{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:SSH26GNRGPLJXPSZE7O6VA4LMR","short_pith_number":"pith:SSH26GNR","schema_version":"1.0","canonical_sha256":"948faf19b133d69bbe5927ddea838b64572d760a4f4e85b946df9c8eaa2d0a37","source":{"kind":"arxiv","id":"1203.4403","version":4},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.4403","created_at":"2026-05-18T01:25:31.057396+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.4403v4","created_at":"2026-05-18T01:25:31.057396+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4403","created_at":"2026-05-18T01:25:31.057396+00:00"},{"alias_kind":"pith_short_12","alias_value":"SSH26GNRGPLJ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"SSH26GNRGPLJXPSZ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"SSH26GNR","created_at":"2026-05-18T12:27:20.899486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR","json":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR.json","graph_json":"https://pith.science/api/pith-number/SSH26GNRGPLJXPSZE7O6VA4LMR/graph.json","events_json":"https://pith.science/api/pith-number/SSH26GNRGPLJXPSZE7O6VA4LMR/events.json","paper":"https://pith.science/paper/SSH26GNR"},"agent_actions":{"view_html":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR","download_json":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR.json","view_paper":"https://pith.science/paper/SSH26GNR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.4403&json=true","fetch_graph":"https://pith.science/api/pith-number/SSH26GNRGPLJXPSZE7O6VA4LMR/graph.json","fetch_events":"https://pith.science/api/pith-number/SSH26GNRGPLJXPSZE7O6VA4LMR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/action/storage_attestation","attest_author":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/action/author_attestation","sign_citation":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/action/citation_signature","submit_replication":"https://pith.science/pith/SSH26GNRGPLJXPSZE7O6VA4LMR/action/replication_record"}},"created_at":"2026-05-18T01:25:31.057396+00:00","updated_at":"2026-05-18T01:25:31.057396+00:00"}