{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WZQ6ZYORNJMDH7W6JUOXF4634Z","short_pith_number":"pith:WZQ6ZYOR","canonical_record":{"source":{"id":"1306.2565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-11T15:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"1c16c390c9eff200373866f96e8c247484ac0b9d51c6b242e8a89320b98333e3","abstract_canon_sha256":"32a298ea611c411de44922bb69745ad59537a98dd6f2bfd4b7303b2a2db1642a"},"schema_version":"1.0"},"canonical_sha256":"b661ece1d16a5833fede4d1d72f3dbe672afed1c77d6504489ccf54f17597a8b","source":{"kind":"arxiv","id":"1306.2565","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2565","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2565v1","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2565","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"WZQ6ZYORNJMD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WZQ6ZYORNJMDH7W6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WZQ6ZYOR","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WZQ6ZYORNJMDH7W6JUOXF4634Z","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-11T15:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"1c16c390c9eff200373866f96e8c247484ac0b9d51c6b242e8a89320b98333e3","abstract_canon_sha256":"32a298ea611c411de44922bb69745ad59537a98dd6f2bfd4b7303b2a2db1642a"},"schema_version":"1.0"},"canonical_sha256":"b661ece1d16a5833fede4d1d72f3dbe672afed1c77d6504489ccf54f17597a8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:11.104629Z","signature_b64":"NuI1Cken5pmw4eImB/UIgPYhY50I/w1a+S/Ar1+sBaPsazIjPl2GFALqcSECHmnULv49R9JIIOM8vqODuCFXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b661ece1d16a5833fede4d1d72f3dbe672afed1c77d6504489ccf54f17597a8b","last_reissued_at":"2026-05-18T03:21:11.104072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:11.104072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2565","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2USpZ6geAR12nEU79c1+/NAA3f+aq0Rku41zyyRHQRvNWXCHE34/E8wguLJEjZ/rlacYCX8NdsJH7ahpXZMuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:35:07.723275Z"},"content_sha256":"fdce79ae75e13ccc5b6968a1b7089714669140024024b12e51cfaefef5846598","schema_version":"1.0","event_id":"sha256:fdce79ae75e13ccc5b6968a1b7089714669140024024b12e51cfaefef5846598"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WZQ6ZYORNJMDH7W6JUOXF4634Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong solutions in the dynamical theory of compressible fluid mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matthias Kotschote, Rico Zacher","submitted_at":"2013-06-11T15:59:13Z","abstract_excerpt":"In this paper we investigate the compressible Navier-Stokes-Cahn-Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinowsky. This model describes the flow of a binary compressible mixture; the fluids are supposed to be macroscopically immiscible, but partial mixing is permitted leading to narrow transition layers. The internal structure and macroscopic dynamics of these layers are induced by a Cahn-Hilliard law that the mixing ratio satisfies. The PDE constitute a strongly coupled hyperbolic-parabolic system. We establish a local existence and uniqueness result for str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2565","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0sCDUWJOzLMpbPWBoWzMNyFQlF1VKrGU0S31BWQEqb7Vdjl1kWr4JAEV1obgDTPig1/uMUpjY/V/f1IDXkZjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:35:07.723650Z"},"content_sha256":"3b8faa592b24d159e8d288473b5f139ec76ee901308a0ae3d98640410643a919","schema_version":"1.0","event_id":"sha256:3b8faa592b24d159e8d288473b5f139ec76ee901308a0ae3d98640410643a919"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZQ6ZYORNJMDH7W6JUOXF4634Z/bundle.json","state_url":"https://pith.science/pith/WZQ6ZYORNJMDH7W6JUOXF4634Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZQ6ZYORNJMDH7W6JUOXF4634Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T04:35:07Z","links":{"resolver":"https://pith.science/pith/WZQ6ZYORNJMDH7W6JUOXF4634Z","bundle":"https://pith.science/pith/WZQ6ZYORNJMDH7W6JUOXF4634Z/bundle.json","state":"https://pith.science/pith/WZQ6ZYORNJMDH7W6JUOXF4634Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZQ6ZYORNJMDH7W6JUOXF4634Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WZQ6ZYORNJMDH7W6JUOXF4634Z","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":"32a298ea611c411de44922bb69745ad59537a98dd6f2bfd4b7303b2a2db1642a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-11T15:59:13Z","title_canon_sha256":"1c16c390c9eff200373866f96e8c247484ac0b9d51c6b242e8a89320b98333e3"},"schema_version":"1.0","source":{"id":"1306.2565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2565","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2565v1","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2565","created_at":"2026-05-18T03:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"WZQ6ZYORNJMD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WZQ6ZYORNJMDH7W6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WZQ6ZYOR","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3b8faa592b24d159e8d288473b5f139ec76ee901308a0ae3d98640410643a919","target":"graph","created_at":"2026-05-18T03:21:11Z","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":"In this paper we investigate the compressible Navier-Stokes-Cahn-Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinowsky. This model describes the flow of a binary compressible mixture; the fluids are supposed to be macroscopically immiscible, but partial mixing is permitted leading to narrow transition layers. The internal structure and macroscopic dynamics of these layers are induced by a Cahn-Hilliard law that the mixing ratio satisfies. The PDE constitute a strongly coupled hyperbolic-parabolic system. We establish a local existence and uniqueness result for str","authors_text":"Matthias Kotschote, Rico Zacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-11T15:59:13Z","title":"Strong solutions in the dynamical theory of compressible fluid mixtures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2565","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:fdce79ae75e13ccc5b6968a1b7089714669140024024b12e51cfaefef5846598","target":"record","created_at":"2026-05-18T03:21:11Z","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":"32a298ea611c411de44922bb69745ad59537a98dd6f2bfd4b7303b2a2db1642a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-11T15:59:13Z","title_canon_sha256":"1c16c390c9eff200373866f96e8c247484ac0b9d51c6b242e8a89320b98333e3"},"schema_version":"1.0","source":{"id":"1306.2565","kind":"arxiv","version":1}},"canonical_sha256":"b661ece1d16a5833fede4d1d72f3dbe672afed1c77d6504489ccf54f17597a8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b661ece1d16a5833fede4d1d72f3dbe672afed1c77d6504489ccf54f17597a8b","first_computed_at":"2026-05-18T03:21:11.104072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:11.104072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NuI1Cken5pmw4eImB/UIgPYhY50I/w1a+S/Ar1+sBaPsazIjPl2GFALqcSECHmnULv49R9JIIOM8vqODuCFXBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:11.104629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdce79ae75e13ccc5b6968a1b7089714669140024024b12e51cfaefef5846598","sha256:3b8faa592b24d159e8d288473b5f139ec76ee901308a0ae3d98640410643a919"],"state_sha256":"d1b931a10dc69e5ac75c79a6acadd4120ccba4abb1489fb4e41dcbec73261038"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GsGWzqwPYfWnnawfj5JYO+9TrqxeFl9dGZrI+YSiYPTt7yEdxFUjCzONsdmcQ5RFv8JHrMZ7B2kTCpveD0jhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:35:07.725611Z","bundle_sha256":"29505e70fa86e1c035d8a956120b07c8109278ecc8600c8a720fadc3bdb5b8a6"}}