{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3HNUI4TIEPKGTORBFCLLAKSAVP","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":"35abe078a698cf3c25c12f8eb500f5058e3ad65856e1bdc7c689d40fee2e8485","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-06T11:14:30Z","title_canon_sha256":"cbb2ec22dfc9f01424d78126d8ec386724119f768830f298c425cdf8c3302d03"},"schema_version":"1.0","source":{"id":"1406.1644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1644","created_at":"2026-05-18T02:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1644v1","created_at":"2026-05-18T02:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1644","created_at":"2026-05-18T02:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"3HNUI4TIEPKG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3HNUI4TIEPKGTORB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3HNUI4TI","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:8465e68b64f12c30fc913c0bb0a0a42e2c9e9de4b560829da1872febcadb8763","target":"graph","created_at":"2026-05-18T02:50:14Z","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":"We shall prove dispersive and smoothing estimates for Bochner type laplacians on some non-compact Riemannian manifolds with negative Ricci curvature, in particular on hyperbolic spaces. These estimates will be used to prove Fujita-Kato type theorems for the incompressible Navier-Stokes equations. We shall also discuss the uniqueness of Leray weak solutions in the two dimensional case.","authors_text":"Vittoria Pierfelice (MAPMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-06T11:14:30Z","title":"The incompressible Navier-Stokes equations on non-compact manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1644","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":"sha256:6427ef6ef23aa1982e1fcd05b4cb5b6a0d33ad98f12506ee84a8b6169297af26","target":"record","created_at":"2026-05-18T02:50:14Z","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":"35abe078a698cf3c25c12f8eb500f5058e3ad65856e1bdc7c689d40fee2e8485","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-06T11:14:30Z","title_canon_sha256":"cbb2ec22dfc9f01424d78126d8ec386724119f768830f298c425cdf8c3302d03"},"schema_version":"1.0","source":{"id":"1406.1644","kind":"arxiv","version":1}},"canonical_sha256":"d9db44726823d469ba212896b02a40abc320f915912f5a127cca850a12590f2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9db44726823d469ba212896b02a40abc320f915912f5a127cca850a12590f2e","first_computed_at":"2026-05-18T02:50:14.291726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:14.291726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jr/y4XeEwNb+PtOoR0QkG+gcrhleRr6W+hI0awlbDAJl4/5MO8XAE790h3QLqAtT+MtPNsIjbW1DXX2+UVn4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:14.293578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6427ef6ef23aa1982e1fcd05b4cb5b6a0d33ad98f12506ee84a8b6169297af26","sha256:8465e68b64f12c30fc913c0bb0a0a42e2c9e9de4b560829da1872febcadb8763"],"state_sha256":"5d67171c07f48914786cb707c80d67c5343ebe3828ab7463192229abb2348a14"}