{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:YMAD4SAORS3WANMQ5WMJUHVZ5X","short_pith_number":"pith:YMAD4SAO","schema_version":"1.0","canonical_sha256":"c3003e480e8cb7603590ed989a1eb9edf1ac62fbf82b8092d8241140c5f9006a","source":{"kind":"arxiv","id":"2301.06481","version":1},"attestation_state":"computed","paper":{"title":"Explicit Birational Geometry of Fano threefold complete intersections","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tiago Duarte Guerreiro","submitted_at":"2023-01-16T15:39:10Z","abstract_excerpt":"We complete the analysis on the birational rigidity of quasismooth Fano 3-fold deformation families appearing in the Graded Ring Database as a complete intersection. When such a deformation family $X$ has Fano index at least 2 and is minimally embedded in a weighted projective space in codimension 2, we determine which cyclic quotient singularity is a maximal centre. If a cyclic quotient singularity is a maximal centre, we construct a Sarkisov link to a non-isomorphic Mori fibre space or a birational involution. This allows, in particular, the construction of new examples of Fano 3-folds of co"},"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":"2301.06481","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2023-01-16T15:39:10Z","cross_cats_sorted":[],"title_canon_sha256":"2909a354cdf3cc273854c514ebe72f420a1d22d7d284e12d9dd1ede3e296305d","abstract_canon_sha256":"65d0792662de3661df11621548fee2199576e3f2c4f00606294bb630e1f69da7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:33:32.307038Z","signature_b64":"3bq1SVH/7JdmZp7wyuPwGe/oH1FPmJ9nkcPucTATiZgekyw0vBvbKBsrp8nh5uEhR8mchgJj0EEozHAwXQRwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3003e480e8cb7603590ed989a1eb9edf1ac62fbf82b8092d8241140c5f9006a","last_reissued_at":"2026-07-05T05:33:32.306640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:33:32.306640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit Birational Geometry of Fano threefold complete intersections","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tiago Duarte Guerreiro","submitted_at":"2023-01-16T15:39:10Z","abstract_excerpt":"We complete the analysis on the birational rigidity of quasismooth Fano 3-fold deformation families appearing in the Graded Ring Database as a complete intersection. When such a deformation family $X$ has Fano index at least 2 and is minimally embedded in a weighted projective space in codimension 2, we determine which cyclic quotient singularity is a maximal centre. If a cyclic quotient singularity is a maximal centre, we construct a Sarkisov link to a non-isomorphic Mori fibre space or a birational involution. This allows, in particular, the construction of new examples of Fano 3-folds of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.06481","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.06481/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":"2301.06481","created_at":"2026-07-05T05:33:32.306687+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.06481v1","created_at":"2026-07-05T05:33:32.306687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.06481","created_at":"2026-07-05T05:33:32.306687+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMAD4SAORS3W","created_at":"2026-07-05T05:33:32.306687+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMAD4SAORS3WANMQ","created_at":"2026-07-05T05:33:32.306687+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMAD4SAO","created_at":"2026-07-05T05:33:32.306687+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.13025","citing_title":"A survey on birational Rigidity of threefold Weighted Complete Intersections","ref_index":2004,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X","json":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X.json","graph_json":"https://pith.science/api/pith-number/YMAD4SAORS3WANMQ5WMJUHVZ5X/graph.json","events_json":"https://pith.science/api/pith-number/YMAD4SAORS3WANMQ5WMJUHVZ5X/events.json","paper":"https://pith.science/paper/YMAD4SAO"},"agent_actions":{"view_html":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X","download_json":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X.json","view_paper":"https://pith.science/paper/YMAD4SAO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.06481&json=true","fetch_graph":"https://pith.science/api/pith-number/YMAD4SAORS3WANMQ5WMJUHVZ5X/graph.json","fetch_events":"https://pith.science/api/pith-number/YMAD4SAORS3WANMQ5WMJUHVZ5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/action/storage_attestation","attest_author":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/action/author_attestation","sign_citation":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/action/citation_signature","submit_replication":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/action/replication_record"}},"created_at":"2026-07-05T05:33:32.306687+00:00","updated_at":"2026-07-05T05:33:32.306687+00:00"}