{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CCOQO4FFDBQG3BY5DEEZD2JKOQ","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":"7906534dfd1d904c996c87d4442e205d2f0eec537b493bb293aaa0b7d4ee8108","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-01T09:19:30Z","title_canon_sha256":"257fc26cdc8054b44aa4fa2590a5aef4138a3042bdb122e5363d078d5998daee"},"schema_version":"1.0","source":{"id":"1311.0125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0125","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0125v1","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0125","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"CCOQO4FFDBQG","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CCOQO4FFDBQG3BY5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CCOQO4FF","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:55f053dcdf9c09eeb1d0bb81b72e6c44db0023682140a34359c215356e8b9216","target":"graph","created_at":"2026-05-18T03:08:15Z","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"},"paper":{"abstract_excerpt":"This paper studies two well-known models for two-phase fluid flow at constant temperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal Navier-Stokes-Cahn-Hilliard equations, both of which consist of equations for the (total) fluid density rho, the (mass-averaged)velocity u and the concentration (of one of the phases,) c. Assuming in either case that both phases are incompressible with different densities, each of the models is shown to reduce to a system of evolution equations in rho and u alone. In the case of the Navier-Stokes-Allen-Cahn model, this reduced system is the class","authors_text":"Heinrich Freistuhler, Matthias Kotschote","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-01T09:19:30Z","title":"Reductions of the Navier-Stokes-Allen-Cahn and the Navier-Stokes-Cahn-Hilliard equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0125","kind":"arxiv","version":1},"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:f28f81fd97e26adee44097d549e9dbafeafe92426c31e85e8e3afcd2f4f59dae","target":"record","created_at":"2026-05-18T03:08:15Z","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":"7906534dfd1d904c996c87d4442e205d2f0eec537b493bb293aaa0b7d4ee8108","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-01T09:19:30Z","title_canon_sha256":"257fc26cdc8054b44aa4fa2590a5aef4138a3042bdb122e5363d078d5998daee"},"schema_version":"1.0","source":{"id":"1311.0125","kind":"arxiv","version":1}},"canonical_sha256":"109d0770a518606d871d190991e92a7409eb0bb9c4ddf7611324fba925ecb182","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"109d0770a518606d871d190991e92a7409eb0bb9c4ddf7611324fba925ecb182","first_computed_at":"2026-05-18T03:08:15.481610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:15.481610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPXg87Em0KLUomOfJEMbyRF8lDAa1TChBN7cHqLKSTRqIoynntlIZCJCOM4gA6f3r2ryPwHrS9TM6w54SrIZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:15.482055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f28f81fd97e26adee44097d549e9dbafeafe92426c31e85e8e3afcd2f4f59dae","sha256:55f053dcdf9c09eeb1d0bb81b72e6c44db0023682140a34359c215356e8b9216"],"state_sha256":"dd509d917ae795daecf333898ef8ce6748c43a4d64f9e4b8fb1ecf794f7ad7b6"}