{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:25LKSKPWREIUVTHS7SQZXOYD3X","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":"a26d5af0482ef90c2e9cc4cb309cb60acfe3abadc61baf8fa9b0ed0dc42f3c65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-09T07:25:54Z","title_canon_sha256":"5ae7a1a602b091bd541b5b71a0627774aa3cbf1eea7e4c684f002ab67057c0d3"},"schema_version":"1.0","source":{"id":"1806.03429","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03429","created_at":"2026-05-18T00:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03429v4","created_at":"2026-05-18T00:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03429","created_at":"2026-05-18T00:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"25LKSKPWREIU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"25LKSKPWREIUVTHS","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"25LKSKPW","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:42be9f90b7ee7937e67ed8fd394fe86d33d6e86cdacf042d00ccb68f2707f598","target":"graph","created_at":"2026-05-18T00:02:54Z","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 show that if a cubic hypersurface with positive dual defect over the complex number field is not a cone, then either the hypersurface coincides with the secant variety of the singular locus, or the hypersurface contains a linear subvariety of dimension greater than the dual defect such that the intersection of the singular locus and a general contact locus is contained in the linear subvariety.","authors_text":"Katsuhisa Furukawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-09T07:25:54Z","title":"Cubic hypersurfaces with positive dual defects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03429","kind":"arxiv","version":4},"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:e37a896dcabfcfde17401d71a97a171e9b6e809c4aa514686db6d398b12c4d2a","target":"record","created_at":"2026-05-18T00:02:54Z","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":"a26d5af0482ef90c2e9cc4cb309cb60acfe3abadc61baf8fa9b0ed0dc42f3c65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-09T07:25:54Z","title_canon_sha256":"5ae7a1a602b091bd541b5b71a0627774aa3cbf1eea7e4c684f002ab67057c0d3"},"schema_version":"1.0","source":{"id":"1806.03429","kind":"arxiv","version":4}},"canonical_sha256":"d756a929f689114accf2fca19bbb03ddf6a1b61da4c5181961db85d47c90ce2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d756a929f689114accf2fca19bbb03ddf6a1b61da4c5181961db85d47c90ce2e","first_computed_at":"2026-05-18T00:02:54.809844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:54.809844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eoMZRXet266dI+OTSMYQckMa6nMJ9aV3pLB16pFMv5mwhV8OKUgr6v7USqz/GicDX30mfaheku3WuPdNU5hJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:54.810568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03429","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e37a896dcabfcfde17401d71a97a171e9b6e809c4aa514686db6d398b12c4d2a","sha256:42be9f90b7ee7937e67ed8fd394fe86d33d6e86cdacf042d00ccb68f2707f598"],"state_sha256":"baf37905b3958c2afaef79f97a1b421092d815f00b677088637086135e3c7bcc"}