{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OSC225AQ5KY4SWNLPNWMASNO3N","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":"5ef86f12828a8b66699d69a8e37cac3ae69c816050048d88340e0df5fe4b5070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-08T03:57:00Z","title_canon_sha256":"8a147339a2029d3c0841775ecf0a222874d8b16c35800e97b8551d4cf8c49a04"},"schema_version":"1.0","source":{"id":"1601.01766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01766","created_at":"2026-05-18T01:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01766v1","created_at":"2026-05-18T01:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01766","created_at":"2026-05-18T01:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"OSC225AQ5KY4","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OSC225AQ5KY4SWNL","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OSC225AQ","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:275e837e6fafa4937697d4f69928e175247d9c611c11df741c33ddcd18b09819","target":"graph","created_at":"2026-05-18T01:23:11Z","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 the present paper, we study the effect of an elliptic operator in divergence form L defined in a bounded open set on the existence and nonexistence of positive solutions of the associated nonlocal Brezis-Nirenberg problem involving powers of L.","authors_text":"Ko-Shin Chen, Marcos Montenegro, Xiaodong Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-08T03:57:00Z","title":"The Brezis-Nirenberg problem for fractional elliptic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01766","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:a310d5445ab8bae2f966885d32d30eb17a488ecb04683f28b1d9b2123244c037","target":"record","created_at":"2026-05-18T01:23:11Z","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":"5ef86f12828a8b66699d69a8e37cac3ae69c816050048d88340e0df5fe4b5070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-08T03:57:00Z","title_canon_sha256":"8a147339a2029d3c0841775ecf0a222874d8b16c35800e97b8551d4cf8c49a04"},"schema_version":"1.0","source":{"id":"1601.01766","kind":"arxiv","version":1}},"canonical_sha256":"7485ad7410eab1c959ab7b6cc049aedb56796f7c876af1a7b57090e25915aeb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7485ad7410eab1c959ab7b6cc049aedb56796f7c876af1a7b57090e25915aeb3","first_computed_at":"2026-05-18T01:23:11.352059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:11.352059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kBc9KQ6qPh+0N1tKt46kRm8yYLghocb3e1iM7P0kuD/X6zMsS2x6dy+36YzM1t2jxKetIE3G1c0zQYMBJvajDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:11.352610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a310d5445ab8bae2f966885d32d30eb17a488ecb04683f28b1d9b2123244c037","sha256:275e837e6fafa4937697d4f69928e175247d9c611c11df741c33ddcd18b09819"],"state_sha256":"02925c824ac3cf9af7a4b001c4b4e906453eb7b53fc3ee45ad485ca24e4cd685"}