{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ICIW73MA6A726B7OIKISBKLYXP","short_pith_number":"pith:ICIW73MA","schema_version":"1.0","canonical_sha256":"40916fed80f03faf07ee429120a978bbe5ee3cbb687797b023e6b3b8dc7d41f6","source":{"kind":"arxiv","id":"1707.00999","version":4},"attestation_state":"computed","paper":{"title":"Congruences of 5-secant conics and the rationality of some admissible 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":"2017-07-04T14:03:23Z","abstract_excerpt":"The works of Hassett and Kuznetsov identify 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 conjecture that the cubics corresponding to these divisors are precisely the rational ones. Rationality has been known classically for the first family $C_{14}$. We use congruences of 5-secant conics to prove rationality for the first three of the families $C_d$, corresponding to $d=14, 26, 38$ in Hassett's notation."},"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":"1707.00999","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T14:03:23Z","cross_cats_sorted":[],"title_canon_sha256":"bbaf6ac8526e9effb5a1f9325f9c690c2628e2adba7dc302ef20388614c3a366","abstract_canon_sha256":"583b6f505864586afa4fcbacf1bdd593c48d488b3b2ebfb70a9c491ea461bb63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:00.129451Z","signature_b64":"UwpaFjXOZAyX+DWOqD8ZV8obgme04KLcBJc9yvB7d02IKVKp4qfbShSK62ZfByqWcYaw9eXLPGL5M5c050FLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40916fed80f03faf07ee429120a978bbe5ee3cbb687797b023e6b3b8dc7d41f6","last_reissued_at":"2026-05-17T23:45:00.128938Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:00.128938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Congruences of 5-secant conics and the rationality of some admissible 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":"2017-07-04T14:03:23Z","abstract_excerpt":"The works of Hassett and Kuznetsov identify 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 conjecture that the cubics corresponding to these divisors are precisely the rational ones. Rationality has been known classically for the first family $C_{14}$. We use congruences of 5-secant conics to prove rationality for the first three of the families $C_d$, corresponding to $d=14, 26, 38$ in Hassett's notation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00999","kind":"arxiv","version":4},"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":"1707.00999","created_at":"2026-05-17T23:45:00.129022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.00999v4","created_at":"2026-05-17T23:45:00.129022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00999","created_at":"2026-05-17T23:45:00.129022+00:00"},{"alias_kind":"pith_short_12","alias_value":"ICIW73MA6A72","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"ICIW73MA6A726B7O","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"ICIW73MA","created_at":"2026-05-18T12:31:21.493067+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/ICIW73MA6A726B7OIKISBKLYXP","json":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP.json","graph_json":"https://pith.science/api/pith-number/ICIW73MA6A726B7OIKISBKLYXP/graph.json","events_json":"https://pith.science/api/pith-number/ICIW73MA6A726B7OIKISBKLYXP/events.json","paper":"https://pith.science/paper/ICIW73MA"},"agent_actions":{"view_html":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP","download_json":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP.json","view_paper":"https://pith.science/paper/ICIW73MA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.00999&json=true","fetch_graph":"https://pith.science/api/pith-number/ICIW73MA6A726B7OIKISBKLYXP/graph.json","fetch_events":"https://pith.science/api/pith-number/ICIW73MA6A726B7OIKISBKLYXP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP/action/storage_attestation","attest_author":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP/action/author_attestation","sign_citation":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP/action/citation_signature","submit_replication":"https://pith.science/pith/ICIW73MA6A726B7OIKISBKLYXP/action/replication_record"}},"created_at":"2026-05-17T23:45:00.129022+00:00","updated_at":"2026-05-17T23:45:00.129022+00:00"}