{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z6BWJPV4NX3LAAI5NOMNZZSGCB","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":"bce563a80db8e3321de4599b11aa753d4b7cd3dacf60fd44f22e66f42a82fdeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-23T01:34:57Z","title_canon_sha256":"58f54031bca4dc37d055216027b54d0adeb36e74d39d7142136133f7b6c3edd2"},"schema_version":"1.0","source":{"id":"1710.08056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08056","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08056v2","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08056","created_at":"2026-05-17T23:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z6BWJPV4NX3L","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z6BWJPV4NX3LAAI5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z6BWJPV4","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:04f0923ddb80f80140d7921e23d56fb422dd7183e84c83325f29c65bdcf043eb","target":"graph","created_at":"2026-05-17T23:55:59Z","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":"We study the moduli space of pairs $(X,H)$ consisting of a cubic threefold $X$ and a hyperplane $H$ in $\\mathbb P^4$. The interest in this moduli comes from two sources: the study of certain weighted hypersurfaces whose middle cohomology admit Hodge structures of $K3$ type and, on the other hand, the study of the singularity $O_{16}$ (the cone over a cubic surface). In this paper, we give a Hodge theoretic construction of the moduli space of cubic pairs by relating $(X,H)$ to certain \"lattice polarized\" cubic fourfolds $Y$. A period map for the pairs $(X,H)$ is then defined using the periods o","authors_text":"Gregory Pearlstein, Radu Laza, Zheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-23T01:34:57Z","title":"On the moduli space of pairs consisting of a cubic threefold and a hyperplane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08056","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":"sha256:073b572c735171429aa420f3240cf4e3e9d478c703d90c656b3c9ce4ca04f954","target":"record","created_at":"2026-05-17T23:55:59Z","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":"bce563a80db8e3321de4599b11aa753d4b7cd3dacf60fd44f22e66f42a82fdeb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-23T01:34:57Z","title_canon_sha256":"58f54031bca4dc37d055216027b54d0adeb36e74d39d7142136133f7b6c3edd2"},"schema_version":"1.0","source":{"id":"1710.08056","kind":"arxiv","version":2}},"canonical_sha256":"cf8364bebc6df6b0011d6b98dce64610627376226d1dff5f0888c574c09e5b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf8364bebc6df6b0011d6b98dce64610627376226d1dff5f0888c574c09e5b2f","first_computed_at":"2026-05-17T23:55:59.936590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:59.936590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PXsEVV4vm5vZy/KRdJPIj+6px1PVRHHTeFxcRqMS2Um5GQP2atyMGHQdCugxll3SpC86wLntdn4/vR75e3GoCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:59.937254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:073b572c735171429aa420f3240cf4e3e9d478c703d90c656b3c9ce4ca04f954","sha256:04f0923ddb80f80140d7921e23d56fb422dd7183e84c83325f29c65bdcf043eb"],"state_sha256":"a78d77aa5c6e9b55c6b4b18d60fb8844d20a2226486b759b79e2a54cc3fac46e"}