{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KDPHIBNDSLBDXYBASKR6F53KU2","short_pith_number":"pith:KDPHIBND","canonical_record":{"source":{"id":"1803.01313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-04T07:43:08Z","cross_cats_sorted":[],"title_canon_sha256":"4172b4920463b496e1e96f277929bdd3f75cd4e58dc68ab158707084e55f62b4","abstract_canon_sha256":"00ad08683ea4822caf1d40328dd48fff82a55e19f908ea712f5218af72cca43e"},"schema_version":"1.0"},"canonical_sha256":"50de7405a392c23be02092a3e2f76aa6a1d2fa7c6773691222b827c6db2a9450","source":{"kind":"arxiv","id":"1803.01313","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01313","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01313v1","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01313","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"KDPHIBNDSLBD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KDPHIBNDSLBDXYBA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KDPHIBND","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KDPHIBNDSLBDXYBASKR6F53KU2","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-04T07:43:08Z","cross_cats_sorted":[],"title_canon_sha256":"4172b4920463b496e1e96f277929bdd3f75cd4e58dc68ab158707084e55f62b4","abstract_canon_sha256":"00ad08683ea4822caf1d40328dd48fff82a55e19f908ea712f5218af72cca43e"},"schema_version":"1.0"},"canonical_sha256":"50de7405a392c23be02092a3e2f76aa6a1d2fa7c6773691222b827c6db2a9450","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:01.104942Z","signature_b64":"eO/10h99Hde7a6WUSoLMLJnoO+XFrlbV97QlV+jpAg0WDGDfNzKqsBbK/YDu6U5GuWDeWSpUSHl5ladsuI12Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50de7405a392c23be02092a3e2f76aa6a1d2fa7c6773691222b827c6db2a9450","last_reissued_at":"2026-05-18T00:22:01.104384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:01.104384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01313","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FKyuMtLaiQJ97sgkgtKmn6DR0IqAkOO7W0jqEsONJq1ATqhJxzA/FRtkuwW+Aa9jMNL8zKbh1HLbueYF1b3rCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:13:12.284506Z"},"content_sha256":"86431a9fb85ca2bb6844494efb518cd664698368ff41276521ee9468ba15db44","schema_version":"1.0","event_id":"sha256:86431a9fb85ca2bb6844494efb518cd664698368ff41276521ee9468ba15db44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KDPHIBNDSLBDXYBASKR6F53KU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on global solutions to random 3D vorticity equations for small initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael R\\\"ockner, Rongchan Zhu, Xiangchan Zhu","submitted_at":"2018-03-04T07:43:08Z","abstract_excerpt":"In this paper, we prove that the solution constructed in \\cite{BR16} satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of controlled rough path introduced in \\cite{G04}. As a result, we obtain the existence and uniqueness of the global solutions to the stochastic vorticity equations in 3D case for the small initial data independent of time, which can be viewed as a stochastic version of the Kato-Fujita result (see \\cite{KF62})."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01313","kind":"arxiv","version":1},"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":"2026-05-18T00:22:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1j/1aTqCgSq+Un54DITX1xi7Aqv60lj+ecLLtBNR/6rseqjcoy2meGgS+YwmvZPFp2qLTgH/HKFpgZVHwOM6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:13:12.284837Z"},"content_sha256":"0e353f40495dc2affa2923ccb03e992d6a306512db0e491ada0d0da919a086d3","schema_version":"1.0","event_id":"sha256:0e353f40495dc2affa2923ccb03e992d6a306512db0e491ada0d0da919a086d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KDPHIBNDSLBDXYBASKR6F53KU2/bundle.json","state_url":"https://pith.science/pith/KDPHIBNDSLBDXYBASKR6F53KU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KDPHIBNDSLBDXYBASKR6F53KU2/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":"2026-06-03T01:13:12Z","links":{"resolver":"https://pith.science/pith/KDPHIBNDSLBDXYBASKR6F53KU2","bundle":"https://pith.science/pith/KDPHIBNDSLBDXYBASKR6F53KU2/bundle.json","state":"https://pith.science/pith/KDPHIBNDSLBDXYBASKR6F53KU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KDPHIBNDSLBDXYBASKR6F53KU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KDPHIBNDSLBDXYBASKR6F53KU2","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":"00ad08683ea4822caf1d40328dd48fff82a55e19f908ea712f5218af72cca43e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-04T07:43:08Z","title_canon_sha256":"4172b4920463b496e1e96f277929bdd3f75cd4e58dc68ab158707084e55f62b4"},"schema_version":"1.0","source":{"id":"1803.01313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01313","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01313v1","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01313","created_at":"2026-05-18T00:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"KDPHIBNDSLBD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KDPHIBNDSLBDXYBA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KDPHIBND","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:0e353f40495dc2affa2923ccb03e992d6a306512db0e491ada0d0da919a086d3","target":"graph","created_at":"2026-05-18T00:22:01Z","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 prove that the solution constructed in \\cite{BR16} satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of controlled rough path introduced in \\cite{G04}. As a result, we obtain the existence and uniqueness of the global solutions to the stochastic vorticity equations in 3D case for the small initial data independent of time, which can be viewed as a stochastic version of the Kato-Fujita result (see \\cite{KF62}).","authors_text":"Michael R\\\"ockner, Rongchan Zhu, Xiangchan Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-04T07:43:08Z","title":"A remark on global solutions to random 3D vorticity equations for small initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01313","kind":"arxiv","version":1},"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":"sha256:86431a9fb85ca2bb6844494efb518cd664698368ff41276521ee9468ba15db44","target":"record","created_at":"2026-05-18T00:22:01Z","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":"00ad08683ea4822caf1d40328dd48fff82a55e19f908ea712f5218af72cca43e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-04T07:43:08Z","title_canon_sha256":"4172b4920463b496e1e96f277929bdd3f75cd4e58dc68ab158707084e55f62b4"},"schema_version":"1.0","source":{"id":"1803.01313","kind":"arxiv","version":1}},"canonical_sha256":"50de7405a392c23be02092a3e2f76aa6a1d2fa7c6773691222b827c6db2a9450","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50de7405a392c23be02092a3e2f76aa6a1d2fa7c6773691222b827c6db2a9450","first_computed_at":"2026-05-18T00:22:01.104384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:01.104384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eO/10h99Hde7a6WUSoLMLJnoO+XFrlbV97QlV+jpAg0WDGDfNzKqsBbK/YDu6U5GuWDeWSpUSHl5ladsuI12Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:01.104942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86431a9fb85ca2bb6844494efb518cd664698368ff41276521ee9468ba15db44","sha256:0e353f40495dc2affa2923ccb03e992d6a306512db0e491ada0d0da919a086d3"],"state_sha256":"0aa5baa2b91a65cbe522a4e24b9c62dc55311065d480d28e0619a808c2eb2339"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IDcwLV/F8ID5+NQvwLJUWhc1Xg4NbWpeo7+OjyhW4uJPa6FKlxdsMZ8gIBE6+9EPE8Pxmh6twUPb69aOgsd2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:13:12.286988Z","bundle_sha256":"b16287f58c2f65bdeb7a3438b7eadb661b3f9cef95def89f03ce3b23f2cfac7b"}}