{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5MJD7FKJHSIFHVP25KV7C4X574","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":"93916c395e82c335c4dea8bc49a7b8968610c891adfc62c21119f7ae93fcee2e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-16T23:07:03Z","title_canon_sha256":"dda8db9e808d20e629ebe1e79b4f69b101b9987aeff5a2aa6767557cff71c3cd"},"schema_version":"1.0","source":{"id":"1109.3738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3738","created_at":"2026-05-18T00:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3738v2","created_at":"2026-05-18T00:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3738","created_at":"2026-05-18T00:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"5MJD7FKJHSIF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5MJD7FKJHSIFHVP2","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5MJD7FKJ","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:ccdf0e9fab4628a817ac44ab2bc3f0ce60c5a1ed3f459ff474644990ce95a551","target":"graph","created_at":"2026-05-18T00:34:10Z","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 show that non-flatness of a morphism f of complex-analytic spaces with a locally irreducible target Y of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of f to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type complex-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module), such that the induced morphism of spectra is dominant. Then a finite type R-algebra A is R-f","authors_text":"Hadi Seyedinejad, Janusz Adamus","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-16T23:07:03Z","title":"Flatness testing over singular bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3738","kind":"arxiv","version":2},"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:b7fd17e532edde4c67d9a207060fd3dbbee34e04fa48a077592ac12752452ccb","target":"record","created_at":"2026-05-18T00:34:10Z","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":"93916c395e82c335c4dea8bc49a7b8968610c891adfc62c21119f7ae93fcee2e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-16T23:07:03Z","title_canon_sha256":"dda8db9e808d20e629ebe1e79b4f69b101b9987aeff5a2aa6767557cff71c3cd"},"schema_version":"1.0","source":{"id":"1109.3738","kind":"arxiv","version":2}},"canonical_sha256":"eb123f95493c9053d5faeaabf172fdff329f287141e2200ed3169fe64ee9f49d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb123f95493c9053d5faeaabf172fdff329f287141e2200ed3169fe64ee9f49d","first_computed_at":"2026-05-18T00:34:10.836468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:10.836468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8FhyI9X5PQ8/KWvUdoZ0/R97UYQTbNjNXnKd04RVOTrBLzp5se+KRMc3b4RPkntIMA9jGxUP7GrZI99nDhXEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:10.837167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7fd17e532edde4c67d9a207060fd3dbbee34e04fa48a077592ac12752452ccb","sha256:ccdf0e9fab4628a817ac44ab2bc3f0ce60c5a1ed3f459ff474644990ce95a551"],"state_sha256":"420f38bbf4fb366c8b0a1d4a4984aa0311c3cc205ff85db47b67d7954c1cea6b"}