{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FN7ALGE2PHWIF77OG23ID7PDSG","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":"a1b51fe9e6a985968b40d39b01ba3d9458e52544bcaa69196cfb619c72398309","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-01T13:26:16Z","title_canon_sha256":"a37fff06d9cf06b0e70a62eb1e6f12d8f7450288a59d0bbff85dce3cd8d5f5e2"},"schema_version":"1.0","source":{"id":"1904.00841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00841","created_at":"2026-05-17T23:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00841v1","created_at":"2026-05-17T23:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00841","created_at":"2026-05-17T23:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"FN7ALGE2PHWI","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FN7ALGE2PHWIF77O","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FN7ALGE2","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:1c18fd5fcf6ea7d374c6699aa0522dff45b59ec69d40fba7e90bc1af0620518a","target":"graph","created_at":"2026-05-17T23:49:45Z","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":"This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator, $$(-\\Delta)^{\\alpha} u=\\lambda u+ (-\\Delta)^{\\beta}|u|^{p-1}u \\quad \\mbox{in}\\quad \\Omega;\\qquad (-\\Delta)^{j}u=0\\quad \\mbox{on}\\quad \\partial\\Omega,\\quad \\mbox{for}\\quad j\\in\\mathbb{Z},\\: 0\\leq j< [\\alpha]$$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^{N}$, $0<\\beta<1$, $\\beta<\\alpha<\\beta+1$ and $\\lambda>0$. In particular, we study the fractional elliptic problem, $$","authors_text":"Alejandro Ortega, Eduardo Colorado, Pablo \\'Alvarez-Caudevilla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-01T13:26:16Z","title":"Positive solutions for semilinear fractional elliptic problems involving an inverse fractional operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00841","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":"sha256:0c85797fd9ff32b18516c1b8b3a2213599bf5dcb5d56b54c03d2dc71606fb65b","target":"record","created_at":"2026-05-17T23:49:45Z","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":"a1b51fe9e6a985968b40d39b01ba3d9458e52544bcaa69196cfb619c72398309","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-01T13:26:16Z","title_canon_sha256":"a37fff06d9cf06b0e70a62eb1e6f12d8f7450288a59d0bbff85dce3cd8d5f5e2"},"schema_version":"1.0","source":{"id":"1904.00841","kind":"arxiv","version":1}},"canonical_sha256":"2b7e05989a79ec82ffee36b681fde391873f29fd8b038598333961facb3c51a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b7e05989a79ec82ffee36b681fde391873f29fd8b038598333961facb3c51a4","first_computed_at":"2026-05-17T23:49:45.346702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:45.346702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fc/jAcSkaBnQoZzZ7xJJoNM6yiTpL1h3feAbFKMGUjoBLhtB4GHGEjby6eODM5+ODH3y1ieaAQLH58SQt0gcBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:45.347123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c85797fd9ff32b18516c1b8b3a2213599bf5dcb5d56b54c03d2dc71606fb65b","sha256:1c18fd5fcf6ea7d374c6699aa0522dff45b59ec69d40fba7e90bc1af0620518a"],"state_sha256":"d47d3c2ed3aa1ad78a6938f284232a86a9d83432051fcef949765bb17c869df0"}