{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2CQLAHNHIAMC45457TQAFF5BWT","short_pith_number":"pith:2CQLAHNH","schema_version":"1.0","canonical_sha256":"d0a0b01da740182e779dfce00297a1b4c4dd2fe4c8ddef346b8f355499a76892","source":{"kind":"arxiv","id":"1506.03060","version":3},"attestation_state":"computed","paper":{"title":"High-low frequency slaving and regularity issues in the 3D Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"J. D. Gibbon","submitted_at":"2015-06-09T19:40:58Z","abstract_excerpt":"The old idea that an infinite dimensional dynamical system may have its high modes or frequencies slaved to low modes or frequencies is re-visited in the context of the $3D$ Navier-Stokes equations. A set of dimensionless frequencies $\\{\\tilde{\\Omega}_{m}(t)\\}$ are used which are based on $L^{2m}$-norms of the vorticity. To avoid using derivatives a closure is assumed that suggests that the $\\tilde{\\Omega}_{m}$ ($m>1$) are slaved to $\\tilde{\\Omega}_{1}$ (the global enstrophy) in the form $\\tilde{\\Omega}_{m} = \\tilde{\\Omega}_{1}\\mathcal{F}_{m}(\\tilde{\\Omega}_{1})$. This is shaped by the constra"},"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":"1506.03060","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-06-09T19:40:58Z","cross_cats_sorted":[],"title_canon_sha256":"d660d692249f4a96f5ddae122d0b90228e127833db87ee74ecbb8e0deb4fc1b9","abstract_canon_sha256":"3b11b274cf518f5bfdded35a241e5e5845d8b749bc548d1a93a3cf032d16316d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:45.997460Z","signature_b64":"L4xwl2d5SLf9HtwZz5PQjIx1vMhdVDXsGqJgIPZMKkW70IZdvHamARmvGaULkvFBbu4MCSad32YN6LX9spWuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0a0b01da740182e779dfce00297a1b4c4dd2fe4c8ddef346b8f355499a76892","last_reissued_at":"2026-05-18T01:27:45.996991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:45.996991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High-low frequency slaving and regularity issues in the 3D Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"J. D. Gibbon","submitted_at":"2015-06-09T19:40:58Z","abstract_excerpt":"The old idea that an infinite dimensional dynamical system may have its high modes or frequencies slaved to low modes or frequencies is re-visited in the context of the $3D$ Navier-Stokes equations. A set of dimensionless frequencies $\\{\\tilde{\\Omega}_{m}(t)\\}$ are used which are based on $L^{2m}$-norms of the vorticity. To avoid using derivatives a closure is assumed that suggests that the $\\tilde{\\Omega}_{m}$ ($m>1$) are slaved to $\\tilde{\\Omega}_{1}$ (the global enstrophy) in the form $\\tilde{\\Omega}_{m} = \\tilde{\\Omega}_{1}\\mathcal{F}_{m}(\\tilde{\\Omega}_{1})$. This is shaped by the constra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03060","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":""},"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":"1506.03060","created_at":"2026-05-18T01:27:45.997065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03060v3","created_at":"2026-05-18T01:27:45.997065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03060","created_at":"2026-05-18T01:27:45.997065+00:00"},{"alias_kind":"pith_short_12","alias_value":"2CQLAHNHIAMC","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2CQLAHNHIAMC4545","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2CQLAHNH","created_at":"2026-05-18T12:28:59.999130+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/2CQLAHNHIAMC45457TQAFF5BWT","json":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT.json","graph_json":"https://pith.science/api/pith-number/2CQLAHNHIAMC45457TQAFF5BWT/graph.json","events_json":"https://pith.science/api/pith-number/2CQLAHNHIAMC45457TQAFF5BWT/events.json","paper":"https://pith.science/paper/2CQLAHNH"},"agent_actions":{"view_html":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT","download_json":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT.json","view_paper":"https://pith.science/paper/2CQLAHNH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03060&json=true","fetch_graph":"https://pith.science/api/pith-number/2CQLAHNHIAMC45457TQAFF5BWT/graph.json","fetch_events":"https://pith.science/api/pith-number/2CQLAHNHIAMC45457TQAFF5BWT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT/action/storage_attestation","attest_author":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT/action/author_attestation","sign_citation":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT/action/citation_signature","submit_replication":"https://pith.science/pith/2CQLAHNHIAMC45457TQAFF5BWT/action/replication_record"}},"created_at":"2026-05-18T01:27:45.997065+00:00","updated_at":"2026-05-18T01:27:45.997065+00:00"}