{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:72NTMBC46N4OPZ3KM7XWQRDDQX","short_pith_number":"pith:72NTMBC4","canonical_record":{"source":{"id":"2311.05193","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-11-09T08:13:01Z","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"title_canon_sha256":"9d8552cb0e4bc2bb7dbb3d06a5e2a5ef1ad41fa106bd234b9b4cf8c860c93167","abstract_canon_sha256":"584be00447a23efe994de94915b3d780fb75c831ae766f5a8c7c2c73193f18f6"},"schema_version":"1.0"},"canonical_sha256":"fe9b36045cf378e7e76a67ef68446385e56d56078f3a0b0ddedf43dce6f59e86","source":{"kind":"arxiv","id":"2311.05193","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.05193","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"arxiv_version","alias_value":"2311.05193v1","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.05193","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"pith_short_12","alias_value":"72NTMBC46N4O","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"pith_short_16","alias_value":"72NTMBC46N4OPZ3K","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"pith_short_8","alias_value":"72NTMBC4","created_at":"2026-07-05T07:10:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:72NTMBC46N4OPZ3KM7XWQRDDQX","target":"record","payload":{"canonical_record":{"source":{"id":"2311.05193","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-11-09T08:13:01Z","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"title_canon_sha256":"9d8552cb0e4bc2bb7dbb3d06a5e2a5ef1ad41fa106bd234b9b4cf8c860c93167","abstract_canon_sha256":"584be00447a23efe994de94915b3d780fb75c831ae766f5a8c7c2c73193f18f6"},"schema_version":"1.0"},"canonical_sha256":"fe9b36045cf378e7e76a67ef68446385e56d56078f3a0b0ddedf43dce6f59e86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:10:55.906299Z","signature_b64":"RDioY6TUhTO0g2J2Z/dMmKRhjaC6BJ6ZMimXu1e1HaMmkNrJJ5qrkthZAlBak+Dm4O2lur6rXWJfrB+TyXkjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe9b36045cf378e7e76a67ef68446385e56d56078f3a0b0ddedf43dce6f59e86","last_reissued_at":"2026-07-05T07:10:55.905774Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:10:55.905774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.05193","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":"2026-07-05T07:10:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uz+2dGgf423SAubvy+am/5yjWSwB54twEfeIWejjHEs8cshU2l/+MWepvCJFWMODE2pb9ZJpmkHqrWgjlDxYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T02:13:49.514638Z"},"content_sha256":"cbeb634b7b6927085a7e2307d4143b107da45b7ff107c0bb809260e09993e5b3","schema_version":"1.0","event_id":"sha256:cbeb634b7b6927085a7e2307d4143b107da45b7ff107c0bb809260e09993e5b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:72NTMBC46N4OPZ3KM7XWQRDDQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Observable full-horseshoes for Lagrangian flows advected by stochastic 2D Navier-Stokes equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Jianhua Zhang, Wen Huang","submitted_at":"2023-11-09T08:13:01Z","abstract_excerpt":"In this paper, we mainly study the turbulence of Lagrangian flow advected by stochastic 2D Navier-Stokes equations. It is proved that this system has observable full-horseshoes. The observable full-horseshoe means that it is a kind of chaotic structure and occurs on any two disjoint non-empty closed balls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.05193","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.05193/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:10:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7VEY1XA5gNvJIwpRWHxTgBROvFYH1JaQ0ca6jbglZ9KhuIL9bf1FczMfndm+OQAcXvxA1ea/UKlPG6aWApbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T02:13:49.515145Z"},"content_sha256":"f9998fff26b9ddd8ccd62ad82f0e30fc21ce404becc3ddf15c54370201719e7b","schema_version":"1.0","event_id":"sha256:f9998fff26b9ddd8ccd62ad82f0e30fc21ce404becc3ddf15c54370201719e7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72NTMBC46N4OPZ3KM7XWQRDDQX/bundle.json","state_url":"https://pith.science/pith/72NTMBC46N4OPZ3KM7XWQRDDQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72NTMBC46N4OPZ3KM7XWQRDDQX/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":"2026-08-19T02:13:49Z","links":{"resolver":"https://pith.science/pith/72NTMBC46N4OPZ3KM7XWQRDDQX","bundle":"https://pith.science/pith/72NTMBC46N4OPZ3KM7XWQRDDQX/bundle.json","state":"https://pith.science/pith/72NTMBC46N4OPZ3KM7XWQRDDQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72NTMBC46N4OPZ3KM7XWQRDDQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:72NTMBC46N4OPZ3KM7XWQRDDQX","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":"584be00447a23efe994de94915b3d780fb75c831ae766f5a8c7c2c73193f18f6","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-11-09T08:13:01Z","title_canon_sha256":"9d8552cb0e4bc2bb7dbb3d06a5e2a5ef1ad41fa106bd234b9b4cf8c860c93167"},"schema_version":"1.0","source":{"id":"2311.05193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.05193","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"arxiv_version","alias_value":"2311.05193v1","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.05193","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"pith_short_12","alias_value":"72NTMBC46N4O","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"pith_short_16","alias_value":"72NTMBC46N4OPZ3K","created_at":"2026-07-05T07:10:55Z"},{"alias_kind":"pith_short_8","alias_value":"72NTMBC4","created_at":"2026-07-05T07:10:55Z"}],"graph_snapshots":[{"event_id":"sha256:f9998fff26b9ddd8ccd62ad82f0e30fc21ce404becc3ddf15c54370201719e7b","target":"graph","created_at":"2026-07-05T07:10:55Z","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/2311.05193/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we mainly study the turbulence of Lagrangian flow advected by stochastic 2D Navier-Stokes equations. It is proved that this system has observable full-horseshoes. The observable full-horseshoe means that it is a kind of chaotic structure and occurs on any two disjoint non-empty closed balls.","authors_text":"Jianhua Zhang, Wen Huang","cross_cats":["math-ph","math.AP","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-11-09T08:13:01Z","title":"Observable full-horseshoes for Lagrangian flows advected by stochastic 2D Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.05193","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:cbeb634b7b6927085a7e2307d4143b107da45b7ff107c0bb809260e09993e5b3","target":"record","created_at":"2026-07-05T07:10:55Z","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":"584be00447a23efe994de94915b3d780fb75c831ae766f5a8c7c2c73193f18f6","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-11-09T08:13:01Z","title_canon_sha256":"9d8552cb0e4bc2bb7dbb3d06a5e2a5ef1ad41fa106bd234b9b4cf8c860c93167"},"schema_version":"1.0","source":{"id":"2311.05193","kind":"arxiv","version":1}},"canonical_sha256":"fe9b36045cf378e7e76a67ef68446385e56d56078f3a0b0ddedf43dce6f59e86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe9b36045cf378e7e76a67ef68446385e56d56078f3a0b0ddedf43dce6f59e86","first_computed_at":"2026-07-05T07:10:55.905774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:10:55.905774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RDioY6TUhTO0g2J2Z/dMmKRhjaC6BJ6ZMimXu1e1HaMmkNrJJ5qrkthZAlBak+Dm4O2lur6rXWJfrB+TyXkjBg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:10:55.906299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.05193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbeb634b7b6927085a7e2307d4143b107da45b7ff107c0bb809260e09993e5b3","sha256:f9998fff26b9ddd8ccd62ad82f0e30fc21ce404becc3ddf15c54370201719e7b"],"state_sha256":"7adceeed08c5eba858aa39477578be7f8149f6dd666c91ef0d543f62dcf573e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9srIDKIv5UR+vCTHw4KVl7oQPGtF1lhvMiBDwvQpy/e2OL3Tb7H8qYGMq7GUjaPwrECM/mpRp2mt6pmAvpAVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T02:13:49.520489Z","bundle_sha256":"655213cb2f51464ba5098543a7b4fcc2c502c13ba44b183a5eff4bc50bd9d12f"}}