{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OBOI57DU5BNN5X6LJTYQ626B5H","short_pith_number":"pith:OBOI57DU","schema_version":"1.0","canonical_sha256":"705c8efc74e85adedfcb4cf10f6bc1e9e6346a286acff7ac37c10ff863b0e377","source":{"kind":"arxiv","id":"1006.5909","version":2},"attestation_state":"computed","paper":{"title":"Weakly--exceptional quotient singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Dmitrijs Sakovics","submitted_at":"2010-06-30T16:26:41Z","abstract_excerpt":"A singularity is said to be weakly--exceptional if it has a unique purely log terminal blow up. In dimension $2$, V. Shokurov proved that weakly--exceptional quotient singularities are exactly those of types $D_{n}$, $E_{6}$, $E_{7}$, $E_{8}$. This paper classifies the weakly--exceptional quotient singularities in dimensions $3$ and $4$."},"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":"1006.5909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-30T16:26:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d785f931c93c51e0d438842624c435a7508b571c05555597ed14ba985b999afa","abstract_canon_sha256":"1983b49bf156e845c247dbd7e1fb45616ce3183eefc145023db96aee60a0d99b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:46.515054Z","signature_b64":"uRcuxj9O9ds6E/PTMsFncDskGZ68npnXg7DdF/h8gmsu3pJVA+s8jkX5fqmL2pizWYC4yZXhCpsXccMBoOAUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"705c8efc74e85adedfcb4cf10f6bc1e9e6346a286acff7ac37c10ff863b0e377","last_reissued_at":"2026-05-18T02:38:46.514644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:46.514644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weakly--exceptional quotient singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Dmitrijs Sakovics","submitted_at":"2010-06-30T16:26:41Z","abstract_excerpt":"A singularity is said to be weakly--exceptional if it has a unique purely log terminal blow up. In dimension $2$, V. Shokurov proved that weakly--exceptional quotient singularities are exactly those of types $D_{n}$, $E_{6}$, $E_{7}$, $E_{8}$. This paper classifies the weakly--exceptional quotient singularities in dimensions $3$ and $4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5909","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":""},"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":"1006.5909","created_at":"2026-05-18T02:38:46.514703+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.5909v2","created_at":"2026-05-18T02:38:46.514703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5909","created_at":"2026-05-18T02:38:46.514703+00:00"},{"alias_kind":"pith_short_12","alias_value":"OBOI57DU5BNN","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OBOI57DU5BNN5X6L","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OBOI57DU","created_at":"2026-05-18T12:26:12.377268+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/OBOI57DU5BNN5X6LJTYQ626B5H","json":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H.json","graph_json":"https://pith.science/api/pith-number/OBOI57DU5BNN5X6LJTYQ626B5H/graph.json","events_json":"https://pith.science/api/pith-number/OBOI57DU5BNN5X6LJTYQ626B5H/events.json","paper":"https://pith.science/paper/OBOI57DU"},"agent_actions":{"view_html":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H","download_json":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H.json","view_paper":"https://pith.science/paper/OBOI57DU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.5909&json=true","fetch_graph":"https://pith.science/api/pith-number/OBOI57DU5BNN5X6LJTYQ626B5H/graph.json","fetch_events":"https://pith.science/api/pith-number/OBOI57DU5BNN5X6LJTYQ626B5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H/action/storage_attestation","attest_author":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H/action/author_attestation","sign_citation":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H/action/citation_signature","submit_replication":"https://pith.science/pith/OBOI57DU5BNN5X6LJTYQ626B5H/action/replication_record"}},"created_at":"2026-05-18T02:38:46.514703+00:00","updated_at":"2026-05-18T02:38:46.514703+00:00"}