{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CSYD6QIRRF3MNAZDX57THZYTJP","short_pith_number":"pith:CSYD6QIR","schema_version":"1.0","canonical_sha256":"14b03f41118976c68323bf7f33e7134bf2d367dc2c6a20bc49bbedd1c77a14e8","source":{"kind":"arxiv","id":"1702.04447","version":5},"attestation_state":"computed","paper":{"title":"On topological fluid mechanics of non-ideal systems and virtual frozen-in dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"physics.flu-dyn","authors_text":"Jian-Zhou Zhu","submitted_at":"2017-02-15T02:46:26Z","abstract_excerpt":"Euler and Navier-Stokes have variant systems with dynamical invariance of helicity and thus (weak) topological equivalence, allowing a strong `frozen-in' (to, or, dually, `Lie-carried' by the \\textit{virtual} velocity $V$) formulation of the vorticity with a flavor of `inverse Helmholtz theorem'. We remark on the non-ideal (statistical) topological fluid mechanics (TFM) for (1) the Constantin-Iyer formulation of Navier-Stokes, (2) our own extension of the Gallavotti-Cohen type dynamical ensembles of modified Navier-Stokes with energy-helicity constraints and (3) the Galerkin truncated Euler, a"},"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":"1702.04447","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2017-02-15T02:46:26Z","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"title_canon_sha256":"de1ac5312c9a50f912f96e5b31a4ce7829691030555d2f579cdf171f3ce41770","abstract_canon_sha256":"1cf62ab8b8e75a6b0560f3c9619dd90e6acc3d109a323457b3a54310c5f4e237"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:59.204504Z","signature_b64":"vI9qarjncOGZfm/PLLn9tIAJN55O1sMxI7HAWF78eFGivvRDwAYoj+TPXpyNjzV50mdy+4Js1PenW27YZOlkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14b03f41118976c68323bf7f33e7134bf2d367dc2c6a20bc49bbedd1c77a14e8","last_reissued_at":"2026-05-18T00:19:59.203998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:59.203998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On topological fluid mechanics of non-ideal systems and virtual frozen-in dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"physics.flu-dyn","authors_text":"Jian-Zhou Zhu","submitted_at":"2017-02-15T02:46:26Z","abstract_excerpt":"Euler and Navier-Stokes have variant systems with dynamical invariance of helicity and thus (weak) topological equivalence, allowing a strong `frozen-in' (to, or, dually, `Lie-carried' by the \\textit{virtual} velocity $V$) formulation of the vorticity with a flavor of `inverse Helmholtz theorem'. We remark on the non-ideal (statistical) topological fluid mechanics (TFM) for (1) the Constantin-Iyer formulation of Navier-Stokes, (2) our own extension of the Gallavotti-Cohen type dynamical ensembles of modified Navier-Stokes with energy-helicity constraints and (3) the Galerkin truncated Euler, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04447","kind":"arxiv","version":5},"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":"1702.04447","created_at":"2026-05-18T00:19:59.204065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.04447v5","created_at":"2026-05-18T00:19:59.204065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04447","created_at":"2026-05-18T00:19:59.204065+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSYD6QIRRF3M","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSYD6QIRRF3MNAZD","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSYD6QIR","created_at":"2026-05-18T12:31:10.602751+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/CSYD6QIRRF3MNAZDX57THZYTJP","json":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP.json","graph_json":"https://pith.science/api/pith-number/CSYD6QIRRF3MNAZDX57THZYTJP/graph.json","events_json":"https://pith.science/api/pith-number/CSYD6QIRRF3MNAZDX57THZYTJP/events.json","paper":"https://pith.science/paper/CSYD6QIR"},"agent_actions":{"view_html":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP","download_json":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP.json","view_paper":"https://pith.science/paper/CSYD6QIR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.04447&json=true","fetch_graph":"https://pith.science/api/pith-number/CSYD6QIRRF3MNAZDX57THZYTJP/graph.json","fetch_events":"https://pith.science/api/pith-number/CSYD6QIRRF3MNAZDX57THZYTJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP/action/storage_attestation","attest_author":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP/action/author_attestation","sign_citation":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP/action/citation_signature","submit_replication":"https://pith.science/pith/CSYD6QIRRF3MNAZDX57THZYTJP/action/replication_record"}},"created_at":"2026-05-18T00:19:59.204065+00:00","updated_at":"2026-05-18T00:19:59.204065+00:00"}