{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2GDRZUMNF36OWVMHQVBC7JSYRQ","short_pith_number":"pith:2GDRZUMN","canonical_record":{"source":{"id":"1205.0237","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-01T19:25:05Z","cross_cats_sorted":[],"title_canon_sha256":"0ef1515eeb6bbd40f8b3d7ff1c87f1537e67857511f3b55019f20c351954162d","abstract_canon_sha256":"44c2f60b1df3962b228c59afcddb385502a1d504654383911aa6fba10d17ac97"},"schema_version":"1.0"},"canonical_sha256":"d1871cd18d2efceb558785422fa6588c127b18fdefa36ba7780c06d998af9118","source":{"kind":"arxiv","id":"1205.0237","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0237","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0237v4","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0237","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"2GDRZUMNF36O","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2GDRZUMNF36OWVMH","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2GDRZUMN","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2GDRZUMNF36OWVMHQVBC7JSYRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0237","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-01T19:25:05Z","cross_cats_sorted":[],"title_canon_sha256":"0ef1515eeb6bbd40f8b3d7ff1c87f1537e67857511f3b55019f20c351954162d","abstract_canon_sha256":"44c2f60b1df3962b228c59afcddb385502a1d504654383911aa6fba10d17ac97"},"schema_version":"1.0"},"canonical_sha256":"d1871cd18d2efceb558785422fa6588c127b18fdefa36ba7780c06d998af9118","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:46.233348Z","signature_b64":"bgo2KQmglonVsKer1jIbK3ghXS6Seh+U7DhaQh7HsqtjhYAerSV2hVbf6A5cb7bp/eYcU34/FvzCqltF9IOaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1871cd18d2efceb558785422fa6588c127b18fdefa36ba7780c06d998af9118","last_reissued_at":"2026-05-18T02:49:46.232983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:46.232983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0237","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":"2026-05-18T02:49:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IYsTm+3Pn/iupTwoZQNZtrLLJRRTe9SAPlFvhzC7G4HAJtyHNcifk4jl0txwRI1oYQv19pn6Ob/SHYgE8SlLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:08:23.801127Z"},"content_sha256":"a43cba20cc5cce98d8b3611d846150b8a9aadbb237fecacef3cb32727c9adf44","schema_version":"1.0","event_id":"sha256:a43cba20cc5cce98d8b3611d846150b8a9aadbb237fecacef3cb32727c9adf44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2GDRZUMNF36OWVMHQVBC7JSYRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cubic fourfolds containing a plane and a quintic del Pezzo surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anthony V\\'arilly-Alvarado, Asher Auel, Marcello Bernardara, Michele Bolognesi","submitted_at":"2012-05-01T19:25:05Z","abstract_excerpt":"We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class of the even Clifford algebra over the K3 surface S of degree 2 arising from X. Specifically, we show that in the moduli space of cubic fourfolds, the intersection of divisors C_8 and C_14 has five irreducible components. In the component corresponding to the existence of a tangent conic to the sextic degeneration curve of the quadric bundle, we prove that the general member is both pfaffi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0237","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":"2026-05-18T02:49:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BwLwTGwv+yLGUWAGkGyswq/Q4uudvKKijRKiRYaFEj/kKLrSJkuAjwodXEMGxXIH50xBEJ/1tR+7EzvFUg+1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:08:23.801796Z"},"content_sha256":"15877b4b859ffcdad11844f13bedb15ea01386cbb6b06bbcd5134ffa9adc90e5","schema_version":"1.0","event_id":"sha256:15877b4b859ffcdad11844f13bedb15ea01386cbb6b06bbcd5134ffa9adc90e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2GDRZUMNF36OWVMHQVBC7JSYRQ/bundle.json","state_url":"https://pith.science/pith/2GDRZUMNF36OWVMHQVBC7JSYRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2GDRZUMNF36OWVMHQVBC7JSYRQ/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":"2026-05-31T02:08:23Z","links":{"resolver":"https://pith.science/pith/2GDRZUMNF36OWVMHQVBC7JSYRQ","bundle":"https://pith.science/pith/2GDRZUMNF36OWVMHQVBC7JSYRQ/bundle.json","state":"https://pith.science/pith/2GDRZUMNF36OWVMHQVBC7JSYRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2GDRZUMNF36OWVMHQVBC7JSYRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2GDRZUMNF36OWVMHQVBC7JSYRQ","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":"44c2f60b1df3962b228c59afcddb385502a1d504654383911aa6fba10d17ac97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-01T19:25:05Z","title_canon_sha256":"0ef1515eeb6bbd40f8b3d7ff1c87f1537e67857511f3b55019f20c351954162d"},"schema_version":"1.0","source":{"id":"1205.0237","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0237","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0237v4","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0237","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"2GDRZUMNF36O","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2GDRZUMNF36OWVMH","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2GDRZUMN","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:15877b4b859ffcdad11844f13bedb15ea01386cbb6b06bbcd5134ffa9adc90e5","target":"graph","created_at":"2026-05-18T02:49:46Z","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 isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class of the even Clifford algebra over the K3 surface S of degree 2 arising from X. Specifically, we show that in the moduli space of cubic fourfolds, the intersection of divisors C_8 and C_14 has five irreducible components. In the component corresponding to the existence of a tangent conic to the sextic degeneration curve of the quadric bundle, we prove that the general member is both pfaffi","authors_text":"Anthony V\\'arilly-Alvarado, Asher Auel, Marcello Bernardara, Michele Bolognesi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-01T19:25:05Z","title":"Cubic fourfolds containing a plane and a quintic del Pezzo surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0237","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:a43cba20cc5cce98d8b3611d846150b8a9aadbb237fecacef3cb32727c9adf44","target":"record","created_at":"2026-05-18T02:49:46Z","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":"44c2f60b1df3962b228c59afcddb385502a1d504654383911aa6fba10d17ac97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-01T19:25:05Z","title_canon_sha256":"0ef1515eeb6bbd40f8b3d7ff1c87f1537e67857511f3b55019f20c351954162d"},"schema_version":"1.0","source":{"id":"1205.0237","kind":"arxiv","version":4}},"canonical_sha256":"d1871cd18d2efceb558785422fa6588c127b18fdefa36ba7780c06d998af9118","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1871cd18d2efceb558785422fa6588c127b18fdefa36ba7780c06d998af9118","first_computed_at":"2026-05-18T02:49:46.232983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:46.232983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bgo2KQmglonVsKer1jIbK3ghXS6Seh+U7DhaQh7HsqtjhYAerSV2hVbf6A5cb7bp/eYcU34/FvzCqltF9IOaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:46.233348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0237","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a43cba20cc5cce98d8b3611d846150b8a9aadbb237fecacef3cb32727c9adf44","sha256:15877b4b859ffcdad11844f13bedb15ea01386cbb6b06bbcd5134ffa9adc90e5"],"state_sha256":"a571f8ee62037fddb46b034e717af1a2248c528ccc36b9d488cee7f6eee67338"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RU3A+gT0gmtRQLsyII8AlPg68h/+8MQdNSRLbcThS+RVH1MWjX24b6hasXi926WfWnIxgRn4GUceBgfV9lLyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:08:23.805087Z","bundle_sha256":"7eab3a1c27c1e82e939da5ea570d4d815e14c6820cfd282dac36db07aa77fba1"}}