{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6SY27A564B4FOK75AG7DLGRLSY","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":"74b383404d0ed05d3facfdd6da3b1ab331673bfec4a8f2c2d4881d33097db2c9","cross_cats_sorted":["math.AP","math.DG","math.MP","physics.flu-dyn","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-01T14:08:51Z","title_canon_sha256":"2344865d5b2ec2ccb0bcdfe86dcb4f37feb9108913cca5899d4d4b23a467efad"},"schema_version":"1.0","source":{"id":"2606.02286","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02286","created_at":"2026-06-02T03:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02286v1","created_at":"2026-06-02T03:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02286","created_at":"2026-06-02T03:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"6SY27A564B4F","created_at":"2026-06-02T03:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"6SY27A564B4FOK75","created_at":"2026-06-02T03:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"6SY27A56","created_at":"2026-06-02T03:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:84c332495fa46b91c9a2dc3278e4b83341e3f30d713fd6bc7bdf5ac10b2cf193","target":"graph","created_at":"2026-06-02T03:04:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.02286/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The deterministic incompressible Navier-Stokes equations are physically incomplete: any viscous fluid at finite temperature must exhibit thermal fluctuations whose form is dictated by the fluctuation-dissipation relation. We formulate the stochastic Navier-Stokes equations with the kinematically selected deformation Laplacian on compact Riemannian manifolds with strictly negative Ricci curvature. The fluctuation-dissipation relation, derived from a topological (Poincar\\'e lemma) argument, uniquely determines the noise from the viscous operator. For the spectrally truncated system, we prove tha","authors_text":"Samuel L. Braunstein, Zhi-Wei Wang","cross_cats":["math.AP","math.DG","math.MP","physics.flu-dyn","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-01T14:08:51Z","title":"Exponential thermalisation of viscous fluids on negatively curved manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02286","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":"sha256:20d57ab79586c9b1ddcb0be2d2cf0f7c66f563928afef0788d025870b4f218e3","target":"record","created_at":"2026-06-02T03:04:55Z","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":"74b383404d0ed05d3facfdd6da3b1ab331673bfec4a8f2c2d4881d33097db2c9","cross_cats_sorted":["math.AP","math.DG","math.MP","physics.flu-dyn","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-01T14:08:51Z","title_canon_sha256":"2344865d5b2ec2ccb0bcdfe86dcb4f37feb9108913cca5899d4d4b23a467efad"},"schema_version":"1.0","source":{"id":"2606.02286","kind":"arxiv","version":1}},"canonical_sha256":"f4b1af83bee078572bfd01be359a2b9639265b097675fd07cafd77ada300b11f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4b1af83bee078572bfd01be359a2b9639265b097675fd07cafd77ada300b11f","first_computed_at":"2026-06-02T03:04:55.091303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:55.091303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8hj9GUz/wZN2+vzmjBIcPSPm2m6MMf5zqzm7LO1TxKumasVxYI86vIJK5exOz+gO0jC1RvA9KsEf9JdVBpnSAQ==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:55.091683Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02286","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20d57ab79586c9b1ddcb0be2d2cf0f7c66f563928afef0788d025870b4f218e3","sha256:84c332495fa46b91c9a2dc3278e4b83341e3f30d713fd6bc7bdf5ac10b2cf193"],"state_sha256":"7d9c9371a8e4c187dcdb987707a5134c86471a5ffde5e87e45372ed922fbfb9a"}