{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GB7R35IPAD6KJRF6B6335JGBE3","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":"2fb907a6ad33435df0829af0de24c537715a8bf198579ab5ba683715dd84c008","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-14T15:00:00Z","title_canon_sha256":"a6105e0271bce447e4f4f40a6deaf3a62cdbbef2fb4ad77388da3226d0a9a165"},"schema_version":"1.0","source":{"id":"1411.3926","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3926","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3926v4","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3926","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"GB7R35IPAD6K","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GB7R35IPAD6KJRF6","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GB7R35IP","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:2a42f51ae978762254bd2afd64655189cbb85b5e9d68974fbb53b384e89538b9","target":"graph","created_at":"2026-05-18T01:31:03Z","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":"For a smooth compact Riemannian manifold with positive Yamabe invariant, positive Q curvature and dimension at least 5, we prove the existence of a conformal metric with constant Q curvature. Our approach is based on the study of extremal problem for a new functional involving the Paneitz operator.","authors_text":"Fengbo Hang, Paul C. Yang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-14T15:00:00Z","title":"Q curvature on a class of manifolds with dimension at least 5"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3926","kind":"arxiv","version":4},"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:f58e68d726bb1ec6d5157a453be2021fb5b39cfcb1a7cd2102ba8cf35eff18f0","target":"record","created_at":"2026-05-18T01:31:03Z","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":"2fb907a6ad33435df0829af0de24c537715a8bf198579ab5ba683715dd84c008","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-14T15:00:00Z","title_canon_sha256":"a6105e0271bce447e4f4f40a6deaf3a62cdbbef2fb4ad77388da3226d0a9a165"},"schema_version":"1.0","source":{"id":"1411.3926","kind":"arxiv","version":4}},"canonical_sha256":"307f1df50f00fca4c4be0fb7bea4c126f644dfad592e732e8ede93a578c9b11b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"307f1df50f00fca4c4be0fb7bea4c126f644dfad592e732e8ede93a578c9b11b","first_computed_at":"2026-05-18T01:31:03.599041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:03.599041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BNXp6mpxP3cE2SwtgHw5cL2nf6IlEr5lnMuTZa2x7/8cenhzNcO6fBrZGe876upRHEvXxiq8YFTrT+kn0JQKCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:03.599769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3926","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f58e68d726bb1ec6d5157a453be2021fb5b39cfcb1a7cd2102ba8cf35eff18f0","sha256:2a42f51ae978762254bd2afd64655189cbb85b5e9d68974fbb53b384e89538b9"],"state_sha256":"5733254829fc21118793ed24b7cdb037abedf3cd8e4812b925782970b97ee859"}