{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SSH26GNRGPLJXPSZE7O6VA4LMR","short_pith_number":"pith:SSH26GNR","canonical_record":{"source":{"id":"1203.4403","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-03-20T11:47:43Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"aed9876d5cd46544bbae00f15e11ea5bff46680f2a96292aefe5c7fe7d5cc120","abstract_canon_sha256":"c96fef976a84f60d82476f171998615654be1851df3eadd1ab6f5251f0eec476"},"schema_version":"1.0"},"canonical_sha256":"948faf19b133d69bbe5927ddea838b64572d760a4f4e85b946df9c8eaa2d0a37","source":{"kind":"arxiv","id":"1203.4403","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4403","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4403v4","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4403","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"pith_short_12","alias_value":"SSH26GNRGPLJ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SSH26GNRGPLJXPSZ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SSH26GNR","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SSH26GNRGPLJXPSZE7O6VA4LMR","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4403","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-03-20T11:47:43Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"aed9876d5cd46544bbae00f15e11ea5bff46680f2a96292aefe5c7fe7d5cc120","abstract_canon_sha256":"c96fef976a84f60d82476f171998615654be1851df3eadd1ab6f5251f0eec476"},"schema_version":"1.0"},"canonical_sha256":"948faf19b133d69bbe5927ddea838b64572d760a4f4e85b946df9c8eaa2d0a37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:31.057741Z","signature_b64":"AtbwR2SJ/VeaolP/gs3NJgLPHpGNKpoe10eUvJg7qjvx/eWD2fg0kvgcgxIExS290HXoTtwaFq5L9UJVx0NiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"948faf19b133d69bbe5927ddea838b64572d760a4f4e85b946df9c8eaa2d0a37","last_reissued_at":"2026-05-18T01:25:31.057330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:31.057330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4403","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLWm6Sslb+mXfblF0o86AgPGzRDKSmEEjLMfQbfNKB9XU+gGvxIAB+Wugt24krZW+q42a6hTmP9pX5yN6yd+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:34:30.523931Z"},"content_sha256":"32de71a0ba417cc8ca62c3e30e63324a52f538f234f083dedbcceadc17ad6c0e","schema_version":"1.0","event_id":"sha256:32de71a0ba417cc8ca62c3e30e63324a52f538f234f083dedbcceadc17ad6c0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SSH26GNRGPLJXPSZE7O6VA4LMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of complex projective towers up to dimension 8 and cohomological rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Dong Youp Suh, Shintar\\^o Kuroki","submitted_at":"2012-03-20T11:47:43Z","abstract_excerpt":"A complex projective tower or simply a $\\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\\mathbb CP$-towers up to diffeomorphism, and as a consequence, we show that all such manifolds are cohomologically rigid, i.e., they are completely determined up to diffeomorphism by their cohomology rings. We also show that cohomological rigidity is not valid for 8-dimensional $\\mathbb CP$-towers by classifying $\\mathbb CP^1$-fibrations over $\\mathbb CP^3$ up to diffeomorphism. As a corollary we show that such $\\mathbb CP$-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4403","kind":"arxiv","version":4},"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":"2026-05-18T01:25:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UTVirQvSY0jBqc7nDEPvN6KkNBmZq/2JjR4FIY4xLzbJ980gdT1zFssNaN+SkkJVKQjmExItjLgA5rZYbsw7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:34:30.524282Z"},"content_sha256":"e1020dbeaa33d0cd972ea6553ddd66d3fcc3517013c54efe92291bb3d6747866","schema_version":"1.0","event_id":"sha256:e1020dbeaa33d0cd972ea6553ddd66d3fcc3517013c54efe92291bb3d6747866"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/bundle.json","state_url":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/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":"2026-06-23T14:34:30Z","links":{"resolver":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR","bundle":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/bundle.json","state":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SSH26GNRGPLJXPSZE7O6VA4LMR","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":"c96fef976a84f60d82476f171998615654be1851df3eadd1ab6f5251f0eec476","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-03-20T11:47:43Z","title_canon_sha256":"aed9876d5cd46544bbae00f15e11ea5bff46680f2a96292aefe5c7fe7d5cc120"},"schema_version":"1.0","source":{"id":"1203.4403","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4403","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4403v4","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4403","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"pith_short_12","alias_value":"SSH26GNRGPLJ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SSH26GNRGPLJXPSZ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SSH26GNR","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:e1020dbeaa33d0cd972ea6553ddd66d3fcc3517013c54efe92291bb3d6747866","target":"graph","created_at":"2026-05-18T01:25:31Z","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":"A complex projective tower or simply a $\\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\\mathbb CP$-towers up to diffeomorphism, and as a consequence, we show that all such manifolds are cohomologically rigid, i.e., they are completely determined up to diffeomorphism by their cohomology rings. We also show that cohomological rigidity is not valid for 8-dimensional $\\mathbb CP$-towers by classifying $\\mathbb CP^1$-fibrations over $\\mathbb CP^3$ up to diffeomorphism. As a corollary we show that such $\\mathbb CP$-t","authors_text":"Dong Youp Suh, Shintar\\^o Kuroki","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-03-20T11:47:43Z","title":"Classification of complex projective towers up to dimension 8 and cohomological rigidity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4403","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":"sha256:32de71a0ba417cc8ca62c3e30e63324a52f538f234f083dedbcceadc17ad6c0e","target":"record","created_at":"2026-05-18T01:25:31Z","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":"c96fef976a84f60d82476f171998615654be1851df3eadd1ab6f5251f0eec476","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-03-20T11:47:43Z","title_canon_sha256":"aed9876d5cd46544bbae00f15e11ea5bff46680f2a96292aefe5c7fe7d5cc120"},"schema_version":"1.0","source":{"id":"1203.4403","kind":"arxiv","version":4}},"canonical_sha256":"948faf19b133d69bbe5927ddea838b64572d760a4f4e85b946df9c8eaa2d0a37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"948faf19b133d69bbe5927ddea838b64572d760a4f4e85b946df9c8eaa2d0a37","first_computed_at":"2026-05-18T01:25:31.057330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:31.057330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AtbwR2SJ/VeaolP/gs3NJgLPHpGNKpoe10eUvJg7qjvx/eWD2fg0kvgcgxIExS290HXoTtwaFq5L9UJVx0NiAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:31.057741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4403","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32de71a0ba417cc8ca62c3e30e63324a52f538f234f083dedbcceadc17ad6c0e","sha256:e1020dbeaa33d0cd972ea6553ddd66d3fcc3517013c54efe92291bb3d6747866"],"state_sha256":"d4bfc8793e0a79c4791bf92d6d54dbb8f84944f34cee060ce43cd35104bf2eaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FtpvH6TaE1PkGfl2uljTb0e8cYPH7iGjBOY8iTokh/1/dU07hEoC1ed65CFE/lKN7EhjtmXAdnS1wE2kaE0rAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:34:30.526330Z","bundle_sha256":"18fec284009ee8c488f8fa51e2c20ee6c38a665889c85909c863f1f85768c5b4"}}