{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:ECOWSBP7W2NS6MYINJADUZA35T","short_pith_number":"pith:ECOWSBP7","schema_version":"1.0","canonical_sha256":"209d6905ffb69b2f33086a403a641bece70f664eca8448dab9204586e6ce6ec2","source":{"kind":"arxiv","id":"2009.02069","version":2},"attestation_state":"computed","paper":{"title":"Large singular solutions for conformal $Q$-curvature equations on $\\mathbb{S}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Yang, Xusheng Du","submitted_at":"2020-09-04T08:45:57Z","abstract_excerpt":"In this paper, we study the existence of positive functions $K \\in C^1(\\mathbb{S}^n)$ such that the conformal $Q$-curvature equation \\begin{equation}\\label{001} P_m (v) =K v^{\\frac{n+2m}{n-2m}}~~~~~~ {on} ~ \\mathbb{S}^n \\{equation} has a singular positive solution $v$ whose singular set is a single point, where $m$ is an integer satisfying $1 \\leq m < n/2$ and $P_m$ is the intertwining operator of order $2m$. More specifically, we show that when $n\\geq 2m+4$, every positive function in $C^1(\\mathbb{S}^n)$ can be approximated in the $C^1(\\mathbb{S}^n)$ norm by a positive function $K\\in C^1(\\mat"},"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":"2009.02069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-09-04T08:45:57Z","cross_cats_sorted":[],"title_canon_sha256":"59c2ef890f069dd84996c4c83404c1991e94ce833b839fac0348575e2a6e8041","abstract_canon_sha256":"be24ca18a18d2b9a98b77e8f818e982aaf82d4becca946bbcb0359f00c6821b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:37:55.653749Z","signature_b64":"1DF40uHZQu6oCa3kY4NKsHXQwIOHV3+9+TGoDoUHCT3q1kSe/YtZiU0wf1c4z000Pn8q6D3PIfn6Onmp5UIzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"209d6905ffb69b2f33086a403a641bece70f664eca8448dab9204586e6ce6ec2","last_reissued_at":"2026-07-05T01:37:55.653343Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:37:55.653343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large singular solutions for conformal $Q$-curvature equations on $\\mathbb{S}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Yang, Xusheng Du","submitted_at":"2020-09-04T08:45:57Z","abstract_excerpt":"In this paper, we study the existence of positive functions $K \\in C^1(\\mathbb{S}^n)$ such that the conformal $Q$-curvature equation \\begin{equation}\\label{001} P_m (v) =K v^{\\frac{n+2m}{n-2m}}~~~~~~ {on} ~ \\mathbb{S}^n \\{equation} has a singular positive solution $v$ whose singular set is a single point, where $m$ is an integer satisfying $1 \\leq m < n/2$ and $P_m$ is the intertwining operator of order $2m$. More specifically, we show that when $n\\geq 2m+4$, every positive function in $C^1(\\mathbb{S}^n)$ can be approximated in the $C^1(\\mathbb{S}^n)$ norm by a positive function $K\\in C^1(\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02069","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.02069/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2009.02069","created_at":"2026-07-05T01:37:55.653401+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.02069v2","created_at":"2026-07-05T01:37:55.653401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.02069","created_at":"2026-07-05T01:37:55.653401+00:00"},{"alias_kind":"pith_short_12","alias_value":"ECOWSBP7W2NS","created_at":"2026-07-05T01:37:55.653401+00:00"},{"alias_kind":"pith_short_16","alias_value":"ECOWSBP7W2NS6MYI","created_at":"2026-07-05T01:37:55.653401+00:00"},{"alias_kind":"pith_short_8","alias_value":"ECOWSBP7","created_at":"2026-07-05T01:37:55.653401+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/ECOWSBP7W2NS6MYINJADUZA35T","json":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T.json","graph_json":"https://pith.science/api/pith-number/ECOWSBP7W2NS6MYINJADUZA35T/graph.json","events_json":"https://pith.science/api/pith-number/ECOWSBP7W2NS6MYINJADUZA35T/events.json","paper":"https://pith.science/paper/ECOWSBP7"},"agent_actions":{"view_html":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T","download_json":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T.json","view_paper":"https://pith.science/paper/ECOWSBP7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.02069&json=true","fetch_graph":"https://pith.science/api/pith-number/ECOWSBP7W2NS6MYINJADUZA35T/graph.json","fetch_events":"https://pith.science/api/pith-number/ECOWSBP7W2NS6MYINJADUZA35T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T/action/storage_attestation","attest_author":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T/action/author_attestation","sign_citation":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T/action/citation_signature","submit_replication":"https://pith.science/pith/ECOWSBP7W2NS6MYINJADUZA35T/action/replication_record"}},"created_at":"2026-07-05T01:37:55.653401+00:00","updated_at":"2026-07-05T01:37:55.653401+00:00"}