{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SPJHNBV4TWJYR3ERA6VHVZ4XD4","short_pith_number":"pith:SPJHNBV4","canonical_record":{"source":{"id":"1010.2300","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-12T05:05:07Z","cross_cats_sorted":[],"title_canon_sha256":"9df70c8603e0ad64b412b28113e617b4982179af4cc9eb6dcf016dd8c2d029c3","abstract_canon_sha256":"6af545cb39fe3b2993919456633e80f56650c15124a46c7a83b71cc0f095a064"},"schema_version":"1.0"},"canonical_sha256":"93d27686bc9d9388ec9107aa7ae7971f0e0b6fbc6b6b81a25b2e2096dd3c8a37","source":{"kind":"arxiv","id":"1010.2300","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2300","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2300v3","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2300","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"SPJHNBV4TWJY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SPJHNBV4TWJYR3ER","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SPJHNBV4","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SPJHNBV4TWJYR3ERA6VHVZ4XD4","target":"record","payload":{"canonical_record":{"source":{"id":"1010.2300","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-12T05:05:07Z","cross_cats_sorted":[],"title_canon_sha256":"9df70c8603e0ad64b412b28113e617b4982179af4cc9eb6dcf016dd8c2d029c3","abstract_canon_sha256":"6af545cb39fe3b2993919456633e80f56650c15124a46c7a83b71cc0f095a064"},"schema_version":"1.0"},"canonical_sha256":"93d27686bc9d9388ec9107aa7ae7971f0e0b6fbc6b6b81a25b2e2096dd3c8a37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:45.864961Z","signature_b64":"AuJBcUpJjuhgEQayt+7MS+lngdUw5VMzgx9mkYaJk4sVQDQidNmSBJbYGabg1bEszE5YkWdjxm2RFmspfvMdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93d27686bc9d9388ec9107aa7ae7971f0e0b6fbc6b6b81a25b2e2096dd3c8a37","last_reissued_at":"2026-05-18T04:09:45.864297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:45.864297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.2300","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zSbEuSYqpzcrN3plc8IznM/9YlOPYuD8NeQO/VhT/8xT9f9aj5MBIXNQec3sS8po2u5lSyr8Od7QseRPEPijCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:29:22.362135Z"},"content_sha256":"8059d9cc883c99a5240f0e91b1600dee175c8c92ec05b1ba08d80db8872139f0","schema_version":"1.0","event_id":"sha256:8059d9cc883c99a5240f0e91b1600dee175c8c92ec05b1ba08d80db8872139f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SPJHNBV4TWJYR3ERA6VHVZ4XD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On projective manifolds swept out by cubic varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kiwamu Watanabe","submitted_at":"2010-10-12T05:05:07Z","abstract_excerpt":"We study structures of embedded projective manifolds swept out by cubic varieties. We show if an embedded projective manifold is swept out by high-dimensional smooth cubic hypersurfaces, then it admits an extremal contraction which is a linear projective bundle or a cubic fibration. As an application, we give a characterization of smooth cubic hypersurfaces. We also classify embedded projective manifolds of dimension at most five swept out by copies of the Segre threefold P^1\\timesP^2. In the course of the proof, we classify projective manifolds of dimension five swept out by planes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2300","kind":"arxiv","version":3},"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":"2026-05-18T04:09:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cyHtYCgve7Xe5/0jh4g4Cxm94Ms9VlH08wDff1QUL7UVpH0fBmQBS3zKUAKSzEBvs2TA60mOm7oTNPS/RZ6MBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:29:22.362488Z"},"content_sha256":"2c5caf49791a7d5716c0ea04839e478057148b8675c889ff67f0dc7b924a4e4a","schema_version":"1.0","event_id":"sha256:2c5caf49791a7d5716c0ea04839e478057148b8675c889ff67f0dc7b924a4e4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPJHNBV4TWJYR3ERA6VHVZ4XD4/bundle.json","state_url":"https://pith.science/pith/SPJHNBV4TWJYR3ERA6VHVZ4XD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPJHNBV4TWJYR3ERA6VHVZ4XD4/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":"2026-06-28T18:29:22Z","links":{"resolver":"https://pith.science/pith/SPJHNBV4TWJYR3ERA6VHVZ4XD4","bundle":"https://pith.science/pith/SPJHNBV4TWJYR3ERA6VHVZ4XD4/bundle.json","state":"https://pith.science/pith/SPJHNBV4TWJYR3ERA6VHVZ4XD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPJHNBV4TWJYR3ERA6VHVZ4XD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SPJHNBV4TWJYR3ERA6VHVZ4XD4","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":"6af545cb39fe3b2993919456633e80f56650c15124a46c7a83b71cc0f095a064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-12T05:05:07Z","title_canon_sha256":"9df70c8603e0ad64b412b28113e617b4982179af4cc9eb6dcf016dd8c2d029c3"},"schema_version":"1.0","source":{"id":"1010.2300","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2300","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2300v3","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2300","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"SPJHNBV4TWJY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SPJHNBV4TWJYR3ER","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SPJHNBV4","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:2c5caf49791a7d5716c0ea04839e478057148b8675c889ff67f0dc7b924a4e4a","target":"graph","created_at":"2026-05-18T04:09:45Z","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 structures of embedded projective manifolds swept out by cubic varieties. We show if an embedded projective manifold is swept out by high-dimensional smooth cubic hypersurfaces, then it admits an extremal contraction which is a linear projective bundle or a cubic fibration. As an application, we give a characterization of smooth cubic hypersurfaces. We also classify embedded projective manifolds of dimension at most five swept out by copies of the Segre threefold P^1\\timesP^2. In the course of the proof, we classify projective manifolds of dimension five swept out by planes.","authors_text":"Kiwamu Watanabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-12T05:05:07Z","title":"On projective manifolds swept out by cubic varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2300","kind":"arxiv","version":3},"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":"sha256:8059d9cc883c99a5240f0e91b1600dee175c8c92ec05b1ba08d80db8872139f0","target":"record","created_at":"2026-05-18T04:09:45Z","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":"6af545cb39fe3b2993919456633e80f56650c15124a46c7a83b71cc0f095a064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-12T05:05:07Z","title_canon_sha256":"9df70c8603e0ad64b412b28113e617b4982179af4cc9eb6dcf016dd8c2d029c3"},"schema_version":"1.0","source":{"id":"1010.2300","kind":"arxiv","version":3}},"canonical_sha256":"93d27686bc9d9388ec9107aa7ae7971f0e0b6fbc6b6b81a25b2e2096dd3c8a37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93d27686bc9d9388ec9107aa7ae7971f0e0b6fbc6b6b81a25b2e2096dd3c8a37","first_computed_at":"2026-05-18T04:09:45.864297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:45.864297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AuJBcUpJjuhgEQayt+7MS+lngdUw5VMzgx9mkYaJk4sVQDQidNmSBJbYGabg1bEszE5YkWdjxm2RFmspfvMdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:45.864961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2300","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8059d9cc883c99a5240f0e91b1600dee175c8c92ec05b1ba08d80db8872139f0","sha256:2c5caf49791a7d5716c0ea04839e478057148b8675c889ff67f0dc7b924a4e4a"],"state_sha256":"ac4e36f4c73c3e1abd3d30afb14cd6dd9cf615cdda1c50301987bb3eca2ac432"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WDqOnYBxRe9YX2HioaYjJFGHOouj0WRivFjKf4TZr22t76TwEoV7/052Yx6j0NCRK1bhkdJjuDUatSJkWnfGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T18:29:22.364321Z","bundle_sha256":"8fe6edd91809070665a0667803ee71853d2c7a1a0a2a839dc7d876895b8e9eaf"}}