{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OE55YHXZRJPEYNXUIKMRBZORFG","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":"ca653f3bd62f35ac58bcd7890fbf6e66236b039be2fb48f4c3a773ed659a9e8b","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-16T15:50:06Z","title_canon_sha256":"5ab537f193a8ca43cdaa1f7a5446046c53c21f86e6bd523cd306ed4b18125c2d"},"schema_version":"1.0","source":{"id":"2412.11904","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11904","created_at":"2026-07-05T09:50:37Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11904v2","created_at":"2026-07-05T09:50:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11904","created_at":"2026-07-05T09:50:37Z"},{"alias_kind":"pith_short_12","alias_value":"OE55YHXZRJPE","created_at":"2026-07-05T09:50:37Z"},{"alias_kind":"pith_short_16","alias_value":"OE55YHXZRJPEYNXU","created_at":"2026-07-05T09:50:37Z"},{"alias_kind":"pith_short_8","alias_value":"OE55YHXZ","created_at":"2026-07-05T09:50:37Z"}],"graph_snapshots":[{"event_id":"sha256:c0d1ccd1b3fd9550c5e978debeb7333a47ee4211a52ddb3572fda65664c08ebc","target":"graph","created_at":"2026-07-05T09:50:37Z","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/2412.11904/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the Navier-Stokes-Cahn-Hilliard system exhibit strong non-local effects due to the velocity divergence constraint and the fourth-order Cahn-Hilliard operator. We suggest a new first-order approximative system for the inviscid sub-system. It relies on the artificial-compressibility ansatz for the Navier-Stokes equations, a friction-type approximation for the Cahn-Hilliard equa","authors_text":"Christian Rohde, Hasel-Cicek Konan, Jens Keim","cross_cats":["physics.comp-ph","physics.flu-dyn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11904","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":"sha256:5055dc28c0e2e9247805ef504175aa59eb91a749cf3211f6043b08d4d982d01b","target":"record","created_at":"2026-07-05T09:50:37Z","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":"ca653f3bd62f35ac58bcd7890fbf6e66236b039be2fb48f4c3a773ed659a9e8b","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-12-16T15:50:06Z","title_canon_sha256":"5ab537f193a8ca43cdaa1f7a5446046c53c21f86e6bd523cd306ed4b18125c2d"},"schema_version":"1.0","source":{"id":"2412.11904","kind":"arxiv","version":2}},"canonical_sha256":"713bdc1ef98a5e4c36f4429910e5d12987ea7e78e60eb9c40e91afb3e8a9973d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"713bdc1ef98a5e4c36f4429910e5d12987ea7e78e60eb9c40e91afb3e8a9973d","first_computed_at":"2026-07-05T09:50:37.258441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:50:37.258441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5eMJmRbjCSWzKbOS1quxjtE+ylE/cbm4csIu2cu8CrzJuplMw9dWhA9P6xrIBpt73riHvtWVhSQ6ifNl+copDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:50:37.258917Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11904","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5055dc28c0e2e9247805ef504175aa59eb91a749cf3211f6043b08d4d982d01b","sha256:c0d1ccd1b3fd9550c5e978debeb7333a47ee4211a52ddb3572fda65664c08ebc"],"state_sha256":"5aaedba1a12a78c5505a41d956ea65d0900b1e012d8d2362aac5c9263ed2643f"}