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This amounts to finding a positive solution to \\[ P_g (u)= c u^{\\frac{N+4}{N-4}}, u>0 {on} M\\] where $P_g$ is the Paneitz operator. We show that for dimensions $N \\geq 25$, the set of all positive solutions to the prescribed $Q$ curvature problem is {\\em non-compact}."},"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":"0903.3446","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-03-20T02:56:26Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"41da246bdd006a4d1b0d4586d4116c70b18f6fab35a57fa8dab128d3e24d7476","abstract_canon_sha256":"fc588fd6715655c46b25e5c0df1a18a17ea986413beee7b07a3c2bcda562ab1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:23.496197Z","signature_b64":"trN7nb0baqBY0qOp7fXr6WKV4B0qsYetMAqhC7coGIjUWQymCz6d+ltVFMEbaPViMqxvirb+5ypGtHiDckJpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bebaa512d2cd8f1efb45b441cd00a84b0a958f32941bca3b571c977c22681139","last_reissued_at":"2026-05-18T04:20:23.495465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:23.495465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-compactness of the Prescribed Q-curvature Problem in Large Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Chunyi Zhao, Juncheng Wei","submitted_at":"2009-03-20T02:56:26Z","abstract_excerpt":"Let $(M, g)$ be a compact Riemannian manifold of dimension $N \\geq 5$ and $Q_g$ be its $Q$ curvature. The prescribed $Q$ curvature problem is concerned with finding metric of constant $Q$ curvature in the conformal class of $g$. This amounts to finding a positive solution to \\[ P_g (u)= c u^{\\frac{N+4}{N-4}}, u>0 {on} M\\] where $P_g$ is the Paneitz operator. We show that for dimensions $N \\geq 25$, the set of all positive solutions to the prescribed $Q$ curvature problem is {\\em non-compact}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3446","kind":"arxiv","version":3},"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":"0903.3446","created_at":"2026-05-18T04:20:23.495596+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.3446v3","created_at":"2026-05-18T04:20:23.495596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3446","created_at":"2026-05-18T04:20:23.495596+00:00"},{"alias_kind":"pith_short_12","alias_value":"X25KKEWSZWHR","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"X25KKEWSZWHR562F","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"X25KKEWS","created_at":"2026-05-18T12:26:02.257875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.20571","citing_title":"Blow-up phenomena for the constant Q/R-curvature equation","ref_index":35,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM","json":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM.json","graph_json":"https://pith.science/api/pith-number/X25KKEWSZWHR562FWRA42AFIJM/graph.json","events_json":"https://pith.science/api/pith-number/X25KKEWSZWHR562FWRA42AFIJM/events.json","paper":"https://pith.science/paper/X25KKEWS"},"agent_actions":{"view_html":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM","download_json":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM.json","view_paper":"https://pith.science/paper/X25KKEWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.3446&json=true","fetch_graph":"https://pith.science/api/pith-number/X25KKEWSZWHR562FWRA42AFIJM/graph.json","fetch_events":"https://pith.science/api/pith-number/X25KKEWSZWHR562FWRA42AFIJM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/action/storage_attestation","attest_author":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/action/author_attestation","sign_citation":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/action/citation_signature","submit_replication":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/action/replication_record"}},"created_at":"2026-05-18T04:20:23.495596+00:00","updated_at":"2026-05-18T04:20:23.495596+00:00"}