{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LOPTOPE3NTQ47R6W6JKDSS2TIB","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":"3708d5b40e600fd5be15a3f904857abd59b20035dc04715e966e1831472f1acd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T13:28:16Z","title_canon_sha256":"70f3ebe1a82f2de043f078c59e81c8c1e45f84bbf55e80a6157b144c1987ce3f"},"schema_version":"1.0","source":{"id":"1310.8492","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8492","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8492v3","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8492","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"pith_short_12","alias_value":"LOPTOPE3NTQ4","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LOPTOPE3NTQ47R6W","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LOPTOPE3","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:3a1bcf94e3001fe43d98ff3fe78e9336fedbc5153a15d6e42c02c90ab9db25c3","target":"graph","created_at":"2026-05-18T02:43:00Z","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 existence of positive bound states for the nonlinear elliptic system \\[ \\begin{cases} - \\Delta u_i + \\lambda_i u_i = \\sum_{j=1}^d \\beta_{ij} u_j^2 u_i & \\text{in $\\Omega$} \\\\ u_1 =\\cdots = u_d=0 & \\text{on $\\partial \\Omega$}, \\end{cases} \\] where $d \\ge 2$, $\\beta_{ij}= \\beta_{ji}$, $\\beta_{ii},\\lambda_i >0$, and $\\Omega$ is either a bounded domain of $\\mathbb{R}^N$, or $\\Omega=\\mathbb{R}^N$, with $N \\le 3$. In light of its applicability in several physical contexts, the problem has been intensively studied in recent years, and several results concerning existence, multiplicity an","authors_text":"Nicola Soave","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T13:28:16Z","title":"On existence and phase separation of solitary waves for nonlinear Schr\\\"odinger systems modelling simultaneous cooperation and competition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8492","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":"sha256:32816624c32035134710e05cdd18b9b25d80aa3a8466b6f4202863271ef4d00a","target":"record","created_at":"2026-05-18T02:43:00Z","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":"3708d5b40e600fd5be15a3f904857abd59b20035dc04715e966e1831472f1acd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T13:28:16Z","title_canon_sha256":"70f3ebe1a82f2de043f078c59e81c8c1e45f84bbf55e80a6157b144c1987ce3f"},"schema_version":"1.0","source":{"id":"1310.8492","kind":"arxiv","version":3}},"canonical_sha256":"5b9f373c9b6ce1cfc7d6f254394b534057cbcf2c1373d5b93d75fdccde06f3e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b9f373c9b6ce1cfc7d6f254394b534057cbcf2c1373d5b93d75fdccde06f3e5","first_computed_at":"2026-05-18T02:43:00.723696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:00.723696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t29hcWpbJqzdEQmuh2TBOU/nfJnvGawa5i4dKg9m9/wovnP0tNRvxcCCSpe/KJJCu5/x2R04809KOoWRngAUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:00.724259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8492","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32816624c32035134710e05cdd18b9b25d80aa3a8466b6f4202863271ef4d00a","sha256:3a1bcf94e3001fe43d98ff3fe78e9336fedbc5153a15d6e42c02c90ab9db25c3"],"state_sha256":"f3286d9412553bbba9876dcc661a6c5f935b9567545de8e33964a2e476d2e486"}