAxQKHPHjrREBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:49:54.639973Z"},"content_sha256":"8b38d3d7a7d1b45a020f87906e240d50f5d99adba0440f62b999e8a2b5f1e3b4","schema_version":"1.0","event_id":"sha256:8b38d3d7a7d1b45a020f87906e240d50f5d99adba0440f62b999e8a2b5f1e3b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QZNOSSAVPWPV2J5OFD4PZ7WNTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on factorization property of some stochastic integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zbigniew J. Jurek","submitted_at":"2013-04-28T19:51:19Z","abstract_excerpt":"In the paper Sato (2006) there are introduced two families of improper random integrals and the corresponding two convolution semigroups of infinitely divisible laws on $\\Rset^d$. Theorem 3.1 gives a relation (a factorization property) between those two integrals. Here, using \\emph{the random integral mappings} $I^{h,r}_{(a,b]}$ (cf. the survey article Jurek (2011)), we give a simpler proof that is also valid for measures on Banach spaces. Furthermore, using our technique we establish yet other relations between those two families of improper stochastic integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7510","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sX30HNBaQBZ2FWRRpiEpXmTWcVuXvI5B/w03VhyqCasXTdp36q8SpVvr0XKXMnzzikCaVQbx0z3S/3AFZowNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:49:54.640331Z"},"content_sha256":"4902e5884976b536313d28d4a574a002a0695224f11fb2aa4fd382cae131aa33","schema_version":"1.0","event_id":"sha256:4902e5884976b536313d28d4a574a002a0695224f11fb2aa4fd382cae131aa33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZNOSSAVPWPV2J5OFD4PZ7WNTP/bundle.json","state_url":"https://pith.science/pith/QZNOSSAVPWPV2J5OFD4PZ7WNTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZNOSSAVPWPV2J5OFD4PZ7WNTP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T00:49:54Z","links":{"resolver":"https://pith.science/pith/QZNOSSAVPWPV2J5OFD4PZ7WNTP","bundle":"https://pith.science/pith/QZNOSSAVPWPV2J5OFD4PZ7WNTP/bundle.json","state":"https://pith.science/pith/QZNOSSAVPWPV2J5OFD4PZ7WNTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZNOSSAVPWPV2J5OFD4PZ7WNTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QZNOSSAVPWPV2J5OFD4PZ7WNTP","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":"399d276dc4f25ab272e4d091fea391b282d5fa86fcfd806d22898fc02d8e9c86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","title_canon_sha256":"1fdf1790ad408cc97f24d076e4173f76bdf34faee1f7795c01cddad29c042c8a"},"schema_version":"1.0","source":{"id":"1304.7510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7510","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7510v2","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7510","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"QZNOSSAVPWPV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QZNOSSAVPWPV2J5O","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QZNOSSAV","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:4902e5884976b536313d28d4a574a002a0695224f11fb2aa4fd382cae131aa33","target":"graph","created_at":"2026-05-18T02:43:09Z","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 the paper Sato (2006) there are introduced two families of improper random integrals and the corresponding two convolution semigroups of infinitely divisible laws on $\\Rset^d$. Theorem 3.1 gives a relation (a factorization property) between those two integrals. Here, using \\emph{the random integral mappings} $I^{h,r}_{(a,b]}$ (cf. the survey article Jurek (2011)), we give a simpler proof that is also valid for measures on Banach spaces. Furthermore, using our technique we establish yet other relations between those two families of improper stochastic integrals.","authors_text":"Zbigniew J. Jurek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","title":"Remarks on factorization property of some stochastic integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7510","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":"sha256:8b38d3d7a7d1b45a020f87906e240d50f5d99adba0440f62b999e8a2b5f1e3b4","target":"record","created_at":"2026-05-18T02:43:09Z","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":"399d276dc4f25ab272e4d091fea391b282d5fa86fcfd806d22898fc02d8e9c86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","title_canon_sha256":"1fdf1790ad408cc97f24d076e4173f76bdf34faee1f7795c01cddad29c042c8a"},"schema_version":"1.0","source":{"id":"1304.7510","kind":"arxiv","version":2}},"canonical_sha256":"865ae948157d9f5d27ae28f8fcfecd9bc9c5bbdea88328de19b521e78089698b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"865ae948157d9f5d27ae28f8fcfecd9bc9c5bbdea88328de19b521e78089698b","first_computed_at":"2026-05-18T02:43:09.448142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.448142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FxMv+b2yj3eevX7PMK6ZCjDMCzP5bUTugd05voOF8CqNARp9deCiS6qw30TUMmbWdmUkyMWVYqxSuE0J6Bp0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.448634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b38d3d7a7d1b45a020f87906e240d50f5d99adba0440f62b999e8a2b5f1e3b4","sha256:4902e5884976b536313d28d4a574a002a0695224f11fb2aa4fd382cae131aa33"],"state_sha256":"7514ec1356ee82bc3d8a36062f5116e98d0eaf0a53f236e3401567d44ab8928f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J36FKJznyN0SXoxvbPLfixfQWWJsJ132dMYr3Zux10ibONkQEDieSus6LNNsj+cYIb946jdta2ecj1NGsI5sBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:49:54.642268Z","bundle_sha256":"f3bcf1c087b9f9f163ef2b40b2b91584e480216ff6ac7cfd13259e4a507560eb"}}