{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GJFAHHODBVSM3YVGHSF3ZZ74RH","short_pith_number":"pith:GJFAHHOD","schema_version":"1.0","canonical_sha256":"324a039dc30d64cde2a63c8bbce7fc89ebb82fd922c8976aae7f9774be545833","source":{"kind":"arxiv","id":"1908.01422","version":1},"attestation_state":"computed","paper":{"title":"Analytic and Numerical Study of Navier-Stokes Loop Equation in Turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"hep-th","authors_text":"Alexander Migdal","submitted_at":"2019-08-04T23:17:55Z","abstract_excerpt":"We developed analytic approach to the non-planar loop equation, which we derived in previous papers \\cite{M19a},\\cite{M19b},\\cite{M19c}. We found quadratic integral equation for the vorticity distribution $\\Omega(r)$ we introduced on a minimal surface. There are no corrections to the minimal surface though: it is still defined by mean external curvature equal to zero, for arbitrary non-planar loop. We also analyzed the loop equations with viscosity term in Navier-Stokes equations. This term creates boundary condition for $\\Omega(r\\in C)$. The leading viscosity correction term mixes the moments"},"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":"1908.01422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-08-04T23:17:55Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"db0479a59cf3dd39b9a9edf61d19159238e20615701360c7899278294ce97976","abstract_canon_sha256":"ec091a05ecb5ecaac2b6e52b2d04f7c4dfbb1904229e48282edf32b1bb04154f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:30.290630Z","signature_b64":"mF/vCMH4eav0HSwAce+scBuTH0n/qvAZRuHRg14+q4o33r7lpZT6UZ9swzKE0ToxLlwXUCJdTE44FvF7GhLNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"324a039dc30d64cde2a63c8bbce7fc89ebb82fd922c8976aae7f9774be545833","last_reissued_at":"2026-07-04T23:51:30.290154Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:30.290154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic and Numerical Study of Navier-Stokes Loop Equation in Turbulence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"hep-th","authors_text":"Alexander Migdal","submitted_at":"2019-08-04T23:17:55Z","abstract_excerpt":"We developed analytic approach to the non-planar loop equation, which we derived in previous papers \\cite{M19a},\\cite{M19b},\\cite{M19c}. We found quadratic integral equation for the vorticity distribution $\\Omega(r)$ we introduced on a minimal surface. There are no corrections to the minimal surface though: it is still defined by mean external curvature equal to zero, for arbitrary non-planar loop. We also analyzed the loop equations with viscosity term in Navier-Stokes equations. This term creates boundary condition for $\\Omega(r\\in C)$. The leading viscosity correction term mixes the moments"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01422","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01422/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":"1908.01422","created_at":"2026-07-04T23:51:30.290213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.01422v1","created_at":"2026-07-04T23:51:30.290213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01422","created_at":"2026-07-04T23:51:30.290213+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJFAHHODBVSM","created_at":"2026-07-04T23:51:30.290213+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJFAHHODBVSM3YVG","created_at":"2026-07-04T23:51:30.290213+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJFAHHOD","created_at":"2026-07-04T23:51:30.290213+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/GJFAHHODBVSM3YVGHSF3ZZ74RH","json":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH.json","graph_json":"https://pith.science/api/pith-number/GJFAHHODBVSM3YVGHSF3ZZ74RH/graph.json","events_json":"https://pith.science/api/pith-number/GJFAHHODBVSM3YVGHSF3ZZ74RH/events.json","paper":"https://pith.science/paper/GJFAHHOD"},"agent_actions":{"view_html":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH","download_json":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH.json","view_paper":"https://pith.science/paper/GJFAHHOD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.01422&json=true","fetch_graph":"https://pith.science/api/pith-number/GJFAHHODBVSM3YVGHSF3ZZ74RH/graph.json","fetch_events":"https://pith.science/api/pith-number/GJFAHHODBVSM3YVGHSF3ZZ74RH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/action/storage_attestation","attest_author":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/action/author_attestation","sign_citation":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/action/citation_signature","submit_replication":"https://pith.science/pith/GJFAHHODBVSM3YVGHSF3ZZ74RH/action/replication_record"}},"created_at":"2026-07-04T23:51:30.290213+00:00","updated_at":"2026-07-04T23:51:30.290213+00:00"}