{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GZUWHJG2YSD4OWF5IAXDKPRUSA","short_pith_number":"pith:GZUWHJG2","schema_version":"1.0","canonical_sha256":"366963a4dac487c758bd402e353e34903cbb13f1840819e1f4e5421e4ac50adb","source":{"kind":"arxiv","id":"1803.11518","version":2},"attestation_state":"computed","paper":{"title":"Weak and strong solutions of the $3D$ Navier-Stokes equations and their relation to a chessboard of convergent inverse length scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"nlin.CD","authors_text":"John D. Gibbon","submitted_at":"2018-03-30T15:38:18Z","abstract_excerpt":"Using the scale invariance of the Navier-Stokes equations to define appropriate space-and-time-averaged inverse length scales associated with weak solutions of the $3D$ Navier-Stokes equations, an infinite `chessboard' of estimates for these inverse length scales is displayed in terms of labels $(n,\\,m)$ corresponding to $n$ derivatives of the velocity field in $L^{2m}$. The $(1,\\,1)$ position corresponds to the inverse Kolmogorov length $Re^{3/4}$. These estimates ultimately converge to a finite limit, $Re^3$, as $n,\\,m\\to \\infty$, although this limit is too large to lie within the physical v"},"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":"1803.11518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2018-03-30T15:38:18Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"76484db42526a9a92c210aaa84a17587cc117f05fadd6ba0b1e0912d01e7f1b9","abstract_canon_sha256":"c01516563e96a9b1edfc7a7aca8231eca644c7e7dbb5e59b8c7fb982720aa498"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:15.149114Z","signature_b64":"m/K/8652rjHLSW7zdepgX96XEge6TPTkHdh9GnIURTbxUv+CVf50noy/kJD21lJmwkSlr3U7KEGVe8q96iiHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"366963a4dac487c758bd402e353e34903cbb13f1840819e1f4e5421e4ac50adb","last_reissued_at":"2026-05-18T00:09:15.148396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:15.148396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak and strong solutions of the $3D$ Navier-Stokes equations and their relation to a chessboard of convergent inverse length scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"nlin.CD","authors_text":"John D. Gibbon","submitted_at":"2018-03-30T15:38:18Z","abstract_excerpt":"Using the scale invariance of the Navier-Stokes equations to define appropriate space-and-time-averaged inverse length scales associated with weak solutions of the $3D$ Navier-Stokes equations, an infinite `chessboard' of estimates for these inverse length scales is displayed in terms of labels $(n,\\,m)$ corresponding to $n$ derivatives of the velocity field in $L^{2m}$. The $(1,\\,1)$ position corresponds to the inverse Kolmogorov length $Re^{3/4}$. These estimates ultimately converge to a finite limit, $Re^3$, as $n,\\,m\\to \\infty$, although this limit is too large to lie within the physical v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11518","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":"1803.11518","created_at":"2026-05-18T00:09:15.148512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.11518v2","created_at":"2026-05-18T00:09:15.148512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.11518","created_at":"2026-05-18T00:09:15.148512+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZUWHJG2YSD4","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZUWHJG2YSD4OWF5","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZUWHJG2","created_at":"2026-05-18T12:32:25.280505+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/GZUWHJG2YSD4OWF5IAXDKPRUSA","json":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA.json","graph_json":"https://pith.science/api/pith-number/GZUWHJG2YSD4OWF5IAXDKPRUSA/graph.json","events_json":"https://pith.science/api/pith-number/GZUWHJG2YSD4OWF5IAXDKPRUSA/events.json","paper":"https://pith.science/paper/GZUWHJG2"},"agent_actions":{"view_html":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA","download_json":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA.json","view_paper":"https://pith.science/paper/GZUWHJG2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.11518&json=true","fetch_graph":"https://pith.science/api/pith-number/GZUWHJG2YSD4OWF5IAXDKPRUSA/graph.json","fetch_events":"https://pith.science/api/pith-number/GZUWHJG2YSD4OWF5IAXDKPRUSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA/action/storage_attestation","attest_author":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA/action/author_attestation","sign_citation":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA/action/citation_signature","submit_replication":"https://pith.science/pith/GZUWHJG2YSD4OWF5IAXDKPRUSA/action/replication_record"}},"created_at":"2026-05-18T00:09:15.148512+00:00","updated_at":"2026-05-18T00:09:15.148512+00:00"}