{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VUN2YTYFO4RN6Q5GIAYWHM5GM2","short_pith_number":"pith:VUN2YTYF","canonical_record":{"source":{"id":"1908.08946","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-23T16:55:50Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"4e37d1126144f99f3e845085dd4f840f58ad5de48909a4b95f45c98576869e4c","abstract_canon_sha256":"0aaf16d5865406803d28abb0d21085eb8aaec23d230b17d6e9cc373ffa799e15"},"schema_version":"1.0"},"canonical_sha256":"ad1bac4f057722df43a6403163b3a666b17616490d7d83ce6268a8a4f4e30b78","source":{"kind":"arxiv","id":"1908.08946","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08946","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08946v3","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08946","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"VUN2YTYFO4RN","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"VUN2YTYFO4RN6Q5G","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"VUN2YTYF","created_at":"2026-07-05T00:39:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VUN2YTYFO4RN6Q5GIAYWHM5GM2","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08946","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-23T16:55:50Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"4e37d1126144f99f3e845085dd4f840f58ad5de48909a4b95f45c98576869e4c","abstract_canon_sha256":"0aaf16d5865406803d28abb0d21085eb8aaec23d230b17d6e9cc373ffa799e15"},"schema_version":"1.0"},"canonical_sha256":"ad1bac4f057722df43a6403163b3a666b17616490d7d83ce6268a8a4f4e30b78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:39:13.491899Z","signature_b64":"b9b8a+P1Xefjza14tsqiWA/ctPy2QHJAnqBR24Vc1HoqUTThXuHgauYuo41abh/PdNTACFZW9vX6VnXuyDmbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad1bac4f057722df43a6403163b3a666b17616490d7d83ce6268a8a4f4e30b78","last_reissued_at":"2026-07-05T00:39:13.491395Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:39:13.491395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08946","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5FYFTiwAZ/5aGS3XucjhAzRIDsH/hKvl9le7VAovSL+yC+y0sVPPZPAq/9gVg/5RFMtsp22KkAB3axBLBxXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:08:45.216393Z"},"content_sha256":"ada798e9b6a6056392d1590b8f45bcf5d3d82e0162671f72f69b9d36a14cf643","schema_version":"1.0","event_id":"sha256:ada798e9b6a6056392d1590b8f45bcf5d3d82e0162671f72f69b9d36a14cf643"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VUN2YTYFO4RN6Q5GIAYWHM5GM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"von K\\'arm\\'an--Howarth and Corrsin equations closures through Liouville theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.ao-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Nicola de Divitiis","submitted_at":"2019-08-23T16:55:50Z","abstract_excerpt":"In this communication, the closure formulas of von K\\'arm\\'an--Howarth and Corrsin equations are obtained through the Liouville theorem and the hypothesis of homogeneous isotropic incompressible turbulence. Such closures, based on the concept that, in fully developed turbulence, contiguous fluid particles trajectories continuously diverge, are of non--diffusive nature, and express a correlations spatial propagation phenomenon between the several scales which occurs with a propagation speed depending on length scale and velocity standard deviation. These closure formulas coincide with those jus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08946","kind":"arxiv","version":3},"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/1908.08946/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":"2026-07-05T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3jwekknK0XQmcxAYqFlJaeOEVb66jk8zBSJaruBc3QB845F8OAr8cfC2l+G9k315234aMltAKbjFRU5AJHjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:08:45.216916Z"},"content_sha256":"d3f5a9802da7a6999fd9b1494c23b01b0cfa83ee3fde3a90b9bc0865cdad1ffd","schema_version":"1.0","event_id":"sha256:d3f5a9802da7a6999fd9b1494c23b01b0cfa83ee3fde3a90b9bc0865cdad1ffd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VUN2YTYFO4RN6Q5GIAYWHM5GM2/bundle.json","state_url":"https://pith.science/pith/VUN2YTYFO4RN6Q5GIAYWHM5GM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VUN2YTYFO4RN6Q5GIAYWHM5GM2/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":"2026-08-16T13:08:45Z","links":{"resolver":"https://pith.science/pith/VUN2YTYFO4RN6Q5GIAYWHM5GM2","bundle":"https://pith.science/pith/VUN2YTYFO4RN6Q5GIAYWHM5GM2/bundle.json","state":"https://pith.science/pith/VUN2YTYFO4RN6Q5GIAYWHM5GM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VUN2YTYFO4RN6Q5GIAYWHM5GM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VUN2YTYFO4RN6Q5GIAYWHM5GM2","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":"0aaf16d5865406803d28abb0d21085eb8aaec23d230b17d6e9cc373ffa799e15","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-23T16:55:50Z","title_canon_sha256":"4e37d1126144f99f3e845085dd4f840f58ad5de48909a4b95f45c98576869e4c"},"schema_version":"1.0","source":{"id":"1908.08946","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08946","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08946v3","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08946","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"VUN2YTYFO4RN","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"VUN2YTYFO4RN6Q5G","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"VUN2YTYF","created_at":"2026-07-05T00:39:13Z"}],"graph_snapshots":[{"event_id":"sha256:d3f5a9802da7a6999fd9b1494c23b01b0cfa83ee3fde3a90b9bc0865cdad1ffd","target":"graph","created_at":"2026-07-05T00:39:13Z","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/1908.08946/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this communication, the closure formulas of von K\\'arm\\'an--Howarth and Corrsin equations are obtained through the Liouville theorem and the hypothesis of homogeneous isotropic incompressible turbulence. Such closures, based on the concept that, in fully developed turbulence, contiguous fluid particles trajectories continuously diverge, are of non--diffusive nature, and express a correlations spatial propagation phenomenon between the several scales which occurs with a propagation speed depending on length scale and velocity standard deviation. These closure formulas coincide with those jus","authors_text":"Nicola de Divitiis","cross_cats":["physics.ao-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-23T16:55:50Z","title":"von K\\'arm\\'an--Howarth and Corrsin equations closures through Liouville theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08946","kind":"arxiv","version":3},"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:ada798e9b6a6056392d1590b8f45bcf5d3d82e0162671f72f69b9d36a14cf643","target":"record","created_at":"2026-07-05T00:39:13Z","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":"0aaf16d5865406803d28abb0d21085eb8aaec23d230b17d6e9cc373ffa799e15","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-23T16:55:50Z","title_canon_sha256":"4e37d1126144f99f3e845085dd4f840f58ad5de48909a4b95f45c98576869e4c"},"schema_version":"1.0","source":{"id":"1908.08946","kind":"arxiv","version":3}},"canonical_sha256":"ad1bac4f057722df43a6403163b3a666b17616490d7d83ce6268a8a4f4e30b78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad1bac4f057722df43a6403163b3a666b17616490d7d83ce6268a8a4f4e30b78","first_computed_at":"2026-07-05T00:39:13.491395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:39:13.491395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b9b8a+P1Xefjza14tsqiWA/ctPy2QHJAnqBR24Vc1HoqUTThXuHgauYuo41abh/PdNTACFZW9vX6VnXuyDmbCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:39:13.491899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08946","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ada798e9b6a6056392d1590b8f45bcf5d3d82e0162671f72f69b9d36a14cf643","sha256:d3f5a9802da7a6999fd9b1494c23b01b0cfa83ee3fde3a90b9bc0865cdad1ffd"],"state_sha256":"646b18d18870ccdaa7fb988c5cb2ff03baacc6f31968807f98178df04ba142d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8aBaQcuv8ddc15P/qplL5Srzv3dtZOK1CvrRs4SLn/x0W+bfAX/My4OL1UHvo2UxG0NIyUZcdXHs1zYt9ahDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:08:45.220704Z","bundle_sha256":"9cd59b94124555650441ad07987105c82bea00342cb2261cab624e4d624d7862"}}