{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:YMAD4SAORS3WANMQ5WMJUHVZ5X","short_pith_number":"pith:YMAD4SAO","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"},"canonical_sha256":"c3003e480e8cb7603590ed989a1eb9edf1ac62fbf82b8092d8241140c5f9006a","source":{"kind":"arxiv","id":"2301.06481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.06481","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"2301.06481v1","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.06481","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"YMAD4SAORS3W","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"pith_short_16","alias_value":"YMAD4SAORS3WANMQ","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"pith_short_8","alias_value":"YMAD4SAO","created_at":"2026-07-05T05:33:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:YMAD4SAORS3WANMQ5WMJUHVZ5X","target":"record","payload":{"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"},"canonical_sha256":"c3003e480e8cb7603590ed989a1eb9edf1ac62fbf82b8092d8241140c5f9006a","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"},"source_kind":"arxiv","source_id":"2301.06481","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IwUSgfs7yJfluE3g/shyiO+i0pshqJJe97xfZ2VzFkh1UmhtZXav3QswcZu/+KVHitTVh5Nh3PPYOu/JYHLgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T17:38:20.961714Z"},"content_sha256":"720279252b26462fcb62497d18f44880e35f9551f6ec6ea2a0d6cc66c7743b8b","schema_version":"1.0","event_id":"sha256:720279252b26462fcb62497d18f44880e35f9551f6ec6ea2a0d6cc66c7743b8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:YMAD4SAORS3WANMQ5WMJUHVZ5X","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5HWGd3NQd/pQbarPTmSkEP3h7KvRjIXI7PJYnTv5duc63dSmSr3GE2VNdi9Ib9SLlV+cJWP9+78lRBihoNjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T17:38:20.962286Z"},"content_sha256":"a488b4c770a75c9acbb66fbb4044b1a73e83329462a512eefc94baf86b532c12","schema_version":"1.0","event_id":"sha256:a488b4c770a75c9acbb66fbb4044b1a73e83329462a512eefc94baf86b532c12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/bundle.json","state_url":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-18T17:38:20Z","links":{"resolver":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X","bundle":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/bundle.json","state":"https://pith.science/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMAD4SAORS3WANMQ5WMJUHVZ5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YMAD4SAORS3WANMQ5WMJUHVZ5X","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":"65d0792662de3661df11621548fee2199576e3f2c4f00606294bb630e1f69da7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2023-01-16T15:39:10Z","title_canon_sha256":"2909a354cdf3cc273854c514ebe72f420a1d22d7d284e12d9dd1ede3e296305d"},"schema_version":"1.0","source":{"id":"2301.06481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.06481","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"2301.06481v1","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.06481","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"YMAD4SAORS3W","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"pith_short_16","alias_value":"YMAD4SAORS3WANMQ","created_at":"2026-07-05T05:33:32Z"},{"alias_kind":"pith_short_8","alias_value":"YMAD4SAO","created_at":"2026-07-05T05:33:32Z"}],"graph_snapshots":[{"event_id":"sha256:a488b4c770a75c9acbb66fbb4044b1a73e83329462a512eefc94baf86b532c12","target":"graph","created_at":"2026-07-05T05:33:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2301.06481/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Tiago Duarte Guerreiro","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2023-01-16T15:39:10Z","title":"Explicit Birational Geometry of Fano threefold complete intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.06481","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":"sha256:720279252b26462fcb62497d18f44880e35f9551f6ec6ea2a0d6cc66c7743b8b","target":"record","created_at":"2026-07-05T05:33:32Z","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":"65d0792662de3661df11621548fee2199576e3f2c4f00606294bb630e1f69da7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2023-01-16T15:39:10Z","title_canon_sha256":"2909a354cdf3cc273854c514ebe72f420a1d22d7d284e12d9dd1ede3e296305d"},"schema_version":"1.0","source":{"id":"2301.06481","kind":"arxiv","version":1}},"canonical_sha256":"c3003e480e8cb7603590ed989a1eb9edf1ac62fbf82b8092d8241140c5f9006a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3003e480e8cb7603590ed989a1eb9edf1ac62fbf82b8092d8241140c5f9006a","first_computed_at":"2026-07-05T05:33:32.306640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:33:32.306640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3bq1SVH/7JdmZp7wyuPwGe/oH1FPmJ9nkcPucTATiZgekyw0vBvbKBsrp8nh5uEhR8mchgJj0EEozHAwXQRwBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:33:32.307038Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.06481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:720279252b26462fcb62497d18f44880e35f9551f6ec6ea2a0d6cc66c7743b8b","sha256:a488b4c770a75c9acbb66fbb4044b1a73e83329462a512eefc94baf86b532c12"],"state_sha256":"0f9576474ee9651d7f08ff6a95e608490e5bb88cbca27a20ab43d1215d37c167"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUWwZ93Ijic4ERGCVY6c4a9yXv+gxMNlV2Kk7mlAjgYlFiNE1TEVFX/XEbV+SWIuq4w4MHkbkmba7gtojqPUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T17:38:20.967041Z","bundle_sha256":"145cb43d6b123a7e8c9aa6e308dacdd570a7e47a0b6ba8b42951845a32912819"}}