{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:X25KKEWSZWHR562FWRA42AFIJM","short_pith_number":"pith:X25KKEWS","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"},"canonical_sha256":"bebaa512d2cd8f1efb45b441cd00a84b0a958f32941bca3b571c977c22681139","source":{"kind":"arxiv","id":"0903.3446","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3446","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3446v3","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3446","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"X25KKEWSZWHR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X25KKEWSZWHR562F","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X25KKEWS","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:X25KKEWSZWHR562FWRA42AFIJM","target":"record","payload":{"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"},"canonical_sha256":"bebaa512d2cd8f1efb45b441cd00a84b0a958f32941bca3b571c977c22681139","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"},"source_kind":"arxiv","source_id":"0903.3446","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0raFCLDdKmYhdG0H2rsGxYIRkVFFm53D0NMPV4BH1sbOvn6+5Sh8hAl4zi+lzmROHyClUJVfrrRE5CaIW0mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:38:31.103037Z"},"content_sha256":"454c759caf0facc35e52e3686e9f25bdb19daa2b35faf9992716a8afef8b9b36","schema_version":"1.0","event_id":"sha256:454c759caf0facc35e52e3686e9f25bdb19daa2b35faf9992716a8afef8b9b36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:X25KKEWSZWHR562FWRA42AFIJM","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k48yAJqvQR3AFjKyVhTKFvyRzFRsQN72x5JfaH7QupQ8++RkLIKaNqERlHz+jEB4SpM4T2JtZVTF18O6Sl0IAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:38:31.103470Z"},"content_sha256":"fb398ccdcccfb69656a19e623ec721b7f365fe3c34513605c42d6e624bb95aba","schema_version":"1.0","event_id":"sha256:fb398ccdcccfb69656a19e623ec721b7f365fe3c34513605c42d6e624bb95aba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/bundle.json","state_url":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X25KKEWSZWHR562FWRA42AFIJM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T20:38:31Z","links":{"resolver":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM","bundle":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/bundle.json","state":"https://pith.science/pith/X25KKEWSZWHR562FWRA42AFIJM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X25KKEWSZWHR562FWRA42AFIJM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:X25KKEWSZWHR562FWRA42AFIJM","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":"fc588fd6715655c46b25e5c0df1a18a17ea986413beee7b07a3c2bcda562ab1c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-03-20T02:56:26Z","title_canon_sha256":"41da246bdd006a4d1b0d4586d4116c70b18f6fab35a57fa8dab128d3e24d7476"},"schema_version":"1.0","source":{"id":"0903.3446","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3446","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3446v3","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3446","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"X25KKEWSZWHR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X25KKEWSZWHR562F","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X25KKEWS","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:fb398ccdcccfb69656a19e623ec721b7f365fe3c34513605c42d6e624bb95aba","target":"graph","created_at":"2026-05-18T04:20:23Z","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":"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}.","authors_text":"Chunyi Zhao, Juncheng Wei","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-03-20T02:56:26Z","title":"Non-compactness of the Prescribed Q-curvature Problem in Large Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3446","kind":"arxiv","version":3},"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":"sha256:454c759caf0facc35e52e3686e9f25bdb19daa2b35faf9992716a8afef8b9b36","target":"record","created_at":"2026-05-18T04:20:23Z","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":"fc588fd6715655c46b25e5c0df1a18a17ea986413beee7b07a3c2bcda562ab1c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-03-20T02:56:26Z","title_canon_sha256":"41da246bdd006a4d1b0d4586d4116c70b18f6fab35a57fa8dab128d3e24d7476"},"schema_version":"1.0","source":{"id":"0903.3446","kind":"arxiv","version":3}},"canonical_sha256":"bebaa512d2cd8f1efb45b441cd00a84b0a958f32941bca3b571c977c22681139","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bebaa512d2cd8f1efb45b441cd00a84b0a958f32941bca3b571c977c22681139","first_computed_at":"2026-05-18T04:20:23.495465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:23.495465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"trN7nb0baqBY0qOp7fXr6WKV4B0qsYetMAqhC7coGIjUWQymCz6d+ltVFMEbaPViMqxvirb+5ypGtHiDckJpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:23.496197Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3446","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:454c759caf0facc35e52e3686e9f25bdb19daa2b35faf9992716a8afef8b9b36","sha256:fb398ccdcccfb69656a19e623ec721b7f365fe3c34513605c42d6e624bb95aba"],"state_sha256":"76523aa6c64e6a785c4eab27db63cce5d2248c84b75b05b36200bc41186bfede"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmp0HbLUv26+jEH7YkPjR9QU5uiRh+So1MKUPyH7iAnL9up4xrHe23iKEhffVgVaddEEU4c7BZsCpW/O0p7oCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:38:31.107051Z","bundle_sha256":"cbf1d34c93b10899ee5236849d2a8407805b5ec637a0f7ee114f1d1f26805fde"}}