{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I2GZY2ZNHXTGTNHLO4OGFPUCS3","short_pith_number":"pith:I2GZY2ZN","canonical_record":{"source":{"id":"1404.1132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-04T02:37:00Z","cross_cats_sorted":[],"title_canon_sha256":"32cd016cdfb8b98ff6cf3c64052c2c172337079efd776ddba36266caf44128bb","abstract_canon_sha256":"77aea7fc078fd2f6b3e08e260a0f90c94ea112024b51b51bc35a5d9daf2b67d9"},"schema_version":"1.0"},"canonical_sha256":"468d9c6b2d3de669b4eb771c62be8296e70bdbc62c5b5748ddbd138cb6f4d15a","source":{"kind":"arxiv","id":"1404.1132","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1132","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1132v2","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1132","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"I2GZY2ZNHXTG","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I2GZY2ZNHXTGTNHL","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I2GZY2ZN","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I2GZY2ZNHXTGTNHLO4OGFPUCS3","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-04T02:37:00Z","cross_cats_sorted":[],"title_canon_sha256":"32cd016cdfb8b98ff6cf3c64052c2c172337079efd776ddba36266caf44128bb","abstract_canon_sha256":"77aea7fc078fd2f6b3e08e260a0f90c94ea112024b51b51bc35a5d9daf2b67d9"},"schema_version":"1.0"},"canonical_sha256":"468d9c6b2d3de669b4eb771c62be8296e70bdbc62c5b5748ddbd138cb6f4d15a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:26.543458Z","signature_b64":"MADU0ezYNcBJKqhMLOarwztXwSsORSyT9XLPOmlC2Dui5n951ViqeLpZRengkuS8aZzk5MUGuJQm5ahBr5vNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"468d9c6b2d3de669b4eb771c62be8296e70bdbc62c5b5748ddbd138cb6f4d15a","last_reissued_at":"2026-05-18T02:25:26.542796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:26.542796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1132","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r+4k69uiKraBsfCq/c4iAL1xrDVZNmSwVjWqX5Snnc26m3w6nIQ2ETXYLPKLfyc6QE7UveaxfZ2O5dpjJQQfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:25:12.066930Z"},"content_sha256":"c828573b0eea2d6af1baa0245a38d865d1e55922acc7d082b41185d7b0154422","schema_version":"1.0","event_id":"sha256:c828573b0eea2d6af1baa0245a38d865d1e55922acc7d082b41185d7b0154422"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I2GZY2ZNHXTGTNHLO4OGFPUCS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinmyoung Seok, Woocheol Choi","submitted_at":"2014-04-04T02:37:00Z","abstract_excerpt":"In this paper, we study a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely many solutions to the fractional Brezis-Nirenberg problems on bounded domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1132","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BpVvKMFNA4rZ8BYCcBRg2tOiKQqGSyZZLDUXBGzRMq2KvF/2dZpBYubn8YPEd7sohxErxvpecrIVZ6mZZG/qDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:25:12.067267Z"},"content_sha256":"82491efd84e396c2c1f972e6f3a5d60c15114071a895c656c3577172f2ec76b0","schema_version":"1.0","event_id":"sha256:82491efd84e396c2c1f972e6f3a5d60c15114071a895c656c3577172f2ec76b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2GZY2ZNHXTGTNHLO4OGFPUCS3/bundle.json","state_url":"https://pith.science/pith/I2GZY2ZNHXTGTNHLO4OGFPUCS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2GZY2ZNHXTGTNHLO4OGFPUCS3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T07:25:12Z","links":{"resolver":"https://pith.science/pith/I2GZY2ZNHXTGTNHLO4OGFPUCS3","bundle":"https://pith.science/pith/I2GZY2ZNHXTGTNHLO4OGFPUCS3/bundle.json","state":"https://pith.science/pith/I2GZY2ZNHXTGTNHLO4OGFPUCS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2GZY2ZNHXTGTNHLO4OGFPUCS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I2GZY2ZNHXTGTNHLO4OGFPUCS3","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":"77aea7fc078fd2f6b3e08e260a0f90c94ea112024b51b51bc35a5d9daf2b67d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-04T02:37:00Z","title_canon_sha256":"32cd016cdfb8b98ff6cf3c64052c2c172337079efd776ddba36266caf44128bb"},"schema_version":"1.0","source":{"id":"1404.1132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1132","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1132v2","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1132","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"I2GZY2ZNHXTG","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I2GZY2ZNHXTGTNHL","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I2GZY2ZN","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:82491efd84e396c2c1f972e6f3a5d60c15114071a895c656c3577172f2ec76b0","target":"graph","created_at":"2026-05-18T02:25:26Z","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 a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely many solutions to the fractional Brezis-Nirenberg problems on bounded domain.","authors_text":"Jinmyoung Seok, Woocheol Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-04T02:37:00Z","title":"Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1132","kind":"arxiv","version":2},"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:c828573b0eea2d6af1baa0245a38d865d1e55922acc7d082b41185d7b0154422","target":"record","created_at":"2026-05-18T02:25:26Z","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":"77aea7fc078fd2f6b3e08e260a0f90c94ea112024b51b51bc35a5d9daf2b67d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-04T02:37:00Z","title_canon_sha256":"32cd016cdfb8b98ff6cf3c64052c2c172337079efd776ddba36266caf44128bb"},"schema_version":"1.0","source":{"id":"1404.1132","kind":"arxiv","version":2}},"canonical_sha256":"468d9c6b2d3de669b4eb771c62be8296e70bdbc62c5b5748ddbd138cb6f4d15a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"468d9c6b2d3de669b4eb771c62be8296e70bdbc62c5b5748ddbd138cb6f4d15a","first_computed_at":"2026-05-18T02:25:26.542796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:26.542796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MADU0ezYNcBJKqhMLOarwztXwSsORSyT9XLPOmlC2Dui5n951ViqeLpZRengkuS8aZzk5MUGuJQm5ahBr5vNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:26.543458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c828573b0eea2d6af1baa0245a38d865d1e55922acc7d082b41185d7b0154422","sha256:82491efd84e396c2c1f972e6f3a5d60c15114071a895c656c3577172f2ec76b0"],"state_sha256":"57aa65f25ad326d8b07b15dd739b9c8df22aefacb1d8c3fd9ce9b1331b3a3bf6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkxEcVsw1hIuMNDXL67gZAfFCSwsVIgu/7j+MlqcqIjguG1K6nrnleyou/pwoWLJGhyz5buBDAsVAPgKDWg1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:25:12.069205Z","bundle_sha256":"35b4fce81b02f02777e51bfba05ac66ae564339c2068dbfde7d33eee064bffa4"}}