{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4AFERF656NVTST74UFIOFGK6BI","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":"c580873054e66c51bb10be01a5a3320a452880298af22db81af63ecbc678f44b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-04T18:53:44Z","title_canon_sha256":"ce68538b27dacbe7beedcbf4899affecdb831acbda865e5d70e638add285dc4d"},"schema_version":"1.0","source":{"id":"1509.01562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01562","created_at":"2026-05-18T01:09:06Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01562v2","created_at":"2026-05-18T01:09:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01562","created_at":"2026-05-18T01:09:06Z"},{"alias_kind":"pith_short_12","alias_value":"4AFERF656NVT","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4AFERF656NVTST74","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4AFERF65","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:7e0285c89455bf7ebd91a023a27bdf842505e295ccf0fa666a46e00eec4aec8a","target":"graph","created_at":"2026-05-18T01:09:06Z","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"},"paper":{"abstract_excerpt":"A special cubic fourfold is a smooth hypersurface of degree three and dimension four that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether-Lefschetz divisors C_d in the moduli space C of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the \"low-weight cusp form trick\" of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of C_d. For example, if d = 6n + 2, then we show that C_d is of general type ","authors_text":"Anthony V\\'arilly-Alvarado, Sho Tanimoto","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-04T18:53:44Z","title":"Kodaira dimension of moduli of special cubic fourfolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01562","kind":"arxiv","version":2},"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:b9f41ed867100a875638384c744e8ac4bbb3c2bd9806fa765bedfbe7cf952fe9","target":"record","created_at":"2026-05-18T01:09:06Z","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":"c580873054e66c51bb10be01a5a3320a452880298af22db81af63ecbc678f44b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-04T18:53:44Z","title_canon_sha256":"ce68538b27dacbe7beedcbf4899affecdb831acbda865e5d70e638add285dc4d"},"schema_version":"1.0","source":{"id":"1509.01562","kind":"arxiv","version":2}},"canonical_sha256":"e00a4897ddf36b394ffca150e2995e0a30d03248b3c4b0fd484a0b4e2ca46f34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e00a4897ddf36b394ffca150e2995e0a30d03248b3c4b0fd484a0b4e2ca46f34","first_computed_at":"2026-05-18T01:09:06.950131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:06.950131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A1ZAP8v7IyTFlWdvqQd06dl5M8FibYc8SNINUFrwApNaPkYcLnBoaZ2mtiYrfUZTd1BBAIuAdKgjSYAQqrSWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:06.950588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9f41ed867100a875638384c744e8ac4bbb3c2bd9806fa765bedfbe7cf952fe9","sha256:7e0285c89455bf7ebd91a023a27bdf842505e295ccf0fa666a46e00eec4aec8a"],"state_sha256":"ccdc2c115a419107d66bdd1960dbe387717034847d54e0ce36b57ed1daf0b086"}