{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6SF54UKBCEHYDS6COGEHMY3UN2","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":"dc9b95a82c54f46e91b0c4f98935e104a724593eec4547ef6eb169a049909ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-20T19:39:05Z","title_canon_sha256":"0c2dc009608745987a534d7f886b3b8cc843da1765057afb6f01d90fe821a9dc"},"schema_version":"1.0","source":{"id":"1501.04928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04928","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04928v1","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04928","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"6SF54UKBCEHY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6SF54UKBCEHYDS6C","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6SF54UKB","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:57015b68f7153c6c29f817e3543086e5fbde8251915495ee316b7111700d5bf8","target":"graph","created_at":"2026-05-18T02:29:01Z","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 problem for the stationary Navier-Stokes equation in 3D under finite Dirichlet norm is open. In this paper we answer the analogous question on the 3D hyperbolic space. We also address other dimensions and more general manifolds.","authors_text":"Chi Hin Chan, Magdalena Czubak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-20T19:39:05Z","title":"Liouville theorems for the Stationary Navier Stokes equation on a hyperbolic space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04928","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:eacc51028b8fe2cf4316fb5e79f84acd64b23d55785d24d34a698b85b1ded1a3","target":"record","created_at":"2026-05-18T02:29:01Z","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":"dc9b95a82c54f46e91b0c4f98935e104a724593eec4547ef6eb169a049909ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-20T19:39:05Z","title_canon_sha256":"0c2dc009608745987a534d7f886b3b8cc843da1765057afb6f01d90fe821a9dc"},"schema_version":"1.0","source":{"id":"1501.04928","kind":"arxiv","version":1}},"canonical_sha256":"f48bde5141110f81cbc271887663746ebdf1d903e9d9b3032037d5f0834a7cb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f48bde5141110f81cbc271887663746ebdf1d903e9d9b3032037d5f0834a7cb1","first_computed_at":"2026-05-18T02:29:01.955962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:01.955962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cNZjR4fNB/rnQZNFWpxgweoHSLN6GmpDrFhDqpnYnj0u2kEFdG/GOIoSAukULbhsDZnNRAqEv5o325PPoGV/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:01.956428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eacc51028b8fe2cf4316fb5e79f84acd64b23d55785d24d34a698b85b1ded1a3","sha256:57015b68f7153c6c29f817e3543086e5fbde8251915495ee316b7111700d5bf8"],"state_sha256":"b53ea368dc3aa92fb98c1e6c09dda4dd66be6b7262426b8535e61f29ccdc23df"}