{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ULYYWG2ONVXGFLQE55YCTDSLUP","short_pith_number":"pith:ULYYWG2O","schema_version":"1.0","canonical_sha256":"a2f18b1b4e6d6e62ae04ef70298e4ba3f3b217b07d333091cde90ec05fa89423","source":{"kind":"arxiv","id":"1610.04077","version":1},"attestation_state":"computed","paper":{"title":"Hypersurfaces with defect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Niels Lindner","submitted_at":"2016-10-13T13:54:47Z","abstract_excerpt":"A projective hypersurface $X \\subseteq \\mathbb P^n$ has defect if $h^i(X) \\neq h^i(\\mathbb P^n)$ for some $i \\in \\{n, \\dots, 2n-2\\}$ in a suitable cohomology theory. This occurs for example when $X \\subseteq \\mathbb P^4$ is not $\\mathbb Q$-factorial. We show that in characteristic 0, the Tjurina number of hypersurfaces with defect is large. For $X$ with mild singularities, there is a similar result in positive characteristic. As an application, we obtain a lower bound on the asymptotic density of hypersurfaces without defect over a finite field."},"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":"1610.04077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-10-13T13:54:47Z","cross_cats_sorted":[],"title_canon_sha256":"e9d260cd2be3782e63bdbaff146403f7d26db020e82e298eb2091c83a7171c96","abstract_canon_sha256":"7a958c2137cbbdcb54f3104f7f9ff5f6990bd39d49412d3891616855ee876c4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:22.429645Z","signature_b64":"D5mihFhg95gibBeMBXp0TTz7oY01IugL1+TZNHfOLC4oVW5hDwEyqqJkThHUxJb5DLLv05fifsdIeJ4h0XBMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2f18b1b4e6d6e62ae04ef70298e4ba3f3b217b07d333091cde90ec05fa89423","last_reissued_at":"2026-05-18T01:02:22.428762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:22.428762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypersurfaces with defect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Niels Lindner","submitted_at":"2016-10-13T13:54:47Z","abstract_excerpt":"A projective hypersurface $X \\subseteq \\mathbb P^n$ has defect if $h^i(X) \\neq h^i(\\mathbb P^n)$ for some $i \\in \\{n, \\dots, 2n-2\\}$ in a suitable cohomology theory. This occurs for example when $X \\subseteq \\mathbb P^4$ is not $\\mathbb Q$-factorial. We show that in characteristic 0, the Tjurina number of hypersurfaces with defect is large. For $X$ with mild singularities, there is a similar result in positive characteristic. As an application, we obtain a lower bound on the asymptotic density of hypersurfaces without defect over a finite field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04077","kind":"arxiv","version":1},"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":"1610.04077","created_at":"2026-05-18T01:02:22.428902+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04077v1","created_at":"2026-05-18T01:02:22.428902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04077","created_at":"2026-05-18T01:02:22.428902+00:00"},{"alias_kind":"pith_short_12","alias_value":"ULYYWG2ONVXG","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"ULYYWG2ONVXGFLQE","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"ULYYWG2O","created_at":"2026-05-18T12:30:46.583412+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/ULYYWG2ONVXGFLQE55YCTDSLUP","json":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP.json","graph_json":"https://pith.science/api/pith-number/ULYYWG2ONVXGFLQE55YCTDSLUP/graph.json","events_json":"https://pith.science/api/pith-number/ULYYWG2ONVXGFLQE55YCTDSLUP/events.json","paper":"https://pith.science/paper/ULYYWG2O"},"agent_actions":{"view_html":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP","download_json":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP.json","view_paper":"https://pith.science/paper/ULYYWG2O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04077&json=true","fetch_graph":"https://pith.science/api/pith-number/ULYYWG2ONVXGFLQE55YCTDSLUP/graph.json","fetch_events":"https://pith.science/api/pith-number/ULYYWG2ONVXGFLQE55YCTDSLUP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP/action/storage_attestation","attest_author":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP/action/author_attestation","sign_citation":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP/action/citation_signature","submit_replication":"https://pith.science/pith/ULYYWG2ONVXGFLQE55YCTDSLUP/action/replication_record"}},"created_at":"2026-05-18T01:02:22.428902+00:00","updated_at":"2026-05-18T01:02:22.428902+00:00"}