{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:53IWUZXZRPR33Q3RLONLEEIDS4","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":"5638e59f79d1d1ee776962d5bba6cd257978f2ee1e99c052368407bc4b9f6823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-30T19:03:43Z","title_canon_sha256":"6a52203dad9a511bd6e814b909b4eb0bbebe2993dfbd06a5591285283bcf3daa"},"schema_version":"1.0","source":{"id":"1401.7954","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7954","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7954v2","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7954","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"53IWUZXZRPR3","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"53IWUZXZRPR33Q3R","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"53IWUZXZ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:ed25358eed1646e350237d4095d25fa2c7ac40757bf0755c213a7769ca576fde","target":"graph","created_at":"2026-05-18T01:33:32Z","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":"We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation. Several results were already proven by two of the present authors. However, in the two-dimensional case, the uniqueness of weak solutions was still open. Here we establish such a result even in the case of degenerate mobility and singular potential. Moreover, we show the strong-weak uniqueness in the case of viscosity depending on the order parameter, provi","authors_text":"Ciprian G. Gal, Maurizio Grasselli, Sergio Frigeri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-30T19:03:43Z","title":"On nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7954","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":"sha256:47614e7500109e90eb134e5176aa232f6758e2022bd98ab9a67c8b8beb224dbc","target":"record","created_at":"2026-05-18T01:33:32Z","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":"5638e59f79d1d1ee776962d5bba6cd257978f2ee1e99c052368407bc4b9f6823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-30T19:03:43Z","title_canon_sha256":"6a52203dad9a511bd6e814b909b4eb0bbebe2993dfbd06a5591285283bcf3daa"},"schema_version":"1.0","source":{"id":"1401.7954","kind":"arxiv","version":2}},"canonical_sha256":"eed16a66f98be3bdc3715b9ab211039703298412a438a8d12bf67e6bc5a992b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eed16a66f98be3bdc3715b9ab211039703298412a438a8d12bf67e6bc5a992b6","first_computed_at":"2026-05-18T01:33:32.730216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:32.730216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7eqdrfZ10vs2DTP5402JkC5H6pVjQtCNFt6Ktil6SLx5Kd/5hm5xsDM2utKPkRSK6m/thZ+gEzcZA4lN9+HcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:32.730813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7954","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47614e7500109e90eb134e5176aa232f6758e2022bd98ab9a67c8b8beb224dbc","sha256:ed25358eed1646e350237d4095d25fa2c7ac40757bf0755c213a7769ca576fde"],"state_sha256":"4a20b56daa0ba18e04b0b32dd9b3e43a56a3890997f4c537d4a5d67714976d4b"}