{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZPVECRKHMV7E7SZPCFL4DUYP5E","short_pith_number":"pith:ZPVECRKH","canonical_record":{"source":{"id":"1205.6355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-29T13:24:04Z","cross_cats_sorted":[],"title_canon_sha256":"e331003cd565d2d41ed8311a6e87ed4623b64ed011cdeb382f3494c2abcc57c6","abstract_canon_sha256":"6b66454bbb67fe244265ac287fa6314130097d3b8852154a34eab8bde3d9996b"},"schema_version":"1.0"},"canonical_sha256":"cbea414547657e4fcb2f1157c1d30fe91dc4d2d1157e2338edd0fa3afab68dd1","source":{"kind":"arxiv","id":"1205.6355","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6355","created_at":"2026-05-18T03:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6355v2","created_at":"2026-05-18T03:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6355","created_at":"2026-05-18T03:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZPVECRKHMV7E","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZPVECRKHMV7E7SZP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZPVECRKH","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZPVECRKHMV7E7SZPCFL4DUYP5E","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-29T13:24:04Z","cross_cats_sorted":[],"title_canon_sha256":"e331003cd565d2d41ed8311a6e87ed4623b64ed011cdeb382f3494c2abcc57c6","abstract_canon_sha256":"6b66454bbb67fe244265ac287fa6314130097d3b8852154a34eab8bde3d9996b"},"schema_version":"1.0"},"canonical_sha256":"cbea414547657e4fcb2f1157c1d30fe91dc4d2d1157e2338edd0fa3afab68dd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:18.143534Z","signature_b64":"E2UQlDUg9TQfVPxPTKTqf1sKH1hviFOwX+5lWKBlug/oQY116f0kW0VODr+47PLzs5yhqhgvHU2h+107uabZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbea414547657e4fcb2f1157c1d30fe91dc4d2d1157e2338edd0fa3afab68dd1","last_reissued_at":"2026-05-18T03:43:18.142824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:18.142824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6355","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iJ3RhWwfex5l9k/bJUJPYQWkCfisE8jflPArf3xarDVlsdYwBo+kOx1PoXyF/D5DAh0esiK4IP9nh0AZ8bA9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:12:48.412010Z"},"content_sha256":"15142111912ca4a417840c2c49114ec639e4e263b1cfbc2000ea1ecf6f2be3d1","schema_version":"1.0","event_id":"sha256:15142111912ca4a417840c2c49114ec639e4e263b1cfbc2000ea1ecf6f2be3d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZPVECRKHMV7E7SZPCFL4DUYP5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant Q-curvature metrics near the Hyperbolic metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gang Li","submitted_at":"2012-05-29T13:24:04Z","abstract_excerpt":"Let $(M,\\,g)$ be a Poincar$\\acute{\\text{e}}$-Einstein manifold with a smooth defining function. In this note, we prove that there are infinitely many asymptotically hyperbolic metrics with constant $Q$-curvature in the conformal class of an asymptotically hyperbolic metric close enough to $g$. These metrics are parametrized by the elements in the kernel of the linearized operator of the prescribed constant $Q$-curvature equation. A similar analysis is applied to a class of fourth order equations arising in spectral theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6355","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":""},"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":"2026-05-18T03:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B0IxVEo9bpcwU6DvqqED8g56v+HSLHX3k8muaxB6dhUpFFBeVEgaORcJNndZ32FX8c7p1KfGG6/0p99BmHCXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:12:48.412407Z"},"content_sha256":"13396b6993cd602b77fdc9479922baa6dae7880aa66e1c4601a9729028390f85","schema_version":"1.0","event_id":"sha256:13396b6993cd602b77fdc9479922baa6dae7880aa66e1c4601a9729028390f85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPVECRKHMV7E7SZPCFL4DUYP5E/bundle.json","state_url":"https://pith.science/pith/ZPVECRKHMV7E7SZPCFL4DUYP5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPVECRKHMV7E7SZPCFL4DUYP5E/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":"2026-05-30T13:12:48Z","links":{"resolver":"https://pith.science/pith/ZPVECRKHMV7E7SZPCFL4DUYP5E","bundle":"https://pith.science/pith/ZPVECRKHMV7E7SZPCFL4DUYP5E/bundle.json","state":"https://pith.science/pith/ZPVECRKHMV7E7SZPCFL4DUYP5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPVECRKHMV7E7SZPCFL4DUYP5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZPVECRKHMV7E7SZPCFL4DUYP5E","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":"6b66454bbb67fe244265ac287fa6314130097d3b8852154a34eab8bde3d9996b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-29T13:24:04Z","title_canon_sha256":"e331003cd565d2d41ed8311a6e87ed4623b64ed011cdeb382f3494c2abcc57c6"},"schema_version":"1.0","source":{"id":"1205.6355","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6355","created_at":"2026-05-18T03:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6355v2","created_at":"2026-05-18T03:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6355","created_at":"2026-05-18T03:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZPVECRKHMV7E","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZPVECRKHMV7E7SZP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZPVECRKH","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:13396b6993cd602b77fdc9479922baa6dae7880aa66e1c4601a9729028390f85","target":"graph","created_at":"2026-05-18T03:43:18Z","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 Poincar$\\acute{\\text{e}}$-Einstein manifold with a smooth defining function. In this note, we prove that there are infinitely many asymptotically hyperbolic metrics with constant $Q$-curvature in the conformal class of an asymptotically hyperbolic metric close enough to $g$. These metrics are parametrized by the elements in the kernel of the linearized operator of the prescribed constant $Q$-curvature equation. A similar analysis is applied to a class of fourth order equations arising in spectral theory.","authors_text":"Gang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-29T13:24:04Z","title":"Constant Q-curvature metrics near the Hyperbolic metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6355","kind":"arxiv","version":2},"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":"sha256:15142111912ca4a417840c2c49114ec639e4e263b1cfbc2000ea1ecf6f2be3d1","target":"record","created_at":"2026-05-18T03:43:18Z","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":"6b66454bbb67fe244265ac287fa6314130097d3b8852154a34eab8bde3d9996b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-29T13:24:04Z","title_canon_sha256":"e331003cd565d2d41ed8311a6e87ed4623b64ed011cdeb382f3494c2abcc57c6"},"schema_version":"1.0","source":{"id":"1205.6355","kind":"arxiv","version":2}},"canonical_sha256":"cbea414547657e4fcb2f1157c1d30fe91dc4d2d1157e2338edd0fa3afab68dd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbea414547657e4fcb2f1157c1d30fe91dc4d2d1157e2338edd0fa3afab68dd1","first_computed_at":"2026-05-18T03:43:18.142824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:18.142824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E2UQlDUg9TQfVPxPTKTqf1sKH1hviFOwX+5lWKBlug/oQY116f0kW0VODr+47PLzs5yhqhgvHU2h+107uabZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:18.143534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6355","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15142111912ca4a417840c2c49114ec639e4e263b1cfbc2000ea1ecf6f2be3d1","sha256:13396b6993cd602b77fdc9479922baa6dae7880aa66e1c4601a9729028390f85"],"state_sha256":"4004e2ad4b36294cf1cc2e423dadfee1d508515937083567932cee6e46bb0f40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gv8gvompaZ+oSonyWqonX7gLObQdnmaCmnSl4Kcu2XIl9Eq5IcVnTXsAHar+k8B+tzP3x50ALn10E1Tb/JvpBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:12:48.414469Z","bundle_sha256":"d8975743353262dfdd8b67b82181fbfd68d0b61e18f7599981f74557fe0a9afa"}}