{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T2QV27MNDHRW4SFWBPUJBWKDCY","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":"e248224cbe0ed90dbaa6634f7bdcd9f3dfd66ae907b43214554c63295ed70548","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T13:34:29Z","title_canon_sha256":"b208c67ae17a32ae9ea770aec5286f6f1f18ebd0291bc83b6244188b8a38a9db"},"schema_version":"1.0","source":{"id":"1612.04161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04161","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04161v1","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04161","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"T2QV27MNDHRW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T2QV27MNDHRW4SFW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T2QV27MN","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:17b48a8dd50141729d7eee2004a9b734f393b6480a91e1ca9db0859dd2fdad2b","target":"graph","created_at":"2026-05-18T00:55:05Z","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":"The transport of single-phase fluid mixtures in porous media is described by cross-diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy's law, and the van der Waals equation of state for mixtures. The model consists of parabolic equations with cross diffusion with a hypocoercive diffusion operator. The global-in-time existence of weak solutions in a bounded domain with equilibrium boundary conditions is proved, extending the boundedness-by-entropy method. Based on the free energy inequality, the large-time convergence","authors_text":"Ansgar J\\\"ungel, Ji\\v{r}\\'i Miky\\v{s}ka, Nicola Zamponi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T13:34:29Z","title":"Existence analysis of a single-phase flow mixture model with van der Waals pressure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04161","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":"sha256:63c14caafc97895824cbc4d331b9dcc5fe8aec54d2a18939dd16db84cc41a821","target":"record","created_at":"2026-05-18T00:55:05Z","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":"e248224cbe0ed90dbaa6634f7bdcd9f3dfd66ae907b43214554c63295ed70548","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T13:34:29Z","title_canon_sha256":"b208c67ae17a32ae9ea770aec5286f6f1f18ebd0291bc83b6244188b8a38a9db"},"schema_version":"1.0","source":{"id":"1612.04161","kind":"arxiv","version":1}},"canonical_sha256":"9ea15d7d8d19e36e48b60be890d943162cf3065a7bf6e01e321f0a9ffcd63cf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ea15d7d8d19e36e48b60be890d943162cf3065a7bf6e01e321f0a9ffcd63cf2","first_computed_at":"2026-05-18T00:55:05.298240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:05.298240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5dDgxNfaWVeKI+lT8rOj4AjmpGt7BilYQlahrCdEm3JEJvlJZ+pI9KDg6GuhUG/slyNuFFBHTFz7ev+kBqhmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:05.298813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c14caafc97895824cbc4d331b9dcc5fe8aec54d2a18939dd16db84cc41a821","sha256:17b48a8dd50141729d7eee2004a9b734f393b6480a91e1ca9db0859dd2fdad2b"],"state_sha256":"f94fcd30b6a736f3d21d3edddcc00d22ea66d28b46bf9cf7df1e5d3a86d2687b"}