{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VREYSV5H3TPQFG27N764Q66H4M","short_pith_number":"pith:VREYSV5H","canonical_record":{"source":{"id":"2407.10594","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-15T10:16:24Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"ee44584b98dcafa8f02a50bb50bb1982c05683544dda8d3152943ffa2be08844","abstract_canon_sha256":"349b03b0eeb011c03dd48e954a5721ad768db79bf1c60f4c99beb16efead6da3"},"schema_version":"1.0"},"canonical_sha256":"ac498957a7dcdf029b5f6ffdc87bc7e329bce46fdbeb76b5c5e42b58651e777f","source":{"kind":"arxiv","id":"2407.10594","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.10594","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"2407.10594v1","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.10594","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"VREYSV5H3TPQ","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"pith_short_16","alias_value":"VREYSV5H3TPQFG27","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"pith_short_8","alias_value":"VREYSV5H","created_at":"2026-07-05T08:44:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VREYSV5H3TPQFG27N764Q66H4M","target":"record","payload":{"canonical_record":{"source":{"id":"2407.10594","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-15T10:16:24Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"ee44584b98dcafa8f02a50bb50bb1982c05683544dda8d3152943ffa2be08844","abstract_canon_sha256":"349b03b0eeb011c03dd48e954a5721ad768db79bf1c60f4c99beb16efead6da3"},"schema_version":"1.0"},"canonical_sha256":"ac498957a7dcdf029b5f6ffdc87bc7e329bce46fdbeb76b5c5e42b58651e777f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:44:01.608677Z","signature_b64":"ixWZ7D0yGs1yr8j+NFOySScp2oRGT57qJPwAk+J0aGtEyDUok3mEzjVDd1IhtOIbaj5BMnVwGtDmxFiZX8YvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac498957a7dcdf029b5f6ffdc87bc7e329bce46fdbeb76b5c5e42b58651e777f","last_reissued_at":"2026-07-05T08:44:01.608184Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:44:01.608184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.10594","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":"2026-07-05T08:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SO9/MBi9MIJnqjBemKMdMYiVKDvbnBR9UzOArl5VbAPTiPvAe+kGdjM229tqWa14YuN+AmMwhGVN3ZS0O0edBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:43:04.812580Z"},"content_sha256":"5ec98c321b3da996b15c549367f07f9096d52afc55af2c4748e0c2a89c01e1d7","schema_version":"1.0","event_id":"sha256:5ec98c321b3da996b15c549367f07f9096d52afc55af2c4748e0c2a89c01e1d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VREYSV5H3TPQFG27N764Q66H4M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Background Vlasov equations and Young measures for passive scalar and vector advection equations under special stochastic scaling limits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Eliseo Luongo, Federico Butori, Franco Flandoli, Yassine Tahraoui","submitted_at":"2024-07-15T10:16:24Z","abstract_excerpt":"In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly converge to the solutions of deterministic equations with a diffusion term. In the background of these stochastic models, we introduce stochastic Vlasov equations which gives additional information on the fluctuations and oscillations of solutions: we prove convergence to non-trivial Young measures satisfying limit PDEs with suitable diffusion terms. In the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10594","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/2407.10594/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":"2026-07-05T08:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s3/nqHyTlA61EGPYODmni6TI4icbu6U2Bq3prghXabd97EqHX1CYnIdk45LH1I8nHf0bQOVtwx/CksRiubzUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:43:04.813827Z"},"content_sha256":"377db268b22bc2e95e3329d258f9d5dc5a3e90590867bb1d3bf659871c85479e","schema_version":"1.0","event_id":"sha256:377db268b22bc2e95e3329d258f9d5dc5a3e90590867bb1d3bf659871c85479e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VREYSV5H3TPQFG27N764Q66H4M/bundle.json","state_url":"https://pith.science/pith/VREYSV5H3TPQFG27N764Q66H4M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VREYSV5H3TPQFG27N764Q66H4M/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":"2026-08-11T12:43:04Z","links":{"resolver":"https://pith.science/pith/VREYSV5H3TPQFG27N764Q66H4M","bundle":"https://pith.science/pith/VREYSV5H3TPQFG27N764Q66H4M/bundle.json","state":"https://pith.science/pith/VREYSV5H3TPQFG27N764Q66H4M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VREYSV5H3TPQFG27N764Q66H4M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VREYSV5H3TPQFG27N764Q66H4M","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":"349b03b0eeb011c03dd48e954a5721ad768db79bf1c60f4c99beb16efead6da3","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-15T10:16:24Z","title_canon_sha256":"ee44584b98dcafa8f02a50bb50bb1982c05683544dda8d3152943ffa2be08844"},"schema_version":"1.0","source":{"id":"2407.10594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.10594","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"2407.10594v1","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.10594","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"VREYSV5H3TPQ","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"pith_short_16","alias_value":"VREYSV5H3TPQFG27","created_at":"2026-07-05T08:44:01Z"},{"alias_kind":"pith_short_8","alias_value":"VREYSV5H","created_at":"2026-07-05T08:44:01Z"}],"graph_snapshots":[{"event_id":"sha256:377db268b22bc2e95e3329d258f9d5dc5a3e90590867bb1d3bf659871c85479e","target":"graph","created_at":"2026-07-05T08:44:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.10594/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly converge to the solutions of deterministic equations with a diffusion term. In the background of these stochastic models, we introduce stochastic Vlasov equations which gives additional information on the fluctuations and oscillations of solutions: we prove convergence to non-trivial Young measures satisfying limit PDEs with suitable diffusion terms. In the c","authors_text":"Eliseo Luongo, Federico Butori, Franco Flandoli, Yassine Tahraoui","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-15T10:16:24Z","title":"Background Vlasov equations and Young measures for passive scalar and vector advection equations under special stochastic scaling limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10594","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":"sha256:5ec98c321b3da996b15c549367f07f9096d52afc55af2c4748e0c2a89c01e1d7","target":"record","created_at":"2026-07-05T08:44:01Z","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":"349b03b0eeb011c03dd48e954a5721ad768db79bf1c60f4c99beb16efead6da3","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-15T10:16:24Z","title_canon_sha256":"ee44584b98dcafa8f02a50bb50bb1982c05683544dda8d3152943ffa2be08844"},"schema_version":"1.0","source":{"id":"2407.10594","kind":"arxiv","version":1}},"canonical_sha256":"ac498957a7dcdf029b5f6ffdc87bc7e329bce46fdbeb76b5c5e42b58651e777f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac498957a7dcdf029b5f6ffdc87bc7e329bce46fdbeb76b5c5e42b58651e777f","first_computed_at":"2026-07-05T08:44:01.608184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:44:01.608184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ixWZ7D0yGs1yr8j+NFOySScp2oRGT57qJPwAk+J0aGtEyDUok3mEzjVDd1IhtOIbaj5BMnVwGtDmxFiZX8YvDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:44:01.608677Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.10594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ec98c321b3da996b15c549367f07f9096d52afc55af2c4748e0c2a89c01e1d7","sha256:377db268b22bc2e95e3329d258f9d5dc5a3e90590867bb1d3bf659871c85479e"],"state_sha256":"fddde59ecc19a12fdbe0729297de20af8f199b25478528897f203778d7ad07ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YjsqsOKGR9VXxHc92sKvszD6sWkFhK0gmBCeGsfrt69PNRlBY6HYrbkjaQshqe552L81Rwgek9WjIBhn0RWrDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:43:04.820643Z","bundle_sha256":"0c7798c984e4c558dd18e83a22880a974cc3ad73750d2633b20f896d381651e4"}}