{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PZ6Y4PKH66EGSEWXG35MTAAN72","short_pith_number":"pith:PZ6Y4PKH","canonical_record":{"source":{"id":"1902.10413","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-27T09:49:20Z","cross_cats_sorted":[],"title_canon_sha256":"fd41367171bf995776163a5790e20f934a43285c18e6a6d5f50ac3645671a21b","abstract_canon_sha256":"d540b7d9156d10748f963f5ef7ca9f48069fc12e0443d3eaf71a5a05a7ba5b93"},"schema_version":"1.0"},"canonical_sha256":"7e7d8e3d47f7886912d736fac9800dfebc6ae4ee1e56f1e8796b9daeee6198b5","source":{"kind":"arxiv","id":"1902.10413","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10413","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10413v1","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10413","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"PZ6Y4PKH66EG","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PZ6Y4PKH66EGSEWX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PZ6Y4PKH","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PZ6Y4PKH66EGSEWXG35MTAAN72","target":"record","payload":{"canonical_record":{"source":{"id":"1902.10413","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-27T09:49:20Z","cross_cats_sorted":[],"title_canon_sha256":"fd41367171bf995776163a5790e20f934a43285c18e6a6d5f50ac3645671a21b","abstract_canon_sha256":"d540b7d9156d10748f963f5ef7ca9f48069fc12e0443d3eaf71a5a05a7ba5b93"},"schema_version":"1.0"},"canonical_sha256":"7e7d8e3d47f7886912d736fac9800dfebc6ae4ee1e56f1e8796b9daeee6198b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:30.912891Z","signature_b64":"ROPJOZeRXhARsrY2W8Xpw706aGfGIEl59a4p5oqmUeQQAwC36Vlq6kdizryQqPfu1GBsjE0l41lPtMtdxKLzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e7d8e3d47f7886912d736fac9800dfebc6ae4ee1e56f1e8796b9daeee6198b5","last_reissued_at":"2026-05-17T23:52:30.912419Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:30.912419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.10413","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":"2026-05-17T23:52:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8fAbQT9HHydA+vBTvt99hRkv8fSJLVJO1aO2ryYM8JjUevKxWMrZNsC0f2Yacl4YnCYtNVXgbuUyxVTGZr1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:15:09.809138Z"},"content_sha256":"9beb8329004cdd2e0914b9420fd0f2ed217de7a9ecc1e1235ec4eb7497448bae","schema_version":"1.0","event_id":"sha256:9beb8329004cdd2e0914b9420fd0f2ed217de7a9ecc1e1235ec4eb7497448bae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PZ6Y4PKH66EGSEWXG35MTAAN72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary solutions of the Navier-Stokes-Fourier system in planar domains with impermeable boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Petrov, E. Feireisl, I. S. Ciuperca, M. Jai","submitted_at":"2019-02-27T09:49:20Z","abstract_excerpt":"The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant constitutive relations. The equation of state of a real fluid is considered, where the admissible range of density is confined to a bounded interval (hard sphere model). The transport coefficients depend on the temperature in a general way including both gases and liquids behavior. The heart of the paper are new a priori bounds resulting from Trudinger-Moser inequali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10413","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":"2026-05-17T23:52:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L/5fsgrVQKrBEQWRkS7e5iOoHJapJWSSvVhp2STDDut+sZBwh3LB4ja8s3PPFD1ScgFf6QzPbv3l5fcqM+WPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:15:09.809509Z"},"content_sha256":"aba837c4065d807d51869f65b236ac0f8fb3d1a87e987d13e70c15358dcde16b","schema_version":"1.0","event_id":"sha256:aba837c4065d807d51869f65b236ac0f8fb3d1a87e987d13e70c15358dcde16b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZ6Y4PKH66EGSEWXG35MTAAN72/bundle.json","state_url":"https://pith.science/pith/PZ6Y4PKH66EGSEWXG35MTAAN72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZ6Y4PKH66EGSEWXG35MTAAN72/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":"2026-06-03T20:15:09Z","links":{"resolver":"https://pith.science/pith/PZ6Y4PKH66EGSEWXG35MTAAN72","bundle":"https://pith.science/pith/PZ6Y4PKH66EGSEWXG35MTAAN72/bundle.json","state":"https://pith.science/pith/PZ6Y4PKH66EGSEWXG35MTAAN72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZ6Y4PKH66EGSEWXG35MTAAN72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PZ6Y4PKH66EGSEWXG35MTAAN72","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":"d540b7d9156d10748f963f5ef7ca9f48069fc12e0443d3eaf71a5a05a7ba5b93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-27T09:49:20Z","title_canon_sha256":"fd41367171bf995776163a5790e20f934a43285c18e6a6d5f50ac3645671a21b"},"schema_version":"1.0","source":{"id":"1902.10413","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10413","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10413v1","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10413","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"PZ6Y4PKH66EG","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PZ6Y4PKH66EGSEWX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PZ6Y4PKH","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:aba837c4065d807d51869f65b236ac0f8fb3d1a87e987d13e70c15358dcde16b","target":"graph","created_at":"2026-05-17T23:52:30Z","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 existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant constitutive relations. The equation of state of a real fluid is considered, where the admissible range of density is confined to a bounded interval (hard sphere model). The transport coefficients depend on the temperature in a general way including both gases and liquids behavior. The heart of the paper are new a priori bounds resulting from Trudinger-Moser inequali","authors_text":"A. Petrov, E. Feireisl, I. S. Ciuperca, M. Jai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-27T09:49:20Z","title":"Stationary solutions of the Navier-Stokes-Fourier system in planar domains with impermeable boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10413","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":"sha256:9beb8329004cdd2e0914b9420fd0f2ed217de7a9ecc1e1235ec4eb7497448bae","target":"record","created_at":"2026-05-17T23:52:30Z","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":"d540b7d9156d10748f963f5ef7ca9f48069fc12e0443d3eaf71a5a05a7ba5b93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-27T09:49:20Z","title_canon_sha256":"fd41367171bf995776163a5790e20f934a43285c18e6a6d5f50ac3645671a21b"},"schema_version":"1.0","source":{"id":"1902.10413","kind":"arxiv","version":1}},"canonical_sha256":"7e7d8e3d47f7886912d736fac9800dfebc6ae4ee1e56f1e8796b9daeee6198b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e7d8e3d47f7886912d736fac9800dfebc6ae4ee1e56f1e8796b9daeee6198b5","first_computed_at":"2026-05-17T23:52:30.912419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:30.912419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ROPJOZeRXhARsrY2W8Xpw706aGfGIEl59a4p5oqmUeQQAwC36Vlq6kdizryQqPfu1GBsjE0l41lPtMtdxKLzDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:30.912891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10413","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9beb8329004cdd2e0914b9420fd0f2ed217de7a9ecc1e1235ec4eb7497448bae","sha256:aba837c4065d807d51869f65b236ac0f8fb3d1a87e987d13e70c15358dcde16b"],"state_sha256":"dd75da2e23b529ead09e336b0095d53bd8c8adeb1a8f306d19a9b9e47e548f83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ma/5Gah0J94ydTyMd2t+kCW5ZGc0aJxVdO1wI7c6g8Yz9k2cTmasnG/AEIUMgIMo2J/YzE012uQOdaL8fSvaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:15:09.811395Z","bundle_sha256":"5d6e2647ee61701557ee0d2f37e4313e8f1f208cff106005651ff67ecd1b0f3b"}}