{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:PCXO5FCUIJMVPJX54VRN37JWOH","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":"1f99a64d99ecb43fa1f194330de9f0fdda9f61f737803c27e52fb78702a76556","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-21T12:34:07Z","title_canon_sha256":"dfc924d3c8e47c51305bfb8e18169352ede6879c14a5f5b8e4a311000a14811a"},"schema_version":"1.0","source":{"id":"2103.11382","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.11382","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"2103.11382v3","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.11382","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"PCXO5FCUIJMV","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"pith_short_16","alias_value":"PCXO5FCUIJMVPJX5","created_at":"2026-07-05T04:43:17Z"},{"alias_kind":"pith_short_8","alias_value":"PCXO5FCU","created_at":"2026-07-05T04:43:17Z"}],"graph_snapshots":[{"event_id":"sha256:56bd57701a4e9c815b1cd3402a337b856d29ab554b3cd022f0a99912f5cf3c92","target":"graph","created_at":"2026-07-05T04:43:17Z","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/2103.11382/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we provide necessary and sufficient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasilinear local and a nonlocal operator, i.e., $$\\mathcal{L}_{p,s} = -\\Delta_p + (-\\Delta)^s_p.$$ Our main result is resemblant to the celebrated work by Brezis-Oswald [10]. In addition, we prove a regularity result of independent interest.","authors_text":"Dimitri Mugnai, Eugenio Vecchi, Stefano Biagi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-21T12:34:07Z","title":"A Brezis-Oswald approach for mixed local and nonlocal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.11382","kind":"arxiv","version":3},"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":"sha256:8c93b9d9ad44084b35d696c20d901e7413b111712336f27fb3569fca3c448719","target":"record","created_at":"2026-07-05T04:43:17Z","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":"1f99a64d99ecb43fa1f194330de9f0fdda9f61f737803c27e52fb78702a76556","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-03-21T12:34:07Z","title_canon_sha256":"dfc924d3c8e47c51305bfb8e18169352ede6879c14a5f5b8e4a311000a14811a"},"schema_version":"1.0","source":{"id":"2103.11382","kind":"arxiv","version":3}},"canonical_sha256":"78aeee9454425957a6fde562ddfd3671eb93ca1fec68983b6990288b8e60a400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78aeee9454425957a6fde562ddfd3671eb93ca1fec68983b6990288b8e60a400","first_computed_at":"2026-07-05T04:43:17.874622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:43:17.874622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SuDqbO6vE2Pt+071gkLo7Ee7U12BxqN3MtbLlS7Sd3hSfsTlK1C+H+C6d1MuKSXArIvwI5lBfs7uziO5z26CAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:43:17.875034Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.11382","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c93b9d9ad44084b35d696c20d901e7413b111712336f27fb3569fca3c448719","sha256:56bd57701a4e9c815b1cd3402a337b856d29ab554b3cd022f0a99912f5cf3c92"],"state_sha256":"61fa76dd1b90e5813f9ef80b276b50c89e740061381e46ba3cf1b224b05ac783"}