{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:25LKSKPWREIUVTHS7SQZXOYD3X","short_pith_number":"pith:25LKSKPW","canonical_record":{"source":{"id":"1806.03429","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-09T07:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"5ae7a1a602b091bd541b5b71a0627774aa3cbf1eea7e4c684f002ab67057c0d3","abstract_canon_sha256":"a26d5af0482ef90c2e9cc4cb309cb60acfe3abadc61baf8fa9b0ed0dc42f3c65"},"schema_version":"1.0"},"canonical_sha256":"d756a929f689114accf2fca19bbb03ddf6a1b61da4c5181961db85d47c90ce2e","source":{"kind":"arxiv","id":"1806.03429","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:25LKSKPWREIUVTHS7SQZXOYD3X","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03429","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-09T07:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"5ae7a1a602b091bd541b5b71a0627774aa3cbf1eea7e4c684f002ab67057c0d3","abstract_canon_sha256":"a26d5af0482ef90c2e9cc4cb309cb60acfe3abadc61baf8fa9b0ed0dc42f3c65"},"schema_version":"1.0"},"canonical_sha256":"d756a929f689114accf2fca19bbb03ddf6a1b61da4c5181961db85d47c90ce2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:54.810568Z","signature_b64":"eoMZRXet266dI+OTSMYQckMa6nMJ9aV3pLB16pFMv5mwhV8OKUgr6v7USqz/GicDX30mfaheku3WuPdNU5hJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d756a929f689114accf2fca19bbb03ddf6a1b61da4c5181961db85d47c90ce2e","last_reissued_at":"2026-05-18T00:02:54.809844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:54.809844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03429","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FoaUIsqi3gzAVHGS/FOEs3DGKBcz0QXq+dcLAWJqxMtMKK8R+i3USnGjpuPKQxTHVYWODjNgR1TIbWCm7lnBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:09:55.803789Z"},"content_sha256":"e37a896dcabfcfde17401d71a97a171e9b6e809c4aa514686db6d398b12c4d2a","schema_version":"1.0","event_id":"sha256:e37a896dcabfcfde17401d71a97a171e9b6e809c4aa514686db6d398b12c4d2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:25LKSKPWREIUVTHS7SQZXOYD3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cubic hypersurfaces with positive dual defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Katsuhisa Furukawa","submitted_at":"2018-06-09T07:25:54Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03429","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MIgEj0/fRpZrjU1NqyJYNZaq0vzukilOtfjvo+7PhpPTnqBhbiVmris6/5QXrk0BIwTNFJanPkCOilKUOBSzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:09:55.804128Z"},"content_sha256":"42be9f90b7ee7937e67ed8fd394fe86d33d6e86cdacf042d00ccb68f2707f598","schema_version":"1.0","event_id":"sha256:42be9f90b7ee7937e67ed8fd394fe86d33d6e86cdacf042d00ccb68f2707f598"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25LKSKPWREIUVTHS7SQZXOYD3X/bundle.json","state_url":"https://pith.science/pith/25LKSKPWREIUVTHS7SQZXOYD3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25LKSKPWREIUVTHS7SQZXOYD3X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T16:09:55Z","links":{"resolver":"https://pith.science/pith/25LKSKPWREIUVTHS7SQZXOYD3X","bundle":"https://pith.science/pith/25LKSKPWREIUVTHS7SQZXOYD3X/bundle.json","state":"https://pith.science/pith/25LKSKPWREIUVTHS7SQZXOYD3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25LKSKPWREIUVTHS7SQZXOYD3X/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F2AGsft5dFmKzP+b6ZlPT3CgkdWw6jV2tqqxBs8n5y8PF5pWQVSK+rqAOF2HglMafDFICNfk3su6rYvoAPSgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:09:55.806051Z","bundle_sha256":"3ae5c17b1990bd492416aaf98ca54cdfca1c357c0918cd2279bd5969400618f1"}}