{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TPCSWCYQCH4JNA53BHHATEUV7H","short_pith_number":"pith:TPCSWCYQ","schema_version":"1.0","canonical_sha256":"9bc52b0b1011f89683bb09ce099295f9c4c289452644c4e66c30b43b129ced1b","source":{"kind":"arxiv","id":"1904.03905","version":1},"attestation_state":"computed","paper":{"title":"A monotonicity result under symmetry and Morse index constraints in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Gladiali","submitted_at":"2019-04-08T09:30:43Z","abstract_excerpt":"This paper deals with solutions of semilinear elliptic equations of the type \\[ \\left\\{\\begin{array}{ll} -\\Delta u = f(|x|, u) \\qquad & \\text{ in } \\Omega, \\\\ u= 0 & \\text{ on } \\partial \\Omega, \\end{array} \\right. \\] where $\\Omega$ is a radially symmetric domain of the plane that can be bounded or unbounded. We consider solutions $u$ that are invariant by rotations of a certain angle $\\theta$ and which have a bound on their Morse index in spaces of functions invariant by these rotations. We can prove that or $u$ is radial, or, else, there exists a direction $e\\in \\mathcal S$ such that $u$ is "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.03905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-08T09:30:43Z","cross_cats_sorted":[],"title_canon_sha256":"7f5e9c13061ebfe2dec3febf861596378ba47ff25d3c1d89d4b7c5a49fd219eb","abstract_canon_sha256":"bbb9b4d17023babf4d92273639c4be16795ac01fd777bfd5a354e8c6265a9223"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:07.744499Z","signature_b64":"eFZI6rNHFYPlxSMo+8epQSxZvL9omQ3WgNhQGEdA4tU+LMvDZPNAW9IKf3ogad6C0jj+Zwl5fy3VXwvGwn0pCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bc52b0b1011f89683bb09ce099295f9c4c289452644c4e66c30b43b129ced1b","last_reissued_at":"2026-05-17T23:49:07.743836Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:07.743836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A monotonicity result under symmetry and Morse index constraints in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Gladiali","submitted_at":"2019-04-08T09:30:43Z","abstract_excerpt":"This paper deals with solutions of semilinear elliptic equations of the type \\[ \\left\\{\\begin{array}{ll} -\\Delta u = f(|x|, u) \\qquad & \\text{ in } \\Omega, \\\\ u= 0 & \\text{ on } \\partial \\Omega, \\end{array} \\right. \\] where $\\Omega$ is a radially symmetric domain of the plane that can be bounded or unbounded. We consider solutions $u$ that are invariant by rotations of a certain angle $\\theta$ and which have a bound on their Morse index in spaces of functions invariant by these rotations. We can prove that or $u$ is radial, or, else, there exists a direction $e\\in \\mathcal S$ such that $u$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03905","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.03905","created_at":"2026-05-17T23:49:07.743919+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.03905v1","created_at":"2026-05-17T23:49:07.743919+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03905","created_at":"2026-05-17T23:49:07.743919+00:00"},{"alias_kind":"pith_short_12","alias_value":"TPCSWCYQCH4J","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"TPCSWCYQCH4JNA53","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"TPCSWCYQ","created_at":"2026-05-18T12:33:30.264802+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H","json":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H.json","graph_json":"https://pith.science/api/pith-number/TPCSWCYQCH4JNA53BHHATEUV7H/graph.json","events_json":"https://pith.science/api/pith-number/TPCSWCYQCH4JNA53BHHATEUV7H/events.json","paper":"https://pith.science/paper/TPCSWCYQ"},"agent_actions":{"view_html":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H","download_json":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H.json","view_paper":"https://pith.science/paper/TPCSWCYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.03905&json=true","fetch_graph":"https://pith.science/api/pith-number/TPCSWCYQCH4JNA53BHHATEUV7H/graph.json","fetch_events":"https://pith.science/api/pith-number/TPCSWCYQCH4JNA53BHHATEUV7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H/action/storage_attestation","attest_author":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H/action/author_attestation","sign_citation":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H/action/citation_signature","submit_replication":"https://pith.science/pith/TPCSWCYQCH4JNA53BHHATEUV7H/action/replication_record"}},"created_at":"2026-05-17T23:49:07.743919+00:00","updated_at":"2026-05-17T23:49:07.743919+00:00"}