{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CJCIAO4UX6LFY5NZOSVUULTOIX","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":"17dc0d2530d30bb673b2cde604380c9ba00f17023843a5a2ad53949e0982c2b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-07T15:21:59Z","title_canon_sha256":"7dae669dc5f580204e4979b7b7c4bd8f98132e56ce25ae683770da09bc611eb0"},"schema_version":"1.0","source":{"id":"1803.02712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02712","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02712v1","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02712","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"CJCIAO4UX6LF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CJCIAO4UX6LFY5NZ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CJCIAO4U","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:011540b42b185af7d4ab806902c1d42d543227e74161c812729a9fdf45312ef1","target":"graph","created_at":"2026-05-18T00:21:49Z","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 consider the Dirichlet problem for the Schr\\\"odinger-H\\'enon system $$ -\\Delta u + \\mu_1 u = |x|^{\\alpha}\\partial_u F(u,v),\\quad \\qquad\n  -\\Delta v + \\mu_2 v = |x|^{\\alpha}\\partial_v F(u,v) $$ in the unit ball $\\Omega \\subset \\mathbb{R}^N, N\\geq 2$, where $\\alpha>-1$ is a parameter and $F: \\mathbb{R}^2 \\to \\mathbb{R}$ is a $p$-homogeneous $C^2$-function for some $p>2$ with $F(u,v)>0$ for $(u,v) \\not = (0,0)$. We show that, as $\\alpha \\to \\infty$, the Morse index of nontrivial radial solutions of this problem (positive or sign-changing) tends to infinity. This result is new even for the corr","authors_text":"Tobias Weth, Zhenluo Lou, Zhitao Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-07T15:21:59Z","title":"Symmetry breaking via Morse index for equations and systems of H\\'enon-Schr\\\"odinger type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02712","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:b78c83f8dbd3efb464cb27ffeec46f0b935bc446d73d9eae314b15c0a65f1d40","target":"record","created_at":"2026-05-18T00:21:49Z","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":"17dc0d2530d30bb673b2cde604380c9ba00f17023843a5a2ad53949e0982c2b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-07T15:21:59Z","title_canon_sha256":"7dae669dc5f580204e4979b7b7c4bd8f98132e56ce25ae683770da09bc611eb0"},"schema_version":"1.0","source":{"id":"1803.02712","kind":"arxiv","version":1}},"canonical_sha256":"1244803b94bf965c75b974ab4a2e6e45fca0a7ebc54bb9ea6afa63a3025c5679","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1244803b94bf965c75b974ab4a2e6e45fca0a7ebc54bb9ea6afa63a3025c5679","first_computed_at":"2026-05-18T00:21:49.441510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:49.441510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jYcEHdrp1s0NLD4ZVMoRKiBC1wiNTlqwEwqvfezZCZqp1foiia/hRgn6HzKPkOcoj2MEs/DdCWH0gaJomKSxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:49.442141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b78c83f8dbd3efb464cb27ffeec46f0b935bc446d73d9eae314b15c0a65f1d40","sha256:011540b42b185af7d4ab806902c1d42d543227e74161c812729a9fdf45312ef1"],"state_sha256":"6eae3a766470ae2652a7c39d5cba2f7f38fa8e4398e32b08ac195a85dce7b06f"}