{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E2WUW2633R5YYIZJPTOFAXT2LC","short_pith_number":"pith:E2WUW263","canonical_record":{"source":{"id":"1712.06215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-18T01:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"414387053d95353b771cd9d990bc42bfc0f3d6d0f28a9ac30234e4036e19a002","abstract_canon_sha256":"582fbe5ccd55243b20a260b26c98d3c4664e2470dd053b8d8baf04320eac92d5"},"schema_version":"1.0"},"canonical_sha256":"26ad4b6bdbdc7b8c23297cdc505e7a589cd956048fc4d960657de36864db17a3","source":{"kind":"arxiv","id":"1712.06215","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06215","created_at":"2026-05-18T00:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06215v1","created_at":"2026-05-18T00:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06215","created_at":"2026-05-18T00:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"E2WUW2633R5Y","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E2WUW2633R5YYIZJ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E2WUW263","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E2WUW2633R5YYIZJPTOFAXT2LC","target":"record","payload":{"canonical_record":{"source":{"id":"1712.06215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-18T01:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"414387053d95353b771cd9d990bc42bfc0f3d6d0f28a9ac30234e4036e19a002","abstract_canon_sha256":"582fbe5ccd55243b20a260b26c98d3c4664e2470dd053b8d8baf04320eac92d5"},"schema_version":"1.0"},"canonical_sha256":"26ad4b6bdbdc7b8c23297cdc505e7a589cd956048fc4d960657de36864db17a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:50.835041Z","signature_b64":"PowcxQ75IUR5Eq924/s1QmkwXy6f1vk1zXrLPxzVj3XyL+nz7KhHfTK25gaYkqA1a8bDcuuddcy6dEx8IwL6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26ad4b6bdbdc7b8c23297cdc505e7a589cd956048fc4d960657de36864db17a3","last_reissued_at":"2026-05-18T00:27:50.834549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:50.834549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.06215","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1CoYgXd6+9ZcJdm+eXEkRFELSPVESbTTmTFofDsrHm+MPhb+rkYPhYIxpOOzxdzw5hL1lvLdRAsA/LhlPVj1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:17:36.064478Z"},"content_sha256":"188c4daa4c5473f35e0aae44a3a6905385200fbf196215bf1dbb5775f520881d","schema_version":"1.0","event_id":"sha256:188c4daa4c5473f35e0aae44a3a6905385200fbf196215bf1dbb5775f520881d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E2WUW2633R5YYIZJPTOFAXT2LC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Uniqueness And Existence of Conformally Compact Einstein Metrics with Homogeneous Conformal Infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gang Li","submitted_at":"2017-12-18T01:17:37Z","abstract_excerpt":"In this paper we show that for a generalized Berger metric $\\hat{g}$ on $S^3$ close to the round metric, the conformally compact Einstein (CCE) manifold $(M, g)$ with $(S^3, [\\hat{g}])$ as its conformal infinity is unique up to isometries. For the high-dimensional case, we show that if $\\hat{g}$ is an $\\text{SU}(k+1)$-invariant metric on $S^{2k+1}$ for $k\\geq1$, the non-positively curved CCE metric on the $(2k+1)$-ball $B_1(0)$ with $(S^{2k+1}, [\\hat{g}])$ as its conformal infinity is unique up to isometries. In particular, since in \\cite{LiQingShi}, we proved that if the Yamabe constant of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06215","kind":"arxiv","version":1},"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":"2026-05-18T00:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sIvH8wz0bRpxJQwsfIhTUENZsSc/4SREN3LwLli2+8R6b1Y4nAcgjNNxX/EvlwkKVxpW3tiztjkCOkaEL7fKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:17:36.064831Z"},"content_sha256":"67adaadd3e3dc3665208fbdc98f1f43c3f360d36b187293d2fb6bf4e01d7b0d7","schema_version":"1.0","event_id":"sha256:67adaadd3e3dc3665208fbdc98f1f43c3f360d36b187293d2fb6bf4e01d7b0d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E2WUW2633R5YYIZJPTOFAXT2LC/bundle.json","state_url":"https://pith.science/pith/E2WUW2633R5YYIZJPTOFAXT2LC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E2WUW2633R5YYIZJPTOFAXT2LC/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":"2026-05-30T07:17:36Z","links":{"resolver":"https://pith.science/pith/E2WUW2633R5YYIZJPTOFAXT2LC","bundle":"https://pith.science/pith/E2WUW2633R5YYIZJPTOFAXT2LC/bundle.json","state":"https://pith.science/pith/E2WUW2633R5YYIZJPTOFAXT2LC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E2WUW2633R5YYIZJPTOFAXT2LC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E2WUW2633R5YYIZJPTOFAXT2LC","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":"582fbe5ccd55243b20a260b26c98d3c4664e2470dd053b8d8baf04320eac92d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-18T01:17:37Z","title_canon_sha256":"414387053d95353b771cd9d990bc42bfc0f3d6d0f28a9ac30234e4036e19a002"},"schema_version":"1.0","source":{"id":"1712.06215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06215","created_at":"2026-05-18T00:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06215v1","created_at":"2026-05-18T00:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06215","created_at":"2026-05-18T00:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"E2WUW2633R5Y","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E2WUW2633R5YYIZJ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E2WUW263","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:67adaadd3e3dc3665208fbdc98f1f43c3f360d36b187293d2fb6bf4e01d7b0d7","target":"graph","created_at":"2026-05-18T00:27:50Z","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":"In this paper we show that for a generalized Berger metric $\\hat{g}$ on $S^3$ close to the round metric, the conformally compact Einstein (CCE) manifold $(M, g)$ with $(S^3, [\\hat{g}])$ as its conformal infinity is unique up to isometries. For the high-dimensional case, we show that if $\\hat{g}$ is an $\\text{SU}(k+1)$-invariant metric on $S^{2k+1}$ for $k\\geq1$, the non-positively curved CCE metric on the $(2k+1)$-ball $B_1(0)$ with $(S^{2k+1}, [\\hat{g}])$ as its conformal infinity is unique up to isometries. In particular, since in \\cite{LiQingShi}, we proved that if the Yamabe constant of th","authors_text":"Gang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-18T01:17:37Z","title":"On Uniqueness And Existence of Conformally Compact Einstein Metrics with Homogeneous Conformal Infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06215","kind":"arxiv","version":1},"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":"sha256:188c4daa4c5473f35e0aae44a3a6905385200fbf196215bf1dbb5775f520881d","target":"record","created_at":"2026-05-18T00:27:50Z","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":"582fbe5ccd55243b20a260b26c98d3c4664e2470dd053b8d8baf04320eac92d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-18T01:17:37Z","title_canon_sha256":"414387053d95353b771cd9d990bc42bfc0f3d6d0f28a9ac30234e4036e19a002"},"schema_version":"1.0","source":{"id":"1712.06215","kind":"arxiv","version":1}},"canonical_sha256":"26ad4b6bdbdc7b8c23297cdc505e7a589cd956048fc4d960657de36864db17a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26ad4b6bdbdc7b8c23297cdc505e7a589cd956048fc4d960657de36864db17a3","first_computed_at":"2026-05-18T00:27:50.834549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:50.834549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PowcxQ75IUR5Eq924/s1QmkwXy6f1vk1zXrLPxzVj3XyL+nz7KhHfTK25gaYkqA1a8bDcuuddcy6dEx8IwL6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:50.835041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:188c4daa4c5473f35e0aae44a3a6905385200fbf196215bf1dbb5775f520881d","sha256:67adaadd3e3dc3665208fbdc98f1f43c3f360d36b187293d2fb6bf4e01d7b0d7"],"state_sha256":"53ca558ab1561ef860756a9db9be0f393a94c7b4fc01604bac36e2cf206874ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CXoeU9Ol0Rn2+69lpxIz1Jcfc1S0TI4LFPXDJ5nTvpckwy3uqXpvGFAwNoDrjyPWYXdaJ8ok8tKUthUCkNoBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:17:36.066942Z","bundle_sha256":"bf57c5f029c86980b75e102a0412ca011a3473ea3c1b3e03d8a015aa9763b67f"}}