{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:I22Z2P5M4NVR6QCJD4BUO5BI6F","short_pith_number":"pith:I22Z2P5M","schema_version":"1.0","canonical_sha256":"46b59d3face36b1f40491f03477428f1670f37acf0933522e515559ac4a81bed","source":{"kind":"arxiv","id":"1101.2193","version":2},"attestation_state":"computed","paper":{"title":"Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"R. Dascaliuc, Z. Grujic","submitted_at":"2011-01-11T20:16:03Z","abstract_excerpt":"Rigorous estimates for the total - (kinetic) energy plus pressure - flux in R^3 are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a condition - involving Taylor length scale and the size of the domain - sufficient for existence of the inertial range and the energy cascade in decaying turbulence (zero driving force, non-increasing global energy). Several manifestations of the locality of the flux under this condition are obtained. All the scales involved are actual physical scales in R^3 and no regularity or homogeneity/scaling assumptions are mad"},"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":"1101.2193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-11T20:16:03Z","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"title_canon_sha256":"14d04147adb6ddae4126cc0a18f78e1782d16879eda6185f777eb5166a2db0c0","abstract_canon_sha256":"65386a3ba3d387d2db1ebc64e8dcc3a65e565fe394bfd7dcbbe85c6b21d27d7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:42.897846Z","signature_b64":"QgwJ2ACqVb4QiYfMymI85+p5Py+Jl1l9Dva3l/PS5guLcFkqYqsmhZW146VNNyxS7DCYoKKOXTsgGn2vP3kuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b59d3face36b1f40491f03477428f1670f37acf0933522e515559ac4a81bed","last_reissued_at":"2026-05-18T02:03:42.897420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:42.897420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy cascades and flux locality in physical scales of the 3D Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"R. Dascaliuc, Z. Grujic","submitted_at":"2011-01-11T20:16:03Z","abstract_excerpt":"Rigorous estimates for the total - (kinetic) energy plus pressure - flux in R^3 are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a condition - involving Taylor length scale and the size of the domain - sufficient for existence of the inertial range and the energy cascade in decaying turbulence (zero driving force, non-increasing global energy). Several manifestations of the locality of the flux under this condition are obtained. All the scales involved are actual physical scales in R^3 and no regularity or homogeneity/scaling assumptions are mad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2193","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":""},"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":"1101.2193","created_at":"2026-05-18T02:03:42.897484+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.2193v2","created_at":"2026-05-18T02:03:42.897484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2193","created_at":"2026-05-18T02:03:42.897484+00:00"},{"alias_kind":"pith_short_12","alias_value":"I22Z2P5M4NVR","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"I22Z2P5M4NVR6QCJ","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"I22Z2P5M","created_at":"2026-05-18T12:26:30.835961+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/I22Z2P5M4NVR6QCJD4BUO5BI6F","json":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F.json","graph_json":"https://pith.science/api/pith-number/I22Z2P5M4NVR6QCJD4BUO5BI6F/graph.json","events_json":"https://pith.science/api/pith-number/I22Z2P5M4NVR6QCJD4BUO5BI6F/events.json","paper":"https://pith.science/paper/I22Z2P5M"},"agent_actions":{"view_html":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F","download_json":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F.json","view_paper":"https://pith.science/paper/I22Z2P5M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.2193&json=true","fetch_graph":"https://pith.science/api/pith-number/I22Z2P5M4NVR6QCJD4BUO5BI6F/graph.json","fetch_events":"https://pith.science/api/pith-number/I22Z2P5M4NVR6QCJD4BUO5BI6F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F/action/storage_attestation","attest_author":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F/action/author_attestation","sign_citation":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F/action/citation_signature","submit_replication":"https://pith.science/pith/I22Z2P5M4NVR6QCJD4BUO5BI6F/action/replication_record"}},"created_at":"2026-05-18T02:03:42.897484+00:00","updated_at":"2026-05-18T02:03:42.897484+00:00"}