{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:72DTNF4ABODNZ5HHSU376H5DVL","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":"b0f8abeb60eff675b5eac90f050bafb3b0c0b09165676b9afd06ebd0b135408d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-01T18:02:01Z","title_canon_sha256":"9a244e25b8d348ffb227816dbbd27efafc17fe1bfaa79361415db40d7ec6c04b"},"schema_version":"1.0","source":{"id":"1708.00457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00457","created_at":"2026-05-18T00:38:47Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00457v1","created_at":"2026-05-18T00:38:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00457","created_at":"2026-05-18T00:38:47Z"},{"alias_kind":"pith_short_12","alias_value":"72DTNF4ABODN","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"72DTNF4ABODNZ5HH","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"72DTNF4A","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:0bd957123c770eae32c19d439bf560d21cfa6bad15cc5ad6050a689fa74a0391","target":"graph","created_at":"2026-05-18T00:38:47Z","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 prove the existence of a nonnegative ground state solution to the following class of coupled systems involving Schr\\\"{o}dinger equations with square root of the Laplacian\n  $$\n  \\left\\{\n  \\begin{array}{lr}\n  (-\\Delta)^{1/2}u+V_{1}(x)u=f_{1}(u)+\\lambda(x)v, & x\\in\\mathbb{R},\n  (-\\Delta)^{1/2}v+V_{2}(x)v=f_{2}(v)+\\lambda(x)u, & x\\in\\mathbb{R},\n  \\end{array}\n  \\right.\n  $$\n  where the nonlinearities $f_{1}(s)$ and $f_{2}(s)$ have exponential critical growth of the Trudinger-Moser type, the potentials $V_{1}(x)$ and $V_{2}(x)$ are nonnegative and periodic. Moreover, we assume that","authors_text":"Jo\\~ao Marcos do \\'O, Jos\\'e Carlos de Albuquerque","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-01T18:02:01Z","title":"Coupled elliptic systems involving the square root of the Laplacian and Trudinger-Moser critical growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00457","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":"sha256:134d8b1b2f00c27416a987777e8afb324f36ec630075932e0f60ff3e25f4508a","target":"record","created_at":"2026-05-18T00:38:47Z","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":"b0f8abeb60eff675b5eac90f050bafb3b0c0b09165676b9afd06ebd0b135408d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-01T18:02:01Z","title_canon_sha256":"9a244e25b8d348ffb227816dbbd27efafc17fe1bfaa79361415db40d7ec6c04b"},"schema_version":"1.0","source":{"id":"1708.00457","kind":"arxiv","version":1}},"canonical_sha256":"fe873697800b86dcf4e79537ff1fa3aacab7d00dff9737b329b91b2d51686e80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe873697800b86dcf4e79537ff1fa3aacab7d00dff9737b329b91b2d51686e80","first_computed_at":"2026-05-18T00:38:47.118804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:47.118804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jN0neA+xLvYfITa5TkjGcXyk9nPy/SYpsgyuRjtMzpuldQDXAOmOVzCxXwRPiK0D2KR0kBZY7+vF6cIfk+CnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:47.119557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:134d8b1b2f00c27416a987777e8afb324f36ec630075932e0f60ff3e25f4508a","sha256:0bd957123c770eae32c19d439bf560d21cfa6bad15cc5ad6050a689fa74a0391"],"state_sha256":"e2be0d1f4db2b8b5d31b917051be56cc41961324b2a091d5cdf8cfabcfb3cf94"}