{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:6CFKWQ5YYC5LIBE4EEVXFYLPR6","short_pith_number":"pith:6CFKWQ5Y","schema_version":"1.0","canonical_sha256":"f08aab43b8c0bab4049c212b72e16f8fb4379097fc5ff1a6469f53e558c249b5","source":{"kind":"arxiv","id":"chao-dyn/9808001","version":1},"attestation_state":"computed","paper":{"title":"Dissipation statistics of a passive scalar in a multidimensional smooth flow","license":"","headline":"","cross_cats":["cond-mat.stat-mech","nlin.CD"],"primary_cat":"chao-dyn","authors_text":"A. Gamba, I. V. Kolokolov","submitted_at":"1998-07-31T17:43:26Z","abstract_excerpt":"We compute analytically the probability distribution function ${\\cal P}(\\epsilon)$ of the dissipation field $\\epsilon =(\\nabla \\theta)^{2}$ of a passive scalar $\\theta$ advected by a $d$-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime). The tail of the distribution is a stretched exponential: for $\\epsilon \\to \\infty$, $\\ln {\\cal P}(\\epsilon)\\sim -(d^2\\epsilon)^{1/3}$."},"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":"chao-dyn/9808001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1998-07-31T17:43:26Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.CD"],"title_canon_sha256":"aa125c66d0ad6d5f794281388e44f05c22a11b60e7f427063c3ff7c2ff8fe6ef","abstract_canon_sha256":"2acaa7416ad15cd1d6fb00dbd626eb960f77048b2752e3f3fbcfed1d59d3d1d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:11.595063Z","signature_b64":"jnDfa8WKDvYNT4gC/feGzA78mDVveW4rbOnBetKNbCCg0NPowebHOQSbq/iuUoanw1OGZ4MAmnw6xk3MRdL8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f08aab43b8c0bab4049c212b72e16f8fb4379097fc5ff1a6469f53e558c249b5","last_reissued_at":"2026-05-18T01:40:11.594389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:11.594389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dissipation statistics of a passive scalar in a multidimensional smooth flow","license":"","headline":"","cross_cats":["cond-mat.stat-mech","nlin.CD"],"primary_cat":"chao-dyn","authors_text":"A. Gamba, I. V. Kolokolov","submitted_at":"1998-07-31T17:43:26Z","abstract_excerpt":"We compute analytically the probability distribution function ${\\cal P}(\\epsilon)$ of the dissipation field $\\epsilon =(\\nabla \\theta)^{2}$ of a passive scalar $\\theta$ advected by a $d$-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime). The tail of the distribution is a stretched exponential: for $\\epsilon \\to \\infty$, $\\ln {\\cal P}(\\epsilon)\\sim -(d^2\\epsilon)^{1/3}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9808001","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":""},"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":"chao-dyn/9808001","created_at":"2026-05-18T01:40:11.594496+00:00"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9808001v1","created_at":"2026-05-18T01:40:11.594496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9808001","created_at":"2026-05-18T01:40:11.594496+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CFKWQ5YYC5L","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CFKWQ5YYC5LIBE4","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CFKWQ5Y","created_at":"2026-05-18T12:25:49.038998+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/6CFKWQ5YYC5LIBE4EEVXFYLPR6","json":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6.json","graph_json":"https://pith.science/api/pith-number/6CFKWQ5YYC5LIBE4EEVXFYLPR6/graph.json","events_json":"https://pith.science/api/pith-number/6CFKWQ5YYC5LIBE4EEVXFYLPR6/events.json","paper":"https://pith.science/paper/6CFKWQ5Y"},"agent_actions":{"view_html":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6","download_json":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6.json","view_paper":"https://pith.science/paper/6CFKWQ5Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=chao-dyn/9808001&json=true","fetch_graph":"https://pith.science/api/pith-number/6CFKWQ5YYC5LIBE4EEVXFYLPR6/graph.json","fetch_events":"https://pith.science/api/pith-number/6CFKWQ5YYC5LIBE4EEVXFYLPR6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6/action/storage_attestation","attest_author":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6/action/author_attestation","sign_citation":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6/action/citation_signature","submit_replication":"https://pith.science/pith/6CFKWQ5YYC5LIBE4EEVXFYLPR6/action/replication_record"}},"created_at":"2026-05-18T01:40:11.594496+00:00","updated_at":"2026-05-18T01:40:11.594496+00:00"}