{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2F2UYD5PIULC6526MOES3HFVR2","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":"82284dc063c2d3b7cb3a802e38213579e5d7a69cab32493fd36e0e8640cb121a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-25T06:54:38Z","title_canon_sha256":"aa03c165e7228ad0b8e1a5f556a13621eafa6662322165014af07ef64ddbbe9a"},"schema_version":"1.0","source":{"id":"1705.09068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09068","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09068v1","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09068","created_at":"2026-05-18T00:43:40Z"},{"alias_kind":"pith_short_12","alias_value":"2F2UYD5PIULC","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2F2UYD5PIULC6526","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2F2UYD5P","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:50152104f294e857caf12ce76c3dd1ea17ce5e8f4e118f9b42e0fd5f4bcfb76e","target":"graph","created_at":"2026-05-18T00:43:40Z","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 investigate existence and non-existence of a nontrivial solution to the pseudo-relativistic nonlinear Schr\\\"odinger equation $$\\left( \\sqrt{-c^2\\Delta + m^2 c^4}-mc^2\\right) u + \\mu u = |u|^{p-1}u\\quad \\textrm{in}~\\mathbb{R}^n~(n \\geq 2)$$ involving an $H^{1/2}$-critical/supercritical power-type nonlinearity, i.e., $p \\geq \\frac{n+1}{n-1}$. We prove that in the non-relativistic regime, there exists a nontrivial solution provided that the nonlinearity is $H^{1/2}$-critical/supercritical but it is $H^1$-subcritical. On the other hand, we also show that there is no nontrivial bo","authors_text":"Jinmyoung Seok, Woocheol Choi, Younghun Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-25T06:54:38Z","title":"On critical and supercritical pseudo-relativistic nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09068","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":"sha256:5c83e2170bac8621340da3f32e84713c66bfbadf91be98f998b47fc36f1cdcfc","target":"record","created_at":"2026-05-18T00:43:40Z","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":"82284dc063c2d3b7cb3a802e38213579e5d7a69cab32493fd36e0e8640cb121a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-25T06:54:38Z","title_canon_sha256":"aa03c165e7228ad0b8e1a5f556a13621eafa6662322165014af07ef64ddbbe9a"},"schema_version":"1.0","source":{"id":"1705.09068","kind":"arxiv","version":1}},"canonical_sha256":"d1754c0faf45162f775e63892d9cb58ea239a34727badf63672091cb8afbecb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1754c0faf45162f775e63892d9cb58ea239a34727badf63672091cb8afbecb0","first_computed_at":"2026-05-18T00:43:40.496858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:40.496858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8kI0lO832l4GdGOdftM+/knsRUGSot9fznFzmIoDdWFYveqw1go7hcr+izM8VzDIljh+excjqZjrilZBIEhqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:40.497339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c83e2170bac8621340da3f32e84713c66bfbadf91be98f998b47fc36f1cdcfc","sha256:50152104f294e857caf12ce76c3dd1ea17ce5e8f4e118f9b42e0fd5f4bcfb76e"],"state_sha256":"f65186f31df815526284d161e1ac6a0cce69c5c183a208bc69b5418bb6b05d15"}