{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WOOWHBPQFVP26VHC3KDIWOXHZ2","short_pith_number":"pith:WOOWHBPQ","canonical_record":{"source":{"id":"2311.12147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-20T19:58:14Z","cross_cats_sorted":["math.AP","math.MP","math.PR"],"title_canon_sha256":"eebe2a5db4cad8639f72981822d378e1b3ee2a18db95c33384c60e0963c40296","abstract_canon_sha256":"04af7475b965f1614f4f085e36e358faa92a4af01f4e9180dc7384b7ab756300"},"schema_version":"1.0"},"canonical_sha256":"b39d6385f02d5faf54e2da868b3ae7ce8988d97ccafd3c3760f2a4eb67e8415a","source":{"kind":"arxiv","id":"2311.12147","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.12147","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"2311.12147v2","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.12147","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"WOOWHBPQFVP2","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"WOOWHBPQFVP26VHC","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"WOOWHBPQ","created_at":"2026-07-05T08:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WOOWHBPQFVP26VHC3KDIWOXHZ2","target":"record","payload":{"canonical_record":{"source":{"id":"2311.12147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-20T19:58:14Z","cross_cats_sorted":["math.AP","math.MP","math.PR"],"title_canon_sha256":"eebe2a5db4cad8639f72981822d378e1b3ee2a18db95c33384c60e0963c40296","abstract_canon_sha256":"04af7475b965f1614f4f085e36e358faa92a4af01f4e9180dc7384b7ab756300"},"schema_version":"1.0"},"canonical_sha256":"b39d6385f02d5faf54e2da868b3ae7ce8988d97ccafd3c3760f2a4eb67e8415a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:25:50.867995Z","signature_b64":"Joiqf0mLqH0eeObqZZYbk+1qBksPJIzKKxzfpzvon788mYUulvO82ZJnVK5XESgKvnvEpTP2aYP9ot4U+0NoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b39d6385f02d5faf54e2da868b3ae7ce8988d97ccafd3c3760f2a4eb67e8415a","last_reissued_at":"2026-07-05T08:25:50.867518Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:25:50.867518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.12147","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":"2026-07-05T08:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKNcJvNlCBHhx5dqq1vLJQOMOeYvqOoOwTapMf5jb8Oxb9Pa8mRth9QlcmF4nzlwUhHvLuXDC7OiC3lI4GzACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T03:55:02.853645Z"},"content_sha256":"361f717488bc2800b78ecfc9d5303097d2f3b1f83f5d1a8f44a3eb71870a2a94","schema_version":"1.0","event_id":"sha256:361f717488bc2800b78ecfc9d5303097d2f3b1f83f5d1a8f44a3eb71870a2a94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WOOWHBPQFVP26VHC3KDIWOXHZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On anomalous diffusion in the Kraichnan model and correlated-in-time variants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Keefer Rowan","submitted_at":"2023-11-20T19:58:14Z","abstract_excerpt":"We provide a concise PDE-based proof of anomalous diffusion in the Kraichan model -- a stochastic, white-in-time model of passive scalar turbulence. That is, we show an exponential rate of $L^2$ decay in expectation of a passive scalar advected by a certain white-in-time, correlated-in-space, divergence-free Gaussian field, uniform in the initial data and the diffusivity of the passive scalar. Additionally, we provide examples of correlated-in-time versions of the Kraichnan model which fail to exhibit anomalous diffusion despite their (formal) white-in-time limits exhibiting anomalous diffusio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.12147","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.12147/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":"2026-07-05T08:25:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R0OdnbgvgmWcSoAYE5IPIRg+bPWYUBK5nkV7K1DMy9h3UOlVOZwAiVZ8bRPtNDXmC5SWxNQofsLJHzb+L3lvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T03:55:02.854145Z"},"content_sha256":"d014c54e582b6b487c4a1a449b50f031c3a1328b0681cb764c443641f0143c26","schema_version":"1.0","event_id":"sha256:d014c54e582b6b487c4a1a449b50f031c3a1328b0681cb764c443641f0143c26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WOOWHBPQFVP26VHC3KDIWOXHZ2/bundle.json","state_url":"https://pith.science/pith/WOOWHBPQFVP26VHC3KDIWOXHZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WOOWHBPQFVP26VHC3KDIWOXHZ2/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":"2026-08-18T03:55:02Z","links":{"resolver":"https://pith.science/pith/WOOWHBPQFVP26VHC3KDIWOXHZ2","bundle":"https://pith.science/pith/WOOWHBPQFVP26VHC3KDIWOXHZ2/bundle.json","state":"https://pith.science/pith/WOOWHBPQFVP26VHC3KDIWOXHZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WOOWHBPQFVP26VHC3KDIWOXHZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WOOWHBPQFVP26VHC3KDIWOXHZ2","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":"04af7475b965f1614f4f085e36e358faa92a4af01f4e9180dc7384b7ab756300","cross_cats_sorted":["math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-20T19:58:14Z","title_canon_sha256":"eebe2a5db4cad8639f72981822d378e1b3ee2a18db95c33384c60e0963c40296"},"schema_version":"1.0","source":{"id":"2311.12147","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.12147","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"arxiv_version","alias_value":"2311.12147v2","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.12147","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"pith_short_12","alias_value":"WOOWHBPQFVP2","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"WOOWHBPQFVP26VHC","created_at":"2026-07-05T08:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"WOOWHBPQ","created_at":"2026-07-05T08:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:d014c54e582b6b487c4a1a449b50f031c3a1328b0681cb764c443641f0143c26","target":"graph","created_at":"2026-07-05T08:25:50Z","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/2311.12147/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a concise PDE-based proof of anomalous diffusion in the Kraichan model -- a stochastic, white-in-time model of passive scalar turbulence. That is, we show an exponential rate of $L^2$ decay in expectation of a passive scalar advected by a certain white-in-time, correlated-in-space, divergence-free Gaussian field, uniform in the initial data and the diffusivity of the passive scalar. Additionally, we provide examples of correlated-in-time versions of the Kraichnan model which fail to exhibit anomalous diffusion despite their (formal) white-in-time limits exhibiting anomalous diffusio","authors_text":"Keefer Rowan","cross_cats":["math.AP","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-20T19:58:14Z","title":"On anomalous diffusion in the Kraichnan model and correlated-in-time variants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.12147","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":"sha256:361f717488bc2800b78ecfc9d5303097d2f3b1f83f5d1a8f44a3eb71870a2a94","target":"record","created_at":"2026-07-05T08:25:50Z","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":"04af7475b965f1614f4f085e36e358faa92a4af01f4e9180dc7384b7ab756300","cross_cats_sorted":["math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-11-20T19:58:14Z","title_canon_sha256":"eebe2a5db4cad8639f72981822d378e1b3ee2a18db95c33384c60e0963c40296"},"schema_version":"1.0","source":{"id":"2311.12147","kind":"arxiv","version":2}},"canonical_sha256":"b39d6385f02d5faf54e2da868b3ae7ce8988d97ccafd3c3760f2a4eb67e8415a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b39d6385f02d5faf54e2da868b3ae7ce8988d97ccafd3c3760f2a4eb67e8415a","first_computed_at":"2026-07-05T08:25:50.867518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:25:50.867518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Joiqf0mLqH0eeObqZZYbk+1qBksPJIzKKxzfpzvon788mYUulvO82ZJnVK5XESgKvnvEpTP2aYP9ot4U+0NoCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:25:50.867995Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.12147","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:361f717488bc2800b78ecfc9d5303097d2f3b1f83f5d1a8f44a3eb71870a2a94","sha256:d014c54e582b6b487c4a1a449b50f031c3a1328b0681cb764c443641f0143c26"],"state_sha256":"b1e33db5e114f8c4a3cb9d055040ff3996099b6f32cf25668943292d900eb636"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9JeGX13oaUj7xCHm2G1xeFM88w+dNhZOaS7RYngavVw61EftJxZ40LfWAkbVj5QdxlKIPDZoBbTuZQ2VCGWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T03:55:02.858446Z","bundle_sha256":"9b6db25bbc2dea341651d7ff5ded76dd249d73323045e2e7c73916b90d8201cb"}}