{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ELSRXNT4RNKCO5HLWZRU3Y5TP3","short_pith_number":"pith:ELSRXNT4","schema_version":"1.0","canonical_sha256":"22e51bb67c8b542774ebb6634de3b37ef0465ea85113d6d14f9fa9cf287eccc7","source":{"kind":"arxiv","id":"2407.16668","version":2},"attestation_state":"computed","paper":{"title":"Anomalous Regularization in Kraichnan's Passive Scalar Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Francesco Grotto, Lucio Galeati, Mario Maurelli","submitted_at":"2024-07-23T17:35:25Z","abstract_excerpt":"We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and H\\\"older regular in space (rough Kraichnan's model), a well established synthetic model of passive scalar turbulence. By studying the evolution of negative Sobolev norms, we show an anomalous regularization effect induced by the dynamics: distributional initial conditions immediately become functions of positive Sobolev regularity."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2407.16668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-23T17:35:25Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a6c46b49030a33d7ee9d06e38bbb1d595fa38b834c7005ee06968b1435b3fa5e","abstract_canon_sha256":"284c1596cb3b13d3953b61a5e1e43ef2be32bf5d4643f1de75a7d77e42a43ff7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:12.963258Z","signature_b64":"ITIXRradGMax4Vpo3pAlDFCw6NPhyld9PKjuqDzkebnUOHPIQ5kFWAue/QG0xcIg1KEbdX64tFH5ONp36A/vCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e51bb67c8b542774ebb6634de3b37ef0465ea85113d6d14f9fa9cf287eccc7","last_reissued_at":"2026-06-23T02:13:12.962596Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:12.962596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anomalous Regularization in Kraichnan's Passive Scalar Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Francesco Grotto, Lucio Galeati, Mario Maurelli","submitted_at":"2024-07-23T17:35:25Z","abstract_excerpt":"We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and H\\\"older regular in space (rough Kraichnan's model), a well established synthetic model of passive scalar turbulence. By studying the evolution of negative Sobolev norms, we show an anomalous regularization effect induced by the dynamics: distributional initial conditions immediately become functions of positive Sobolev regularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16668","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/2407.16668/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2407.16668","created_at":"2026-06-23T02:13:12.962669+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.16668v2","created_at":"2026-06-23T02:13:12.962669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16668","created_at":"2026-06-23T02:13:12.962669+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELSRXNT4RNKC","created_at":"2026-06-23T02:13:12.962669+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELSRXNT4RNKCO5HL","created_at":"2026-06-23T02:13:12.962669+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELSRXNT4","created_at":"2026-06-23T02:13:12.962669+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3","json":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3.json","graph_json":"https://pith.science/api/pith-number/ELSRXNT4RNKCO5HLWZRU3Y5TP3/graph.json","events_json":"https://pith.science/api/pith-number/ELSRXNT4RNKCO5HLWZRU3Y5TP3/events.json","paper":"https://pith.science/paper/ELSRXNT4"},"agent_actions":{"view_html":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3","download_json":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3.json","view_paper":"https://pith.science/paper/ELSRXNT4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.16668&json=true","fetch_graph":"https://pith.science/api/pith-number/ELSRXNT4RNKCO5HLWZRU3Y5TP3/graph.json","fetch_events":"https://pith.science/api/pith-number/ELSRXNT4RNKCO5HLWZRU3Y5TP3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3/action/storage_attestation","attest_author":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3/action/author_attestation","sign_citation":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3/action/citation_signature","submit_replication":"https://pith.science/pith/ELSRXNT4RNKCO5HLWZRU3Y5TP3/action/replication_record"}},"created_at":"2026-06-23T02:13:12.962669+00:00","updated_at":"2026-06-23T02:13:12.962669+00:00"}