{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WVKPJBKNYCX5FD3ORNIUXJR6IF","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":"909d0fdeaeee5522703032ee3513b8726c3c0bf5240c134c30eb437e511609e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-26T15:51:12Z","title_canon_sha256":"caa8c2f3105485d50c3b411193573fb2c525c6e7a13c0d826427287d0ead3c13"},"schema_version":"1.0","source":{"id":"1001.4729","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4729","created_at":"2026-05-18T02:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4729v1","created_at":"2026-05-18T02:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4729","created_at":"2026-05-18T02:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"WVKPJBKNYCX5","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WVKPJBKNYCX5FD3O","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WVKPJBKN","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d9b8a7ea7ad494c8b53a5f2e0121c1e8dd248173040431134a071e57fb578f5a","target":"graph","created_at":"2026-05-18T02:09:29Z","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 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 $[0,\\infty)$.","authors_text":"Carmen Cortazar, Cecilia Yarur, Marta Garcia-Huidobro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-26T15:51:12Z","title":"On the uniqueness of sign changing bound state solutions of a semilinear equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4729","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:f2aba810d370b3752f609966eceeca8dc9aa699f9f1d6cdc23b15742ea9df7bf","target":"record","created_at":"2026-05-18T02:09:29Z","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":"909d0fdeaeee5522703032ee3513b8726c3c0bf5240c134c30eb437e511609e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-26T15:51:12Z","title_canon_sha256":"caa8c2f3105485d50c3b411193573fb2c525c6e7a13c0d826427287d0ead3c13"},"schema_version":"1.0","source":{"id":"1001.4729","kind":"arxiv","version":1}},"canonical_sha256":"b554f4854dc0afd28f6e8b514ba63e41443605417e785dd00858690c43e41683","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b554f4854dc0afd28f6e8b514ba63e41443605417e785dd00858690c43e41683","first_computed_at":"2026-05-18T02:09:29.710314Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:29.710314Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cnx1XWABjDZibfA7WllYL0h4Rko9IdOKNIvh91MMJBSXKs0zcntr/OUkRgWGf5Y9BxfHvdR8B/UomFowrxg7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:29.711016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.4729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2aba810d370b3752f609966eceeca8dc9aa699f9f1d6cdc23b15742ea9df7bf","sha256:d9b8a7ea7ad494c8b53a5f2e0121c1e8dd248173040431134a071e57fb578f5a"],"state_sha256":"ec86538ae58fd786c1d321c23a545520ca0fee5eb2ae5b7e74dc5527a9ca04cd"}