{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DLADBYXHDSNHJ7MDI7XMCHULYT","short_pith_number":"pith:DLADBYXH","canonical_record":{"source":{"id":"1904.08316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-17T15:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"203b10a15ccebe76c3b0badc469e6e6ec927d3499720c3ee9dbd35a490bea994","abstract_canon_sha256":"332ddce398702974d33e8069d8964bb6d81eda5167c791f06551f39201b5ed7c"},"schema_version":"1.0"},"canonical_sha256":"1ac030e2e71c9a74fd8347eec11e8bc4cf32325574547c1efc6dcfefcb13404b","source":{"kind":"arxiv","id":"1904.08316","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08316","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08316v1","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08316","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"DLADBYXHDSNH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DLADBYXHDSNHJ7MD","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DLADBYXH","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DLADBYXHDSNHJ7MDI7XMCHULYT","target":"record","payload":{"canonical_record":{"source":{"id":"1904.08316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-17T15:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"203b10a15ccebe76c3b0badc469e6e6ec927d3499720c3ee9dbd35a490bea994","abstract_canon_sha256":"332ddce398702974d33e8069d8964bb6d81eda5167c791f06551f39201b5ed7c"},"schema_version":"1.0"},"canonical_sha256":"1ac030e2e71c9a74fd8347eec11e8bc4cf32325574547c1efc6dcfefcb13404b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:18.037955Z","signature_b64":"mPGaNq0OjQQHFRA/ZTIm0fh4ehnGseJdz4eZOA8yWqpLVgTfHhV1TZSL9S1ig463mzu2bf5CIv6nhQN3DkOzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ac030e2e71c9a74fd8347eec11e8bc4cf32325574547c1efc6dcfefcb13404b","last_reissued_at":"2026-05-17T23:48:18.037462Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:18.037462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.08316","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BoA6CkcT7aXbKuZ7gJmDOAqy6cnAp9XoaAdcKK2A5pjp4iJNRgMCLbsiyyQe2CbsBT8YhJW8FBsEyT1XbGK6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:59:39.272008Z"},"content_sha256":"1d015591ee1f50e94445c87bff052fe20c8035f7ac0e11198de65b967da1d4fe","schema_version":"1.0","event_id":"sha256:1d015591ee1f50e94445c87bff052fe20c8035f7ac0e11198de65b967da1d4fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DLADBYXHDSNHJ7MDI7XMCHULYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solutions for fractional operator problem via local Pohozaev identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianjun Nie, Ting Liu, Yuxia Guo","submitted_at":"2019-04-17T15:26:33Z","abstract_excerpt":"We consider the following fractional Schr\\\"{o}dinger equation involving critical exponent: \\begin{equation*} \\left\\{\\begin{array}{ll} (-\\Delta)^s u+V(|y'|,y'')u=u^{2^*_s-1} \\ \\hbox{ in } \\ \\mathbb{R}^N, \\\\ u>0, \\ y \\in \\mathbb{R}^N, \\end{array}\\right. \\end{equation*} where $s\\in(\\frac{1}{2}, 1)$, $(y',y'')\\in \\mathbb{R}^2\\times \\mathbb{R}^{N-2}$, $V(|y'|,y'')$ is a bounded nonnegative function with a weaker symmetry condition. We prove the existence of infinitely many solutions for the above problem by a finite dimensional reduction method combining various Pohazaev identies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08316","kind":"arxiv","version":1},"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":"2026-05-17T23:48:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oL4xj+9vikFvwkmFNjwk0JaCUpv4Yt8V1Dkme3whS3W2S5fPxPJKV4WhQPrQkkw3txriTERijHkzbpI4i3KbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:59:39.272730Z"},"content_sha256":"2a413e68594281819e8554b97ab22aac19663e008edf2ad76982056f00b6e5d2","schema_version":"1.0","event_id":"sha256:2a413e68594281819e8554b97ab22aac19663e008edf2ad76982056f00b6e5d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DLADBYXHDSNHJ7MDI7XMCHULYT/bundle.json","state_url":"https://pith.science/pith/DLADBYXHDSNHJ7MDI7XMCHULYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DLADBYXHDSNHJ7MDI7XMCHULYT/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":"2026-05-28T21:59:39Z","links":{"resolver":"https://pith.science/pith/DLADBYXHDSNHJ7MDI7XMCHULYT","bundle":"https://pith.science/pith/DLADBYXHDSNHJ7MDI7XMCHULYT/bundle.json","state":"https://pith.science/pith/DLADBYXHDSNHJ7MDI7XMCHULYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DLADBYXHDSNHJ7MDI7XMCHULYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DLADBYXHDSNHJ7MDI7XMCHULYT","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":"332ddce398702974d33e8069d8964bb6d81eda5167c791f06551f39201b5ed7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-17T15:26:33Z","title_canon_sha256":"203b10a15ccebe76c3b0badc469e6e6ec927d3499720c3ee9dbd35a490bea994"},"schema_version":"1.0","source":{"id":"1904.08316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08316","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08316v1","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08316","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"DLADBYXHDSNH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DLADBYXHDSNHJ7MD","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DLADBYXH","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:2a413e68594281819e8554b97ab22aac19663e008edf2ad76982056f00b6e5d2","target":"graph","created_at":"2026-05-17T23:48:18Z","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":"We consider the following fractional Schr\\\"{o}dinger equation involving critical exponent: \\begin{equation*} \\left\\{\\begin{array}{ll} (-\\Delta)^s u+V(|y'|,y'')u=u^{2^*_s-1} \\ \\hbox{ in } \\ \\mathbb{R}^N, \\\\ u>0, \\ y \\in \\mathbb{R}^N, \\end{array}\\right. \\end{equation*} where $s\\in(\\frac{1}{2}, 1)$, $(y',y'')\\in \\mathbb{R}^2\\times \\mathbb{R}^{N-2}$, $V(|y'|,y'')$ is a bounded nonnegative function with a weaker symmetry condition. We prove the existence of infinitely many solutions for the above problem by a finite dimensional reduction method combining various Pohazaev identies.","authors_text":"Jianjun Nie, Ting Liu, Yuxia Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-17T15:26:33Z","title":"Solutions for fractional operator problem via local Pohozaev identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08316","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":"sha256:1d015591ee1f50e94445c87bff052fe20c8035f7ac0e11198de65b967da1d4fe","target":"record","created_at":"2026-05-17T23:48:18Z","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":"332ddce398702974d33e8069d8964bb6d81eda5167c791f06551f39201b5ed7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-17T15:26:33Z","title_canon_sha256":"203b10a15ccebe76c3b0badc469e6e6ec927d3499720c3ee9dbd35a490bea994"},"schema_version":"1.0","source":{"id":"1904.08316","kind":"arxiv","version":1}},"canonical_sha256":"1ac030e2e71c9a74fd8347eec11e8bc4cf32325574547c1efc6dcfefcb13404b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ac030e2e71c9a74fd8347eec11e8bc4cf32325574547c1efc6dcfefcb13404b","first_computed_at":"2026-05-17T23:48:18.037462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:18.037462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPGaNq0OjQQHFRA/ZTIm0fh4ehnGseJdz4eZOA8yWqpLVgTfHhV1TZSL9S1ig463mzu2bf5CIv6nhQN3DkOzCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:18.037955Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d015591ee1f50e94445c87bff052fe20c8035f7ac0e11198de65b967da1d4fe","sha256:2a413e68594281819e8554b97ab22aac19663e008edf2ad76982056f00b6e5d2"],"state_sha256":"9a976d20845e2bc17c679c21eb20b7377068c3fef0de9c3d3ad01020eeb543f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RskU7q1ZZkr3ZdhFt/mrYbL1kjurcR+ZnqptEVhW8jKEz5tqxXRwLbq7eYlYMR8SbGnYKdQS6lEeyaXyE70eDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:59:39.276439Z","bundle_sha256":"3f364b0ed3ce998a5695be4dfa89732b1084e8b5285976ce22d0bb6adb4872c4"}}