{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PWFJIYEGJ3NG3HRW7LDN2G27HE","short_pith_number":"pith:PWFJIYEG","canonical_record":{"source":{"id":"1608.02343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-08T07:59:47Z","cross_cats_sorted":[],"title_canon_sha256":"333d1ab5619276759d2689ded0617323857d856bbe063ef54a9be5161a8ef361","abstract_canon_sha256":"ba54f94ac1a7466c3a5009bbd55b4feb8e50cb28c79e485f0854f240de98a2e3"},"schema_version":"1.0"},"canonical_sha256":"7d8a9460864eda6d9e36fac6dd1b5f391b744273781f58ed811b2cfea8507194","source":{"kind":"arxiv","id":"1608.02343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02343","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02343v1","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02343","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"pith_short_12","alias_value":"PWFJIYEGJ3NG","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWFJIYEGJ3NG3HRW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWFJIYEG","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PWFJIYEGJ3NG3HRW7LDN2G27HE","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-08T07:59:47Z","cross_cats_sorted":[],"title_canon_sha256":"333d1ab5619276759d2689ded0617323857d856bbe063ef54a9be5161a8ef361","abstract_canon_sha256":"ba54f94ac1a7466c3a5009bbd55b4feb8e50cb28c79e485f0854f240de98a2e3"},"schema_version":"1.0"},"canonical_sha256":"7d8a9460864eda6d9e36fac6dd1b5f391b744273781f58ed811b2cfea8507194","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:11.191151Z","signature_b64":"i4UWr7E1DwgiPw0vBnkIjN/DKJeZgEmewGAApJlEL8D8d8oadNWQfmth1Jg5Yzt/5M8DU+aHtjs7lHAu9x0fCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d8a9460864eda6d9e36fac6dd1b5f391b744273781f58ed811b2cfea8507194","last_reissued_at":"2026-05-18T00:57:11.190681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:11.190681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02343","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":"2026-05-18T00:57:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X8PKFl+tKm3FGSWOI4UsCcv4UFzddvLttsI6XqSCcizLQBd6qlDk0vZcdeBLSAYkRh+w7Cj6rJbUhv9ac0ZODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:30:55.805358Z"},"content_sha256":"3e2cc94f95da1ec69410aa7aa67a6e60ad64ba5426e96c01deee85cf77d759b7","schema_version":"1.0","event_id":"sha256:3e2cc94f95da1ec69410aa7aa67a6e60ad64ba5426e96c01deee85cf77d759b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PWFJIYEGJ3NG3HRW7LDN2G27HE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension reduction for the full Navier-Stokes-Fourier system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jan B\\v{r}ezina, Ond\\v{r}ej Kreml, V\\'aclav M\\'acha","submitted_at":"2016-08-08T07:59:47Z","abstract_excerpt":"It is well known that the full Navier-Stokes-Fourier system does not possess a strong solution in three dimensions which causes problems in applications. However, when modeling the flow of a fluid in a thin long pipe, the influence of the cross section can be neglected and the flow is basically one-dimensional. This allows us to deal with strong solutions which are more convenient for numerical computations. The goal of this paper is to provide a rigorous justification of this approach. Namely, we prove that any suitable weak solution to the three-dimensional NSF system tends to a strong solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02343","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":"2026-05-18T00:57:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WEo27VT7ZiBXJ8nzFnviE3qelT8Jn/ZsTB9kF/6svGR2q27+y1kKK8jMJ1y6e+NPMjEgGA6J1S2twX1LwLgwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:30:55.806052Z"},"content_sha256":"3d7c88bd0d938889fdc63db0dbd3cb1d007c094d0f1ebb053c237afeca117e42","schema_version":"1.0","event_id":"sha256:3d7c88bd0d938889fdc63db0dbd3cb1d007c094d0f1ebb053c237afeca117e42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWFJIYEGJ3NG3HRW7LDN2G27HE/bundle.json","state_url":"https://pith.science/pith/PWFJIYEGJ3NG3HRW7LDN2G27HE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWFJIYEGJ3NG3HRW7LDN2G27HE/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":"2026-05-27T09:30:55Z","links":{"resolver":"https://pith.science/pith/PWFJIYEGJ3NG3HRW7LDN2G27HE","bundle":"https://pith.science/pith/PWFJIYEGJ3NG3HRW7LDN2G27HE/bundle.json","state":"https://pith.science/pith/PWFJIYEGJ3NG3HRW7LDN2G27HE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWFJIYEGJ3NG3HRW7LDN2G27HE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PWFJIYEGJ3NG3HRW7LDN2G27HE","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":"ba54f94ac1a7466c3a5009bbd55b4feb8e50cb28c79e485f0854f240de98a2e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-08T07:59:47Z","title_canon_sha256":"333d1ab5619276759d2689ded0617323857d856bbe063ef54a9be5161a8ef361"},"schema_version":"1.0","source":{"id":"1608.02343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02343","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02343v1","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02343","created_at":"2026-05-18T00:57:11Z"},{"alias_kind":"pith_short_12","alias_value":"PWFJIYEGJ3NG","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWFJIYEGJ3NG3HRW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWFJIYEG","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:3d7c88bd0d938889fdc63db0dbd3cb1d007c094d0f1ebb053c237afeca117e42","target":"graph","created_at":"2026-05-18T00:57:11Z","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":"It is well known that the full Navier-Stokes-Fourier system does not possess a strong solution in three dimensions which causes problems in applications. However, when modeling the flow of a fluid in a thin long pipe, the influence of the cross section can be neglected and the flow is basically one-dimensional. This allows us to deal with strong solutions which are more convenient for numerical computations. The goal of this paper is to provide a rigorous justification of this approach. Namely, we prove that any suitable weak solution to the three-dimensional NSF system tends to a strong solut","authors_text":"Jan B\\v{r}ezina, Ond\\v{r}ej Kreml, V\\'aclav M\\'acha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-08T07:59:47Z","title":"Dimension reduction for the full Navier-Stokes-Fourier system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02343","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":"sha256:3e2cc94f95da1ec69410aa7aa67a6e60ad64ba5426e96c01deee85cf77d759b7","target":"record","created_at":"2026-05-18T00:57:11Z","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":"ba54f94ac1a7466c3a5009bbd55b4feb8e50cb28c79e485f0854f240de98a2e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-08T07:59:47Z","title_canon_sha256":"333d1ab5619276759d2689ded0617323857d856bbe063ef54a9be5161a8ef361"},"schema_version":"1.0","source":{"id":"1608.02343","kind":"arxiv","version":1}},"canonical_sha256":"7d8a9460864eda6d9e36fac6dd1b5f391b744273781f58ed811b2cfea8507194","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d8a9460864eda6d9e36fac6dd1b5f391b744273781f58ed811b2cfea8507194","first_computed_at":"2026-05-18T00:57:11.190681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:11.190681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i4UWr7E1DwgiPw0vBnkIjN/DKJeZgEmewGAApJlEL8D8d8oadNWQfmth1Jg5Yzt/5M8DU+aHtjs7lHAu9x0fCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:11.191151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e2cc94f95da1ec69410aa7aa67a6e60ad64ba5426e96c01deee85cf77d759b7","sha256:3d7c88bd0d938889fdc63db0dbd3cb1d007c094d0f1ebb053c237afeca117e42"],"state_sha256":"91abbafa26f1e0bbdcce842bf85046f667d96b564669cd47e243afc7632c43ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xB8WcWipyFaFoQAo7kpIy9K/Wo8OaqZZvmnItIC9kSt03DogLe/5ANqESaiX7wQZTPWdM+tqleaAoNbLRhWEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:30:55.808467Z","bundle_sha256":"96c34f6f0335992730922d9ab6e80cc44ea13b68fd62bc0c5dfa3fd541b0440b"}}