{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WVKPJBKNYCX5FD3ORNIUXJR6IF","short_pith_number":"pith:WVKPJBKN","schema_version":"1.0","canonical_sha256":"b554f4854dc0afd28f6e8b514ba63e41443605417e785dd00858690c43e41683","source":{"kind":"arxiv","id":"1001.4729","version":1},"attestation_state":"computed","paper":{"title":"On the uniqueness of sign changing bound state solutions of a semilinear equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carmen Cortazar, Cecilia Yarur, Marta Garcia-Huidobro","submitted_at":"2010-01-26T15:51:12Z","abstract_excerpt":"We establish the uniqueness of the higher radial bound state solutions of $$ \\Delta u +f(u)=0,\\quad x\\in \\RR^n. \\leqno(P) $$ We assume that the nonlinearity $f\\in C(-\\infty,\\infty)$ is an odd function satisfying some convexity and growth conditions, and either has one zero at $b>0$, is non positive and not identically 0 in $(0,b)$, and is differentiable and positive $[b,\\infty)$, or is positive and differentiable in $[0,\\infty)$."},"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":"1001.4729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-26T15:51:12Z","cross_cats_sorted":[],"title_canon_sha256":"caa8c2f3105485d50c3b411193573fb2c525c6e7a13c0d826427287d0ead3c13","abstract_canon_sha256":"909d0fdeaeee5522703032ee3513b8726c3c0bf5240c134c30eb437e511609e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:29.711016Z","signature_b64":"cnx1XWABjDZibfA7WllYL0h4Rko9IdOKNIvh91MMJBSXKs0zcntr/OUkRgWGf5Y9BxfHvdR8B/UomFowrxg7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b554f4854dc0afd28f6e8b514ba63e41443605417e785dd00858690c43e41683","last_reissued_at":"2026-05-18T02:09:29.710314Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:29.710314Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the uniqueness of sign changing bound state solutions of a semilinear equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carmen Cortazar, Cecilia Yarur, Marta Garcia-Huidobro","submitted_at":"2010-01-26T15:51:12Z","abstract_excerpt":"We establish the uniqueness of the higher radial bound state solutions of $$ \\Delta u +f(u)=0,\\quad x\\in \\RR^n. \\leqno(P) $$ We assume that the nonlinearity $f\\in C(-\\infty,\\infty)$ is an odd function satisfying some convexity and growth conditions, and either has one zero at $b>0$, is non positive and not identically 0 in $(0,b)$, and is differentiable and positive $[b,\\infty)$, or is positive and differentiable in $[0,\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4729","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":"1001.4729","created_at":"2026-05-18T02:09:29.710423+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.4729v1","created_at":"2026-05-18T02:09:29.710423+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4729","created_at":"2026-05-18T02:09:29.710423+00:00"},{"alias_kind":"pith_short_12","alias_value":"WVKPJBKNYCX5","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"WVKPJBKNYCX5FD3O","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"WVKPJBKN","created_at":"2026-05-18T12:26:17.028572+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/WVKPJBKNYCX5FD3ORNIUXJR6IF","json":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF.json","graph_json":"https://pith.science/api/pith-number/WVKPJBKNYCX5FD3ORNIUXJR6IF/graph.json","events_json":"https://pith.science/api/pith-number/WVKPJBKNYCX5FD3ORNIUXJR6IF/events.json","paper":"https://pith.science/paper/WVKPJBKN"},"agent_actions":{"view_html":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF","download_json":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF.json","view_paper":"https://pith.science/paper/WVKPJBKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.4729&json=true","fetch_graph":"https://pith.science/api/pith-number/WVKPJBKNYCX5FD3ORNIUXJR6IF/graph.json","fetch_events":"https://pith.science/api/pith-number/WVKPJBKNYCX5FD3ORNIUXJR6IF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF/action/storage_attestation","attest_author":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF/action/author_attestation","sign_citation":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF/action/citation_signature","submit_replication":"https://pith.science/pith/WVKPJBKNYCX5FD3ORNIUXJR6IF/action/replication_record"}},"created_at":"2026-05-18T02:09:29.710423+00:00","updated_at":"2026-05-18T02:09:29.710423+00:00"}