{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZKE7IVLBCTZVZBJYSLXNXS6Y7J","short_pith_number":"pith:ZKE7IVLB","canonical_record":{"source":{"id":"1209.4026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:46:34Z","cross_cats_sorted":[],"title_canon_sha256":"210be8f70456b82361ac211c01357b655a197934e3c25ee5148f1f12d8b681ba","abstract_canon_sha256":"d6f96afaf6ffa7f2c478cabac970aa96f812217a2d9436339fa3723e2d64965d"},"schema_version":"1.0"},"canonical_sha256":"ca89f4556114f35c853892eedbcbd8fa6c2ddaca5de717439e4a7694e0fe5201","source":{"kind":"arxiv","id":"1209.4026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4026","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4026v1","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4026","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZKE7IVLBCTZV","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZKE7IVLBCTZVZBJY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZKE7IVLB","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZKE7IVLBCTZVZBJYSLXNXS6Y7J","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:46:34Z","cross_cats_sorted":[],"title_canon_sha256":"210be8f70456b82361ac211c01357b655a197934e3c25ee5148f1f12d8b681ba","abstract_canon_sha256":"d6f96afaf6ffa7f2c478cabac970aa96f812217a2d9436339fa3723e2d64965d"},"schema_version":"1.0"},"canonical_sha256":"ca89f4556114f35c853892eedbcbd8fa6c2ddaca5de717439e4a7694e0fe5201","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:21.965740Z","signature_b64":"Ok6fJllb6cV7wKCb5FQBD6imCuUXOskcqgm+eKWPC8nReYkPYSQFMQ6/kmRui7LLiX2TC19i9pDRvzJ80bMoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca89f4556114f35c853892eedbcbd8fa6c2ddaca5de717439e4a7694e0fe5201","last_reissued_at":"2026-05-18T03:45:21.964826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:21.964826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4026","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":"2026-05-18T03:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ikzio2FLFvJUY8ln9COUe/QF/xs7wVHNAuvjXaygEGElelQvpfkOFSh1DyvftSvLwn+cv3aJ+Y3NdYe/FgdJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:58:20.869990Z"},"content_sha256":"10241f8346fd37ba5d79a5215a68cc8f30c77d874f3ca8c20b2ecf8956892807","schema_version":"1.0","event_id":"sha256:10241f8346fd37ba5d79a5215a68cc8f30c77d874f3ca8c20b2ecf8956892807"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZKE7IVLBCTZVZBJYSLXNXS6Y7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The generalized Frankel conjecture in Sasaki geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Song Sun, Weiyong He","submitted_at":"2012-09-18T16:46:34Z","abstract_excerpt":"We prove some structure results for \\emph{transverse reducible} Sasaki manifolds. In particular, we show Sasaki manifolds with positive Ricci curvature is transversely irreducible, and so there is no join (product) construction for irregular Sasaki-Einstein manifolds, as opposed to the quasi-regular case done by Wang-Ziller and Boyer-Galicki. As an application, we classify compact Sasaki manifolds with non-negative transverse bisectional curvature, which can be viewed as the generalized Frankel conjecture (N. Mok's theorem) in Sasaki geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4026","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":"2026-05-18T03:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AHufBJ30oG5A97XU4V7XrRb1GRvI2EqV1Kax7FHKeIFiOkwQXkOpRoq8QBjoN/VvAyS7SVH5c+5pzdEYn5E4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:58:20.870365Z"},"content_sha256":"2b2c74fb78a640ec09e75d7cd2ed44892fce58cf24da11fae8ba04fd97776e88","schema_version":"1.0","event_id":"sha256:2b2c74fb78a640ec09e75d7cd2ed44892fce58cf24da11fae8ba04fd97776e88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKE7IVLBCTZVZBJYSLXNXS6Y7J/bundle.json","state_url":"https://pith.science/pith/ZKE7IVLBCTZVZBJYSLXNXS6Y7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKE7IVLBCTZVZBJYSLXNXS6Y7J/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":"2026-05-31T05:58:20Z","links":{"resolver":"https://pith.science/pith/ZKE7IVLBCTZVZBJYSLXNXS6Y7J","bundle":"https://pith.science/pith/ZKE7IVLBCTZVZBJYSLXNXS6Y7J/bundle.json","state":"https://pith.science/pith/ZKE7IVLBCTZVZBJYSLXNXS6Y7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKE7IVLBCTZVZBJYSLXNXS6Y7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZKE7IVLBCTZVZBJYSLXNXS6Y7J","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":"d6f96afaf6ffa7f2c478cabac970aa96f812217a2d9436339fa3723e2d64965d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:46:34Z","title_canon_sha256":"210be8f70456b82361ac211c01357b655a197934e3c25ee5148f1f12d8b681ba"},"schema_version":"1.0","source":{"id":"1209.4026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4026","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4026v1","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4026","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZKE7IVLBCTZV","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZKE7IVLBCTZVZBJY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZKE7IVLB","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:2b2c74fb78a640ec09e75d7cd2ed44892fce58cf24da11fae8ba04fd97776e88","target":"graph","created_at":"2026-05-18T03:45:21Z","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":"We prove some structure results for \\emph{transverse reducible} Sasaki manifolds. In particular, we show Sasaki manifolds with positive Ricci curvature is transversely irreducible, and so there is no join (product) construction for irregular Sasaki-Einstein manifolds, as opposed to the quasi-regular case done by Wang-Ziller and Boyer-Galicki. As an application, we classify compact Sasaki manifolds with non-negative transverse bisectional curvature, which can be viewed as the generalized Frankel conjecture (N. Mok's theorem) in Sasaki geometry.","authors_text":"Song Sun, Weiyong He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:46:34Z","title":"The generalized Frankel conjecture in Sasaki geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4026","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":"sha256:10241f8346fd37ba5d79a5215a68cc8f30c77d874f3ca8c20b2ecf8956892807","target":"record","created_at":"2026-05-18T03:45:21Z","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":"d6f96afaf6ffa7f2c478cabac970aa96f812217a2d9436339fa3723e2d64965d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-18T16:46:34Z","title_canon_sha256":"210be8f70456b82361ac211c01357b655a197934e3c25ee5148f1f12d8b681ba"},"schema_version":"1.0","source":{"id":"1209.4026","kind":"arxiv","version":1}},"canonical_sha256":"ca89f4556114f35c853892eedbcbd8fa6c2ddaca5de717439e4a7694e0fe5201","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca89f4556114f35c853892eedbcbd8fa6c2ddaca5de717439e4a7694e0fe5201","first_computed_at":"2026-05-18T03:45:21.964826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:21.964826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ok6fJllb6cV7wKCb5FQBD6imCuUXOskcqgm+eKWPC8nReYkPYSQFMQ6/kmRui7LLiX2TC19i9pDRvzJ80bMoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:21.965740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10241f8346fd37ba5d79a5215a68cc8f30c77d874f3ca8c20b2ecf8956892807","sha256:2b2c74fb78a640ec09e75d7cd2ed44892fce58cf24da11fae8ba04fd97776e88"],"state_sha256":"69c5a0a90d616f94771b448e0c41374bb4b57b03ab712b0eb14549f267991def"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIlx6s/Q9Eo2X7n29ie1iwY9LPbeYCgD+oIXEZVdp9k7KO4tntIFqFzHy6HQa687csspEtFvS1kZEOkO8S3PAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:58:20.872540Z","bundle_sha256":"77de7af598ac39483f0abccad886a3de1141f7762be42461a47393305f238bc8"}}