{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RCP65SH4WPNYBW7AF7MXXOEWVU","short_pith_number":"pith:RCP65SH4","schema_version":"1.0","canonical_sha256":"889feec8fcb3db80dbe02fd97bb896ad18f129ef56b83946caee07fde241d366","source":{"kind":"arxiv","id":"1110.1157","version":1},"attestation_state":"computed","paper":{"title":"Construction of Blow-up Sequence for the Conformal Scalar Curvature Equation on S^n. I, II, and Appendix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Man Chun Leung","submitted_at":"2011-10-06T06:01:40Z","abstract_excerpt":"Using the Lyapunov-Schmidt reduction method, we describe how to use annular domains to construct (scalar curvature) functions on S^n, (n > 5), so that each one of them enables the conformal scalar curvature equation to have a blowing-up sequence of positive solutions. The prescribed scalar curvature function is shown to have C^{n - 1, \\beta} smoothness."},"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":"1110.1157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-06T06:01:40Z","cross_cats_sorted":[],"title_canon_sha256":"27648c00b9eaa6c9c08d3aec08c159ea06f4a12b4e065df71226beb49ea32e0d","abstract_canon_sha256":"81f56dacc2d3ec309da040743cec50384745ad4212da534073a92b1fcc3d6eca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:39.137728Z","signature_b64":"3wTvau0Cpqy8cL2Y7VuiUpvrd+aQhfoicFboGwvbxXWmf8bQkfsJx5MXrfB3JyHzSyH+pyob4DcQp+X/NnvNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"889feec8fcb3db80dbe02fd97bb896ad18f129ef56b83946caee07fde241d366","last_reissued_at":"2026-05-18T04:11:39.137224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:39.137224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of Blow-up Sequence for the Conformal Scalar Curvature Equation on S^n. I, II, and Appendix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Man Chun Leung","submitted_at":"2011-10-06T06:01:40Z","abstract_excerpt":"Using the Lyapunov-Schmidt reduction method, we describe how to use annular domains to construct (scalar curvature) functions on S^n, (n > 5), so that each one of them enables the conformal scalar curvature equation to have a blowing-up sequence of positive solutions. The prescribed scalar curvature function is shown to have C^{n - 1, \\beta} smoothness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1157","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":"1110.1157","created_at":"2026-05-18T04:11:39.137297+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1157v1","created_at":"2026-05-18T04:11:39.137297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1157","created_at":"2026-05-18T04:11:39.137297+00:00"},{"alias_kind":"pith_short_12","alias_value":"RCP65SH4WPNY","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RCP65SH4WPNYBW7A","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RCP65SH4","created_at":"2026-05-18T12:26:41.206345+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/RCP65SH4WPNYBW7AF7MXXOEWVU","json":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU.json","graph_json":"https://pith.science/api/pith-number/RCP65SH4WPNYBW7AF7MXXOEWVU/graph.json","events_json":"https://pith.science/api/pith-number/RCP65SH4WPNYBW7AF7MXXOEWVU/events.json","paper":"https://pith.science/paper/RCP65SH4"},"agent_actions":{"view_html":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU","download_json":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU.json","view_paper":"https://pith.science/paper/RCP65SH4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1157&json=true","fetch_graph":"https://pith.science/api/pith-number/RCP65SH4WPNYBW7AF7MXXOEWVU/graph.json","fetch_events":"https://pith.science/api/pith-number/RCP65SH4WPNYBW7AF7MXXOEWVU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU/action/storage_attestation","attest_author":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU/action/author_attestation","sign_citation":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU/action/citation_signature","submit_replication":"https://pith.science/pith/RCP65SH4WPNYBW7AF7MXXOEWVU/action/replication_record"}},"created_at":"2026-05-18T04:11:39.137297+00:00","updated_at":"2026-05-18T04:11:39.137297+00:00"}