{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F2G5I5CRZYV4TQEMMIZQ64SKEK","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":"1b7deb393edaa524cb5579156a85eb3ab7b35ac95486ba835e2c1335eb117948","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-05T09:13:15Z","title_canon_sha256":"0f101d08546624a22d5c93deeb8e41bf7141981fc970082299a294f0d9a35d86"},"schema_version":"1.0","source":{"id":"1810.02578","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02578","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02578v2","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02578","created_at":"2026-05-17T23:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"F2G5I5CRZYV4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F2G5I5CRZYV4TQEM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F2G5I5CR","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:d9e3377ff8e6b6aa3e655dd997095722258ad6d10adcf3c9e5e72c7679456dab","target":"graph","created_at":"2026-05-17T23:52:15Z","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 consider complete non-compact manifolds with either a sub-quadratic growth of the norm of the Riemann curvature, or a sub-quadratic growth of both the norm of the Ricci curvature and the squared inverse of the injectivity radius. We show the existence on such a manifold of a distance-like function with bounded gradient and mild growth of the Hessian. As a main application, we prove that smooth compactly supported functions are dense in $W^{2,p}$. The result is improved for $p=2$ avoiding both the upper bound on the Ricci tensor, and the injectivity radius assumption. As further applications","authors_text":"Debora Impera, Giona Veronelli, Michele Rimoldi","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-05T09:13:15Z","title":"Density problems for second order Sobolev spaces and cut-off functions on manifolds with unbounded geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02578","kind":"arxiv","version":2},"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":"sha256:73f1d6217f9e5d189874aba933eb761a8ef8be1781878755b3411368e15e4a48","target":"record","created_at":"2026-05-17T23:52:15Z","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":"1b7deb393edaa524cb5579156a85eb3ab7b35ac95486ba835e2c1335eb117948","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-05T09:13:15Z","title_canon_sha256":"0f101d08546624a22d5c93deeb8e41bf7141981fc970082299a294f0d9a35d86"},"schema_version":"1.0","source":{"id":"1810.02578","kind":"arxiv","version":2}},"canonical_sha256":"2e8dd47451ce2bc9c08c62330f724a228bf8ea3d9600fcc32bf97a1017eb5428","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e8dd47451ce2bc9c08c62330f724a228bf8ea3d9600fcc32bf97a1017eb5428","first_computed_at":"2026-05-17T23:52:15.463893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:15.463893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mkoGo9Ro7AnO3RpUzcvYg25JDG3+2hHC/PuwqlOGksOcV+25etDHgX9e92Ch56c+SZIo/6QN+B11vyXbg40pAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:15.464641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02578","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73f1d6217f9e5d189874aba933eb761a8ef8be1781878755b3411368e15e4a48","sha256:d9e3377ff8e6b6aa3e655dd997095722258ad6d10adcf3c9e5e72c7679456dab"],"state_sha256":"35ef3884e5d31be45bab500c449c58e9a302b6021c5c1645b4531b1c3bd1800d"}