{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:GRX2HNMZCV7O6DTWE4ZAKZBPU2","short_pith_number":"pith:GRX2HNMZ","schema_version":"1.0","canonical_sha256":"346fa3b599157eef0e76273205642fa6897a21e2b31896bed981bbe2950fcbfc","source":{"kind":"arxiv","id":"math/0111245","version":2},"attestation_state":"computed","paper":{"title":"Deformation types of real and complex manifolds","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Fabrizio M.E. Catanese (University of Bayreuth)","submitted_at":"2001-11-22T15:08:30Z","abstract_excerpt":"The Leit-Faden of the article (which is partially a survey) is a negative answer to the question whether, for a compact complex manifold which is a $K(\\pi, 1)$ the diffeomorphism type determines the deformation type. We show that a deformation in the large of complex tori is again a complex torus, and then that the same holds for products of a torus with a curve of genus $g\\geq 2$. Together with old results of Blanchard, Calabi, and Sommese, who showed the existence of non K\\\"ahler complex structures on the product of a curve with a two dimensional complex torus, this gives the first counterex"},"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":"math/0111245","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-11-22T15:08:30Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"eb29b8affbeea2bba71a6cbd7434a1a2588acbe3de22b09fc30adfcc03f91ce4","abstract_canon_sha256":"14258bd337743560294de7c5050f6472facefca48e69fb3a47abe737b2276e59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:46.148644Z","signature_b64":"5g+xK/HJ25aPcoT3W/a/2ou/suaEQAnUPs1gBlKVxTK+oTVc2h8Jp5SDcgsFe7sxQxNZUtiLZu5lqZJUodspAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"346fa3b599157eef0e76273205642fa6897a21e2b31896bed981bbe2950fcbfc","last_reissued_at":"2026-07-04T14:35:46.148266Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:46.148266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformation types of real and complex manifolds","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Fabrizio M.E. Catanese (University of Bayreuth)","submitted_at":"2001-11-22T15:08:30Z","abstract_excerpt":"The Leit-Faden of the article (which is partially a survey) is a negative answer to the question whether, for a compact complex manifold which is a $K(\\pi, 1)$ the diffeomorphism type determines the deformation type. We show that a deformation in the large of complex tori is again a complex torus, and then that the same holds for products of a torus with a curve of genus $g\\geq 2$. Together with old results of Blanchard, Calabi, and Sommese, who showed the existence of non K\\\"ahler complex structures on the product of a curve with a two dimensional complex torus, this gives the first counterex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0111245","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0111245/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0111245","created_at":"2026-07-04T14:35:46.148336+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0111245v2","created_at":"2026-07-04T14:35:46.148336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0111245","created_at":"2026-07-04T14:35:46.148336+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRX2HNMZCV7O","created_at":"2026-07-04T14:35:46.148336+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRX2HNMZCV7O6DTW","created_at":"2026-07-04T14:35:46.148336+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRX2HNMZ","created_at":"2026-07-04T14:35:46.148336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.18179","citing_title":"Exotic hypercomplex structures on a torus do not exist","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2","json":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2.json","graph_json":"https://pith.science/api/pith-number/GRX2HNMZCV7O6DTWE4ZAKZBPU2/graph.json","events_json":"https://pith.science/api/pith-number/GRX2HNMZCV7O6DTWE4ZAKZBPU2/events.json","paper":"https://pith.science/paper/GRX2HNMZ"},"agent_actions":{"view_html":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2","download_json":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2.json","view_paper":"https://pith.science/paper/GRX2HNMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0111245&json=true","fetch_graph":"https://pith.science/api/pith-number/GRX2HNMZCV7O6DTWE4ZAKZBPU2/graph.json","fetch_events":"https://pith.science/api/pith-number/GRX2HNMZCV7O6DTWE4ZAKZBPU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2/action/storage_attestation","attest_author":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2/action/author_attestation","sign_citation":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2/action/citation_signature","submit_replication":"https://pith.science/pith/GRX2HNMZCV7O6DTWE4ZAKZBPU2/action/replication_record"}},"created_at":"2026-07-04T14:35:46.148336+00:00","updated_at":"2026-07-04T14:35:46.148336+00:00"}