{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AJNWQ4TW53P4P3RGAH3BNULJMO","short_pith_number":"pith:AJNWQ4TW","canonical_record":{"source":{"id":"1911.09995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-22T12:23:10Z","cross_cats_sorted":["math.PR","physics.flu-dyn"],"title_canon_sha256":"3eddd6450239b8afe01e9b7e34f67d3f0bd09bb23365eeee7d6b763a14434a9d","abstract_canon_sha256":"a066f56f9a0d253b7e849276d48acc82483a669a1bdffc31073436bf3c257c91"},"schema_version":"1.0"},"canonical_sha256":"025b687276eedfc7ee2601f616d16963b352eb13ccdd82f2d0741c169acc6063","source":{"kind":"arxiv","id":"1911.09995","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.09995","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"arxiv_version","alias_value":"1911.09995v1","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.09995","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"pith_short_12","alias_value":"AJNWQ4TW53P4","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"pith_short_16","alias_value":"AJNWQ4TW53P4P3RG","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"pith_short_8","alias_value":"AJNWQ4TW","created_at":"2026-07-05T00:21:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AJNWQ4TW53P4P3RGAH3BNULJMO","target":"record","payload":{"canonical_record":{"source":{"id":"1911.09995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-22T12:23:10Z","cross_cats_sorted":["math.PR","physics.flu-dyn"],"title_canon_sha256":"3eddd6450239b8afe01e9b7e34f67d3f0bd09bb23365eeee7d6b763a14434a9d","abstract_canon_sha256":"a066f56f9a0d253b7e849276d48acc82483a669a1bdffc31073436bf3c257c91"},"schema_version":"1.0"},"canonical_sha256":"025b687276eedfc7ee2601f616d16963b352eb13ccdd82f2d0741c169acc6063","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:21:19.562810Z","signature_b64":"f5FpmBxRDa2mT9RfJCCb3QCcGfAQmqKfl55ALD2QervFv7XUrrzG67w8XUHTq9TLUb05xQlb4VK3oxx59Sc7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"025b687276eedfc7ee2601f616d16963b352eb13ccdd82f2d0741c169acc6063","last_reissued_at":"2026-07-05T00:21:19.562468Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:21:19.562468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.09995","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":"2026-07-05T00:21:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZVVl44XEoxI4JVCW4OCvGBJ7DGp3hfTSrWiYpASrw1vV8KLCt1RS4S1NFivhH/GltyA1d8PlaCH2ItqeUNMEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:54:50.470633Z"},"content_sha256":"b17b51e03a44fca54ee2623d830ab82ad60770e588719a408397bce16c426531","schema_version":"1.0","event_id":"sha256:b17b51e03a44fca54ee2623d830ab82ad60770e588719a408397bce16c426531"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AJNWQ4TW53P4P3RGAH3BNULJMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A stochastic approach to enhanced diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Michele Coti Zelati, Theodore D. Drivas","submitted_at":"2019-11-22T12:23:10Z","abstract_excerpt":"We provide examples of initial data which saturate the enhanced diffusion rates proved for general shear flows which are H\\\"{o}lder regular or Lipschitz continuous with critical points, and for regular circular flows, establishing the sharpness of those results. Our proof makes use of a probabilistic interpretation of the dissipation of solutions to the advection diffusion equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09995","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/1911.09995/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":"2026-07-05T00:21:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i32bLnXOFtxt9tOf/8f0OtqG8HIxUNSZ5AWjuGgaz7e5+qOgZG03j4NGGkj7NqZ2SIFIpsEa5fkKi4vYzK8PDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:54:50.471148Z"},"content_sha256":"a3d3713d796a73c62e59ff766c975516d36546d099f48896bab0ae0c71ea09c6","schema_version":"1.0","event_id":"sha256:a3d3713d796a73c62e59ff766c975516d36546d099f48896bab0ae0c71ea09c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJNWQ4TW53P4P3RGAH3BNULJMO/bundle.json","state_url":"https://pith.science/pith/AJNWQ4TW53P4P3RGAH3BNULJMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJNWQ4TW53P4P3RGAH3BNULJMO/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":"2026-08-09T06:54:50Z","links":{"resolver":"https://pith.science/pith/AJNWQ4TW53P4P3RGAH3BNULJMO","bundle":"https://pith.science/pith/AJNWQ4TW53P4P3RGAH3BNULJMO/bundle.json","state":"https://pith.science/pith/AJNWQ4TW53P4P3RGAH3BNULJMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJNWQ4TW53P4P3RGAH3BNULJMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AJNWQ4TW53P4P3RGAH3BNULJMO","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":"a066f56f9a0d253b7e849276d48acc82483a669a1bdffc31073436bf3c257c91","cross_cats_sorted":["math.PR","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-22T12:23:10Z","title_canon_sha256":"3eddd6450239b8afe01e9b7e34f67d3f0bd09bb23365eeee7d6b763a14434a9d"},"schema_version":"1.0","source":{"id":"1911.09995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.09995","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"arxiv_version","alias_value":"1911.09995v1","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.09995","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"pith_short_12","alias_value":"AJNWQ4TW53P4","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"pith_short_16","alias_value":"AJNWQ4TW53P4P3RG","created_at":"2026-07-05T00:21:19Z"},{"alias_kind":"pith_short_8","alias_value":"AJNWQ4TW","created_at":"2026-07-05T00:21:19Z"}],"graph_snapshots":[{"event_id":"sha256:a3d3713d796a73c62e59ff766c975516d36546d099f48896bab0ae0c71ea09c6","target":"graph","created_at":"2026-07-05T00:21:19Z","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/1911.09995/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide examples of initial data which saturate the enhanced diffusion rates proved for general shear flows which are H\\\"{o}lder regular or Lipschitz continuous with critical points, and for regular circular flows, establishing the sharpness of those results. Our proof makes use of a probabilistic interpretation of the dissipation of solutions to the advection diffusion equation.","authors_text":"Michele Coti Zelati, Theodore D. Drivas","cross_cats":["math.PR","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-22T12:23:10Z","title":"A stochastic approach to enhanced diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09995","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:b17b51e03a44fca54ee2623d830ab82ad60770e588719a408397bce16c426531","target":"record","created_at":"2026-07-05T00:21:19Z","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":"a066f56f9a0d253b7e849276d48acc82483a669a1bdffc31073436bf3c257c91","cross_cats_sorted":["math.PR","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-22T12:23:10Z","title_canon_sha256":"3eddd6450239b8afe01e9b7e34f67d3f0bd09bb23365eeee7d6b763a14434a9d"},"schema_version":"1.0","source":{"id":"1911.09995","kind":"arxiv","version":1}},"canonical_sha256":"025b687276eedfc7ee2601f616d16963b352eb13ccdd82f2d0741c169acc6063","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"025b687276eedfc7ee2601f616d16963b352eb13ccdd82f2d0741c169acc6063","first_computed_at":"2026-07-05T00:21:19.562468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:21:19.562468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f5FpmBxRDa2mT9RfJCCb3QCcGfAQmqKfl55ALD2QervFv7XUrrzG67w8XUHTq9TLUb05xQlb4VK3oxx59Sc7Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T00:21:19.562810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.09995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b17b51e03a44fca54ee2623d830ab82ad60770e588719a408397bce16c426531","sha256:a3d3713d796a73c62e59ff766c975516d36546d099f48896bab0ae0c71ea09c6"],"state_sha256":"1f51236accafff3b9980c6981d3051d81289ec62050372441230798017dfe8a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RY1j2OonBksFMtZF2netOrWPc98wrGjAwTBJgEf0AXFeL29Rtivq+kyws4T1AVCOs2CVOQqxmrZV3of0x0FqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:54:50.475503Z","bundle_sha256":"533cf042a848704d8ab0f2062d22d1141f3034d9ef78ea466e720f39cbf1a125"}}