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\\nu \\Delta \\widetilde{v}^{n+2} + \\nabla q^{n+2}=f(x) \\notag \\\\ &\\nabla \\cdot \\widetilde{v}^{n+2} = 0 \\notag \\\\ \\text{Analysis step: } \\quad &\\frac{3v^{n+2}-3\\widetilde{v}^{n+2}}{2\\Delta t}-\\chi I_H(u(t^{n+2})-v^{n+2})=0. \\notag \\end{align} If $I_H=I_H^2$, the analysis s"},"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":"2606.19508","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-17T18:46:49Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"69c610585118f9bb39c89e25c02bbc503fc978ab73397557b0ce80f1c8ee5fba","abstract_canon_sha256":"1c5ce17fbfec39624022d3f6fbdd8e8e6f06b37bf38783516b33ecc43f81c16f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:27.474286Z","signature_b64":"Ga4N8sTQ64wSfl7m76y4rS2upYKYyKP8yLjjJBLn6lO1Oibh4P6Ws+4QYhHHa36iRUZ4MOVnpXkF9lB/8J22CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62816169830805c5c4fe3579874ba155c671985ec93b7a5cc9dc00c57442aa1d","last_reissued_at":"2026-06-19T16:12:27.473938Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:27.473938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Accuracy Modular Data Assimilation for the Navier-Stokes Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Troy Yang","submitted_at":"2026-06-17T18:46:49Z","abstract_excerpt":"This paper develops an accurate and effective combination of second order backward differentiation time discretization (BDF2) with modular, 2-step nudging-based data assimilation \\begin{align} \\text{Forecast step: } \\quad &\\frac{3\\widetilde{v}^{n+2}-4v^{n+1}+v^n}{2\\Delta t}+\\widetilde{v}^{n+2} \\cdot \\nabla \\widetilde{v}^{n+2} - 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