{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GNR7PYADDXCL4ZYPXED33MHOKB","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":"2cbd047d7982bc6d507f30fed49d27997abbe3196b3cfa4ba125e4bf620dafd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-17T10:04:41Z","title_canon_sha256":"0dc593b81643e3ce829f179f9f538fddeafa93a8899915c1478c7df9673e6215"},"schema_version":"1.0","source":{"id":"1508.03964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03964","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03964v1","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03964","created_at":"2026-05-18T01:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"GNR7PYADDXCL","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GNR7PYADDXCL4ZYP","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GNR7PYAD","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:46ea0714bc2b23361a7fe1ad22d9cdc38527472d75769fabb847be3df49a3a69","target":"graph","created_at":"2026-05-18T01:35:13Z","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":"In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation $$ \\epsilon^{2s} (-\\Delta)^{s}{u}+V(z)u=f(u)\\,\\,\\, \\mbox{in} \\,\\,\\, \\mathbb{R}^{N}, $$ where $\\epsilon$ is a positive parameter, $f$ has a subcritical growth, $V$ possesses a local minimum, $N > 2s,$ $s \\in (0,1),$ and $ (-\\Delta)^{s}u$ is the fractional laplacian.","authors_text":"Claudianor O. Alves, Olimpio H. Miyagaki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-17T10:04:41Z","title":"Existence and concentration of solution for a class of fractional elliptic equation in $\\mathbb{R}^N$ via penalization method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03964","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":"sha256:8d59a4ea91f8e186062430b2d60f937b2f67a65b2f4c6dc528037a923b673cbb","target":"record","created_at":"2026-05-18T01:35:13Z","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":"2cbd047d7982bc6d507f30fed49d27997abbe3196b3cfa4ba125e4bf620dafd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-17T10:04:41Z","title_canon_sha256":"0dc593b81643e3ce829f179f9f538fddeafa93a8899915c1478c7df9673e6215"},"schema_version":"1.0","source":{"id":"1508.03964","kind":"arxiv","version":1}},"canonical_sha256":"3363f7e0031dc4be670fb907bdb0ee507a727aeb83f25b9a3c5c17f49771260e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3363f7e0031dc4be670fb907bdb0ee507a727aeb83f25b9a3c5c17f49771260e","first_computed_at":"2026-05-18T01:35:13.241023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:13.241023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ysn5Ey+pEhdo24iYJa01qaRqDAKTjfKsJx2gc/pvEQ3EzSgEGMzPs5fLmEWzvZoEoX9HN6WqwhWXKGVndhn1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:13.241652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d59a4ea91f8e186062430b2d60f937b2f67a65b2f4c6dc528037a923b673cbb","sha256:46ea0714bc2b23361a7fe1ad22d9cdc38527472d75769fabb847be3df49a3a69"],"state_sha256":"5ac67ca715087a719435539a3fdb1aa22d0d0042e8551f298c1ce5ac8c0b0e91"}