{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4OLXKYPWM6PQIH4SNTAON4FC6O","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":"6a8f3714793ba81b690dbf0c960ed17affc2d21828849d9971d19da561813efd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-20T11:43:43Z","title_canon_sha256":"91208b6ac90cc87ee16e9b90a50be09f11d2b67015d3c8f0ce06868a0f99e862"},"schema_version":"1.0","source":{"id":"1408.4613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4613","created_at":"2026-05-18T01:28:05Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4613v1","created_at":"2026-05-18T01:28:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4613","created_at":"2026-05-18T01:28:05Z"},{"alias_kind":"pith_short_12","alias_value":"4OLXKYPWM6PQ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4OLXKYPWM6PQIH4S","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4OLXKYPW","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:09417db3d02339ba05c14f482e18c4de21421e0fae39236b92589f3c53ed14f4","target":"graph","created_at":"2026-05-18T01:28:05Z","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 study local bifurcations of an indefinite elliptic system with multiple components: \\begin{equation*}\n  \\left\\{\\begin{array}{ll}\n  -\\Delta u_j + au_j = \\mu_ju_j^3+\\beta\\sum_{k\\ne j}u_k^2u_j,\n  u_j>0\\ \\ \\hbox{in}\\ \\Omega, u_j=0 \\ \\ \\hbox{on}\\ \\partial\\Omega,\\ j=1,\\dots,n.\n  \\end{array}\n  \\right. \\end{equation*} Here $\\Omega\\subset{\\mathbb{R}}^N$ is a smooth and bounded domain, $n\\ge3$, $a<-\\Lambda_1$ where $\\Lambda_1$ is the principal eigenvalue of $(-\\Delta, H_0^1(\\Omega))$; $\\mu_j$ and $\\beta$ are real constants. Using the positive and non-degenerate solution of the scalar e","authors_text":"Rushun Tian, Thomas Bartsch, Zhi-qiang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-20T11:43:43Z","title":"Bifurcations for a Coupled Schr\\\"odinger System with Multiple Components"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4613","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":"sha256:9371b31dacd2f30d3d5df876ed1048bbaf74934762a4f2fb15d6300813dfda8e","target":"record","created_at":"2026-05-18T01:28:05Z","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":"6a8f3714793ba81b690dbf0c960ed17affc2d21828849d9971d19da561813efd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-20T11:43:43Z","title_canon_sha256":"91208b6ac90cc87ee16e9b90a50be09f11d2b67015d3c8f0ce06868a0f99e862"},"schema_version":"1.0","source":{"id":"1408.4613","kind":"arxiv","version":1}},"canonical_sha256":"e3977561f6679f041f926cc0e6f0a2f399ae0e94ef3da8645153cbae629fb386","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3977561f6679f041f926cc0e6f0a2f399ae0e94ef3da8645153cbae629fb386","first_computed_at":"2026-05-18T01:28:05.879409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:05.879409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yucAGhI50PGSYbgsQ6t+GypaOAP3DFUi7F7Lg/0YA8vzt+4luJZQOSpd1UWOWN4X/9MIIg8/rhmvWVf32IWKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:05.879942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9371b31dacd2f30d3d5df876ed1048bbaf74934762a4f2fb15d6300813dfda8e","sha256:09417db3d02339ba05c14f482e18c4de21421e0fae39236b92589f3c53ed14f4"],"state_sha256":"91e6e2267969e8bba961d583225ff1be0c79abcb95f29623e08bc729a2700314"}