{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IG7SB5DELRDJ4IFYYRCMQVNGIZ","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":"b9f67d711e37b98aed3e1cf53ba6a43cac88360bd8ba8107dec809fcf44e76d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-25T20:10:58Z","title_canon_sha256":"ce9c69f0df6f12e2adfc02726242df1284ba8d69fc15b3c7351f75e15003a93b"},"schema_version":"1.0","source":{"id":"1005.4689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4689","created_at":"2026-05-18T02:07:08Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4689v1","created_at":"2026-05-18T02:07:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4689","created_at":"2026-05-18T02:07:08Z"},{"alias_kind":"pith_short_12","alias_value":"IG7SB5DELRDJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IG7SB5DELRDJ4IFY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IG7SB5DE","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:fd255c9aaf274f194d51ad7bda72c559e8bf173ae7b61d783440e9766759f540","target":"graph","created_at":"2026-05-18T02:07:08Z","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":"Let $f :\\R\\to\\R$ be a continuous function. We prove that under some additional assumptions on $f$ and $A:\\R\\to\\R_{+}$, weak $\\Cuno$ solutions of the differential inequality $-\\diver(A(\\abs{\\nabla u})\\nabla u)\\ge f(u)$ on $\\RN$ are nonnegative. Some extensions of the result in the framework of subelliptic operators on Carnot Groups are considered.","authors_text":"Enzo Mitidieri, Lorenzo D'Ambrosio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-25T20:10:58Z","title":"Nonnegative solutions of some quasilinear elliptic inequalities and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4689","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":"sha256:6f0d2bd82c52beeaa4390bf3bd727905fd22377e642e76d697f0447c68cce4bc","target":"record","created_at":"2026-05-18T02:07:08Z","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":"b9f67d711e37b98aed3e1cf53ba6a43cac88360bd8ba8107dec809fcf44e76d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-25T20:10:58Z","title_canon_sha256":"ce9c69f0df6f12e2adfc02726242df1284ba8d69fc15b3c7351f75e15003a93b"},"schema_version":"1.0","source":{"id":"1005.4689","kind":"arxiv","version":1}},"canonical_sha256":"41bf20f4645c469e20b8c444c855a6467916e2f3f7af5d364a9e582c18af55d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41bf20f4645c469e20b8c444c855a6467916e2f3f7af5d364a9e582c18af55d9","first_computed_at":"2026-05-18T02:07:08.165763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:08.165763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zc5jdRuvdKdUDzrVsrJouNQGdbwWHL2x6p+9lQZJB+vWxD0z0SQn/XA8UqOKGU0K6oeAwdV5k1V8YKxdW1aVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:08.166664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f0d2bd82c52beeaa4390bf3bd727905fd22377e642e76d697f0447c68cce4bc","sha256:fd255c9aaf274f194d51ad7bda72c559e8bf173ae7b61d783440e9766759f540"],"state_sha256":"ab6a8da709a8d7309e912b3931dedd1faa90ab74411f7212de4ba286b16879d7"}