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Rationality has been proved by Fano for the first divisor $C_{14}$ and in [arXiv:1707.00999] for the divisors $C_{26}$ and $C_{38}$. In this note we describe explicit birational maps from a general cubic fourfold in $C_{14}$, in $C_{26}$ and in $C_{38}$ to $\\mathbb{P}^4$, prov"},"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":"1811.03502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-08T15:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"b45b1375f5ebf99bc43ab04d74a1a260730c580c376f47f4b47a4caaf40afffa","abstract_canon_sha256":"4352b32fc29a5418df8aa0dd6aec7f9a1edc5484688e4dad743d96d8713dd11b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:53.111694Z","signature_b64":"7dV2511Fa4osrS79Vlvw1CRhd02XyFF0QOxdFmRCEUdVGaHtNYvoDkwN4BqUJrZB5nC23uFfDyE+VXN+mWpqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b1c5cf10f122171f9bbfc432bea277e62275fcd86df7141cc303a28838569cd","last_reissued_at":"2026-07-05T00:00:53.111303Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:53.111303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit rationality of some cubic fourfolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Russo, Giovanni Staglian\\`o","submitted_at":"2018-11-08T15:44:39Z","abstract_excerpt":"Recent results of Hassett, Kuznetsov and others pointed out countably many divisors $C_d$ in the open subset of $\\mathbb{P}^{55}=\\mathbb{P}(H^0(\\mathcal{O}_{\\mathbb{P}^5}(3)))$ parametrizing all cubic 4-folds and lead to the conjecture that the cubics corresponding to these divisors should be precisely the rational ones. Rationality has been proved by Fano for the first divisor $C_{14}$ and in [arXiv:1707.00999] for the divisors $C_{26}$ and $C_{38}$. In this note we describe explicit birational maps from a general cubic fourfold in $C_{14}$, in $C_{26}$ and in $C_{38}$ to $\\mathbb{P}^4$, prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03502","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.03502/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":"1811.03502","created_at":"2026-07-05T00:00:53.111367+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.03502v2","created_at":"2026-07-05T00:00:53.111367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03502","created_at":"2026-07-05T00:00:53.111367+00:00"},{"alias_kind":"pith_short_12","alias_value":"FMOFZ4IPCIQX","created_at":"2026-07-05T00:00:53.111367+00:00"},{"alias_kind":"pith_short_16","alias_value":"FMOFZ4IPCIQXD6N3","created_at":"2026-07-05T00:00:53.111367+00:00"},{"alias_kind":"pith_short_8","alias_value":"FMOFZ4IP","created_at":"2026-07-05T00:00:53.111367+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.01263","citing_title":"Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ","json":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ.json","graph_json":"https://pith.science/api/pith-number/FMOFZ4IPCIQXD6N37RBSX2RHPZ/graph.json","events_json":"https://pith.science/api/pith-number/FMOFZ4IPCIQXD6N37RBSX2RHPZ/events.json","paper":"https://pith.science/paper/FMOFZ4IP"},"agent_actions":{"view_html":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ","download_json":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ.json","view_paper":"https://pith.science/paper/FMOFZ4IP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.03502&json=true","fetch_graph":"https://pith.science/api/pith-number/FMOFZ4IPCIQXD6N37RBSX2RHPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/FMOFZ4IPCIQXD6N37RBSX2RHPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/action/storage_attestation","attest_author":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/action/author_attestation","sign_citation":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/action/citation_signature","submit_replication":"https://pith.science/pith/FMOFZ4IPCIQXD6N37RBSX2RHPZ/action/replication_record"}},"created_at":"2026-07-05T00:00:53.111367+00:00","updated_at":"2026-07-05T00:00:53.111367+00:00"}