{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VNZ5MAOR4OBCIGP3W7ESNGYS6W","short_pith_number":"pith:VNZ5MAOR","schema_version":"1.0","canonical_sha256":"ab73d601d1e3822419fbb7c9269b12f5a6a81f7e0ba0a91e057eaf27dee8f8c7","source":{"kind":"arxiv","id":"1904.01077","version":2},"attestation_state":"computed","paper":{"title":"From Cracked Polytopes to Fano Threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thomas Prince","submitted_at":"2019-04-01T19:31:15Z","abstract_excerpt":"We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes - polytopes whose intersection with a complete fan forms a set of unimodular polytopes - using Laurent inversion; a method developed jointly with Coates-Kasprzyk. We also give constructions of rank one Fano threefolds from cracked polytopes, following work of Christophersen-Ilten and Galkin. We explore the problem of classifying polytopes cracked along a given fan in three dimensions, and classify the unimodular polytopes which can occur as 'pieces' of a cracked polytope."},"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":"1904.01077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-01T19:31:15Z","cross_cats_sorted":[],"title_canon_sha256":"28cfde70fd8b254fd882b52756e3754728b7523d5a5867a5f21102ff3b019773","abstract_canon_sha256":"24a52a386e6a2628025e6d13bcce376b45ec2cc83d6585cdcc79c68ae14f0e66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:24.497868Z","signature_b64":"fjpv3ksqWRUby+WMPaWN44e4Sf9qN0cfpQL7uAA6truyWSgZTtGck19AStCeHMdHbiT+CK4txdsI6tDcq4JCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab73d601d1e3822419fbb7c9269b12f5a6a81f7e0ba0a91e057eaf27dee8f8c7","last_reissued_at":"2026-05-17T23:39:24.495615Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:24.495615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Cracked Polytopes to Fano Threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thomas Prince","submitted_at":"2019-04-01T19:31:15Z","abstract_excerpt":"We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes - polytopes whose intersection with a complete fan forms a set of unimodular polytopes - using Laurent inversion; a method developed jointly with Coates-Kasprzyk. We also give constructions of rank one Fano threefolds from cracked polytopes, following work of Christophersen-Ilten and Galkin. We explore the problem of classifying polytopes cracked along a given fan in three dimensions, and classify the unimodular polytopes which can occur as 'pieces' of a cracked polytope."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01077","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":"1904.01077","created_at":"2026-05-17T23:39:24.497190+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.01077v2","created_at":"2026-05-17T23:39:24.497190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01077","created_at":"2026-05-17T23:39:24.497190+00:00"},{"alias_kind":"pith_short_12","alias_value":"VNZ5MAOR4OBC","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VNZ5MAOR4OBCIGP3","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VNZ5MAOR","created_at":"2026-05-18T12:33:30.264802+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/VNZ5MAOR4OBCIGP3W7ESNGYS6W","json":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W.json","graph_json":"https://pith.science/api/pith-number/VNZ5MAOR4OBCIGP3W7ESNGYS6W/graph.json","events_json":"https://pith.science/api/pith-number/VNZ5MAOR4OBCIGP3W7ESNGYS6W/events.json","paper":"https://pith.science/paper/VNZ5MAOR"},"agent_actions":{"view_html":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W","download_json":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W.json","view_paper":"https://pith.science/paper/VNZ5MAOR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.01077&json=true","fetch_graph":"https://pith.science/api/pith-number/VNZ5MAOR4OBCIGP3W7ESNGYS6W/graph.json","fetch_events":"https://pith.science/api/pith-number/VNZ5MAOR4OBCIGP3W7ESNGYS6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W/action/storage_attestation","attest_author":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W/action/author_attestation","sign_citation":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W/action/citation_signature","submit_replication":"https://pith.science/pith/VNZ5MAOR4OBCIGP3W7ESNGYS6W/action/replication_record"}},"created_at":"2026-05-17T23:39:24.497190+00:00","updated_at":"2026-05-17T23:39:24.497190+00:00"}