{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XAEVJ7LGXSBLEROKD24BGJ3I2I","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":"abee0c53c66fef0985e9313f765f4a3e7b9c1256a2f5b59092662f87979b8197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-07-08T10:32:39Z","title_canon_sha256":"e519d0722319b8caee2fc3c167d34e1813c1d56860aaf89a5b943b63d1269103"},"schema_version":"1.0","source":{"id":"2107.03737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03737","created_at":"2026-07-05T02:56:18Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03737v1","created_at":"2026-07-05T02:56:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03737","created_at":"2026-07-05T02:56:18Z"},{"alias_kind":"pith_short_12","alias_value":"XAEVJ7LGXSBL","created_at":"2026-07-05T02:56:18Z"},{"alias_kind":"pith_short_16","alias_value":"XAEVJ7LGXSBLEROK","created_at":"2026-07-05T02:56:18Z"},{"alias_kind":"pith_short_8","alias_value":"XAEVJ7LG","created_at":"2026-07-05T02:56:18Z"}],"graph_snapshots":[{"event_id":"sha256:897a83c9725d3ceb28f78e6b5486f123bf743c4ef955eea1b869bc28290a5512","target":"graph","created_at":"2026-07-05T02:56:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.03737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the existence of bound and ground states for a class of nonlinear elliptic systems in $\\mathbb{R}^N$. These equations involve critical power nonlinearities and Hardy-type singular potentials, coupled by a term containing up to critical powers. More precisely, we find ground states either the positive coupling parameter $\\nu$ is large or $\\nu$ is small under suitable assumptions on the other parameters of the problem. Furthermore, bound states are found as Mountain-Pass-type critical points of the underlying functional constrained on the Nehari manifold. Our variational approach improv","authors_text":"Alejandro Ortega, Eduardo Colorado, Rafael L\\'opez-Soriano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-07-08T10:32:39Z","title":"Existence of bound and ground states for an elliptic system with double criticality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03737","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":"sha256:16fa0861d4a91518354582e2a24798542cf0d7e44ff4d7d4818bb26781ae6d1e","target":"record","created_at":"2026-07-05T02:56:18Z","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":"abee0c53c66fef0985e9313f765f4a3e7b9c1256a2f5b59092662f87979b8197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-07-08T10:32:39Z","title_canon_sha256":"e519d0722319b8caee2fc3c167d34e1813c1d56860aaf89a5b943b63d1269103"},"schema_version":"1.0","source":{"id":"2107.03737","kind":"arxiv","version":1}},"canonical_sha256":"b80954fd66bc82b245ca1eb8132768d206ed8440528c056b477ef7a76f1b0b6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b80954fd66bc82b245ca1eb8132768d206ed8440528c056b477ef7a76f1b0b6c","first_computed_at":"2026-07-05T02:56:18.820672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:56:18.820672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VgWLzIB8pbojDrH+mtXTBlm1IkieApBCvke9fbSvJv+husKxgudsZbnp2aq0ts14FhJRwzz1QVEFnoqW/0j4Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:56:18.821078Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.03737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16fa0861d4a91518354582e2a24798542cf0d7e44ff4d7d4818bb26781ae6d1e","sha256:897a83c9725d3ceb28f78e6b5486f123bf743c4ef955eea1b869bc28290a5512"],"state_sha256":"17b04199829e6093c3fda923438f8643cff1228180bc54b5c01ece3e7d5df9a9"}