{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:CR6GJ2HDQOOYOQ2QP65LRNWG25","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":"c36a6507c98fd8627ffd060e53029eeab0bbaf44e6b0d5d9bea9b1bb54ce7c5a","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2005-09-30T15:24:39Z","title_canon_sha256":"8c776e3070941427de407acef209a089cbe6476d655428ad9b88f7d259ee63ac"},"schema_version":"1.0","source":{"id":"math/0509725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509725","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509725v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509725","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"CR6GJ2HDQOOY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"CR6GJ2HDQOOYOQ2Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"CR6GJ2HD","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f68f8bea42969662f0837b44045d7ea4157da2fa7872c89fd5cbd9624f884ca0","target":"graph","created_at":"2026-05-18T01:05:23Z","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 introduce a new equivalence relation, denoted by $A.Q.E.D.$ (= Algebraic-Quasi-\\'Etale- Deformation) for complete algebraic varieties with canonical singularities: it is generated by birational equivalence, by flat algebraic deformations, and by quasi-\\'etale morphisms, i.e., morphisms which are unramified in codimension $1$. $\\C$-Q.E.D is the similar relation for compact complex manifolds and spaces. By a recent theorem of Siu dimension and Kodaira dimension are invariants for $A.Q.E.D.$. The question whether conversely two algebraic varieties of the same dimension and with the same Kodair","authors_text":"Fabrizio Catanese (Universitaet Bayreuth)","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-09-30T15:24:39Z","title":"Q.E.D. for algebraic varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509725","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":"sha256:80dabf8ae5ebb0e684eac9c30745f74d07e1eb7050a058a61d1962c38f741ae3","target":"record","created_at":"2026-05-18T01:05:23Z","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":"c36a6507c98fd8627ffd060e53029eeab0bbaf44e6b0d5d9bea9b1bb54ce7c5a","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2005-09-30T15:24:39Z","title_canon_sha256":"8c776e3070941427de407acef209a089cbe6476d655428ad9b88f7d259ee63ac"},"schema_version":"1.0","source":{"id":"math/0509725","kind":"arxiv","version":1}},"canonical_sha256":"147c64e8e3839d8743507fbab8b6c6d774fc533dd0052f84c313255ea0303fb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"147c64e8e3839d8743507fbab8b6c6d774fc533dd0052f84c313255ea0303fb9","first_computed_at":"2026-05-18T01:05:23.041237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.041237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xF5t5cx5xZy+TwwN/IIXNe7d7UdKyzZ5tRVg+fKEAR+WXJxDNLmnPLmGOm9wnTi3oKNuveeTivDDBFAE8ZNFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.041774Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0509725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80dabf8ae5ebb0e684eac9c30745f74d07e1eb7050a058a61d1962c38f741ae3","sha256:f68f8bea42969662f0837b44045d7ea4157da2fa7872c89fd5cbd9624f884ca0"],"state_sha256":"2dcc2cfa6f20c9844f886380ea094ae666502e956e072a487b93e65e50205f4c"}