{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZMLOTYQVNM3WDBBOCZEYVGUKG4","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":"7eb5badd4c6a2da62b6c3d3b747b0acc3200c0385aef5d10031257251f28ef4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-13T09:34:34Z","title_canon_sha256":"7d90606b93d1855a3d9c2b7cbf58226df769d7a588436be9b5bacf01107d79f0"},"schema_version":"1.0","source":{"id":"1403.3211","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3211","created_at":"2026-05-18T02:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3211v3","created_at":"2026-05-18T02:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3211","created_at":"2026-05-18T02:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZMLOTYQVNM3W","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZMLOTYQVNM3WDBBO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZMLOTYQV","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:66c4d376a2cc477a074c5cec99692bd163beec115bc68d440bf1daacf4fbfdd0","target":"graph","created_at":"2026-05-18T02:47:15Z","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 study the following problem \\[ \\begin{cases} -\\Delta u = \\lambda u + u^{2^*-2} v & \\hbox{in} \\Omega,\\\\ -\\Delta v= \\mu v^{2^*-1} + u^{2^*-1} & \\hbox{in} \\Omega,\\\\ u> 0,v> 0 & \\hbox{in} \\Omega,\\\\ u=v=0 & \\hbox{on} \\partial \\Omega, \\end{cases} \\] where $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $N\\geq 4$, $2^*=2N/(N-2)$, $\\lambda\\in\\mathbb{R}$ and $\\mu\\geq 0$ and we obtain existence and nonexistence results, depending on the value of the parameters $\\lambda$ and $\\mu$.","authors_text":"Jaros{\\l}aw Mederski, Pietro d'Avenia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-13T09:34:34Z","title":"Positive ground states for a system of Schr\\\"odinger equations with critically growing nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3211","kind":"arxiv","version":3},"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":"sha256:4ad1af0e37b08fe5992b91cef1656abaa00f24fd889ed1f51a3b9e35bfcac0f7","target":"record","created_at":"2026-05-18T02:47:15Z","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":"7eb5badd4c6a2da62b6c3d3b747b0acc3200c0385aef5d10031257251f28ef4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-13T09:34:34Z","title_canon_sha256":"7d90606b93d1855a3d9c2b7cbf58226df769d7a588436be9b5bacf01107d79f0"},"schema_version":"1.0","source":{"id":"1403.3211","kind":"arxiv","version":3}},"canonical_sha256":"cb16e9e2156b3761842e16498a9a8a372dbf93885c47efd7e2f1f89dcaebf423","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb16e9e2156b3761842e16498a9a8a372dbf93885c47efd7e2f1f89dcaebf423","first_computed_at":"2026-05-18T02:47:15.511189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:15.511189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7COrtVTjNGKnBk3p1afGIIimIkDRr/j/tJjhurDB2buYuhnWxwJim+DK7e3iN3DaCfni8M0oGBKqHZGZUTrOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:15.511926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3211","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ad1af0e37b08fe5992b91cef1656abaa00f24fd889ed1f51a3b9e35bfcac0f7","sha256:66c4d376a2cc477a074c5cec99692bd163beec115bc68d440bf1daacf4fbfdd0"],"state_sha256":"1cda711ce78163467db8e786b55275b4127c19d272efdc23220ad49b3a1679fd"}