{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HASOOKA3HEN32K7PMRSKWNPFBK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f42358121278de3fe10653eaf1807ec367ed41ef0f10a5c0edc44bea16c433c7","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-08T13:39:43Z","title_canon_sha256":"20daeaf3721739f51dd988f8a1db32655edfeafe53a1118fc00703ddb05adeb0"},"schema_version":"1.0","source":{"id":"2506.07141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07141","created_at":"2026-07-05T11:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07141v2","created_at":"2026-07-05T11:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07141","created_at":"2026-07-05T11:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"HASOOKA3HEN3","created_at":"2026-07-05T11:51:28Z"},{"alias_kind":"pith_short_16","alias_value":"HASOOKA3HEN32K7P","created_at":"2026-07-05T11:51:28Z"},{"alias_kind":"pith_short_8","alias_value":"HASOOKA3","created_at":"2026-07-05T11:51:28Z"}],"graph_snapshots":[{"event_id":"sha256:b1292c75696f624e6ba1c46d5d54b12904c4cb4ff136a16cac7440ae80ad87c4","target":"graph","created_at":"2026-07-05T11:51:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.07141/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy dissipation law. By leveraging Crank-Nicolson schemes and backward differentiation formulas, we develop four first- and second-order time-discrete schemes. These schemes exactly preserve the original energy dissipation law at each time step, requiring only the solutions of three linear Stokes systems and one $2\\times 2$ system of linear equations. Furthermore, the fin","authors_text":"Chunwu Wang, Qi Hong, Yuezheng Gong, Zihan Weng","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-08T13:39:43Z","title":"Original-energy-dissipation-preserving methods for the incompressible Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07141","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ce7fefc24673333fc2936c64996a82262beb3ff3702c1468703a25a27abda091","target":"record","created_at":"2026-07-05T11:51:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f42358121278de3fe10653eaf1807ec367ed41ef0f10a5c0edc44bea16c433c7","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-08T13:39:43Z","title_canon_sha256":"20daeaf3721739f51dd988f8a1db32655edfeafe53a1118fc00703ddb05adeb0"},"schema_version":"1.0","source":{"id":"2506.07141","kind":"arxiv","version":2}},"canonical_sha256":"3824e7281b391bbd2bef6464ab35e50a915f51031dfad2fc9bf769791d4a23d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3824e7281b391bbd2bef6464ab35e50a915f51031dfad2fc9bf769791d4a23d7","first_computed_at":"2026-07-05T11:51:28.336828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:51:28.336828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u0WZ/b6PdhcrK/9GDt16mhoROMGlWtnHKolBbDC756/qwGJWzSpE0OoisBBzKT9ri4Fykw9Q7Jj/Jf54dxAZCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:51:28.337324Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce7fefc24673333fc2936c64996a82262beb3ff3702c1468703a25a27abda091","sha256:b1292c75696f624e6ba1c46d5d54b12904c4cb4ff136a16cac7440ae80ad87c4"],"state_sha256":"c988cddd034b84b57a9e32bd58cf3b02141b92b989ec00e6786c6f12823f960a"}