{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2JZ4DRZMPSPXMC6Z4J5T3C36UY","short_pith_number":"pith:2JZ4DRZM","canonical_record":{"source":{"id":"1308.0949","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-05T11:45:40Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"1bb3fca0b9e14b6401bbfc70ca509601e83688b70bf14ceabf197f5a7460be02","abstract_canon_sha256":"91bf68e807a6705b12966af0123254b5312856b7758b2e1052f69fdc5e95ad66"},"schema_version":"1.0"},"canonical_sha256":"d273c1c72c7c9f760bd9e27b3d8b7ea61630d2bb6d676d75a9edd7200078b6e1","source":{"kind":"arxiv","id":"1308.0949","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0949","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0949v2","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0949","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"2JZ4DRZMPSPX","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2JZ4DRZMPSPXMC6Z","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2JZ4DRZM","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2JZ4DRZMPSPXMC6Z4J5T3C36UY","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0949","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-05T11:45:40Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"1bb3fca0b9e14b6401bbfc70ca509601e83688b70bf14ceabf197f5a7460be02","abstract_canon_sha256":"91bf68e807a6705b12966af0123254b5312856b7758b2e1052f69fdc5e95ad66"},"schema_version":"1.0"},"canonical_sha256":"d273c1c72c7c9f760bd9e27b3d8b7ea61630d2bb6d676d75a9edd7200078b6e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:17.126296Z","signature_b64":"o3ktLYv2G/J1Hs5hHcEKN93W+FMJM/pn8FgWoFXzPoOr3rdqsYxBcGEfxAEtzWSmQ/4mPDTalEToY0kAVl69Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d273c1c72c7c9f760bd9e27b3d8b7ea61630d2bb6d676d75a9edd7200078b6e1","last_reissued_at":"2026-05-18T02:38:17.125685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:17.125685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0949","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d011JrT+8jMCTXeR6wSZeFH67QxalX9e+OERilY1Q1Tdl+EpBevAxG56v0hlEFoIP7hlWG/Kih8gAWD0dzUmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:35:17.409117Z"},"content_sha256":"dd89cf80d8dde07d60c769ce262bffd04f4ccd55b0d242a975316ea1398c082a","schema_version":"1.0","event_id":"sha256:dd89cf80d8dde07d60c769ce262bffd04f4ccd55b0d242a975316ea1398c082a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2JZ4DRZMPSPXMC6Z4J5T3C36UY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K-theory, LQEL manifolds and Severi varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Oliver Nash","submitted_at":"2013-08-05T11:45:40Z","abstract_excerpt":"We use topological K-theory to study non-singular varieties with quadratic entry locus. We thus obtain a new proof of Russo's Divisibility Property for locally quadratic entry locus manifolds. In particular we obtain a K-theoretic proof of Zak's theorem that the dimension of a Severi variety must be 2, 4, 8 or 16 and so resolve a conjecture of Atiyah and Berndt. We also show how the same methods applied to dual varieties recover the Landman parity theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0949","kind":"arxiv","version":2},"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":"2026-05-18T02:38:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcu/LCjpThfWU6THWJ4/iNdeBb4liusnudrEDeLXacOQaBpOF9vr4nqjuZszCjzUKYxh8R6kf78i2fZn5FU+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:35:17.409469Z"},"content_sha256":"ba9ec31caac065e66f33c43ed6b91b06be3674af412a8173f27a7eb5faaa2782","schema_version":"1.0","event_id":"sha256:ba9ec31caac065e66f33c43ed6b91b06be3674af412a8173f27a7eb5faaa2782"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JZ4DRZMPSPXMC6Z4J5T3C36UY/bundle.json","state_url":"https://pith.science/pith/2JZ4DRZMPSPXMC6Z4J5T3C36UY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JZ4DRZMPSPXMC6Z4J5T3C36UY/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":"2026-06-03T00:35:17Z","links":{"resolver":"https://pith.science/pith/2JZ4DRZMPSPXMC6Z4J5T3C36UY","bundle":"https://pith.science/pith/2JZ4DRZMPSPXMC6Z4J5T3C36UY/bundle.json","state":"https://pith.science/pith/2JZ4DRZMPSPXMC6Z4J5T3C36UY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JZ4DRZMPSPXMC6Z4J5T3C36UY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2JZ4DRZMPSPXMC6Z4J5T3C36UY","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":"91bf68e807a6705b12966af0123254b5312856b7758b2e1052f69fdc5e95ad66","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-05T11:45:40Z","title_canon_sha256":"1bb3fca0b9e14b6401bbfc70ca509601e83688b70bf14ceabf197f5a7460be02"},"schema_version":"1.0","source":{"id":"1308.0949","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0949","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0949v2","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0949","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"2JZ4DRZMPSPX","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2JZ4DRZMPSPXMC6Z","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2JZ4DRZM","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:ba9ec31caac065e66f33c43ed6b91b06be3674af412a8173f27a7eb5faaa2782","target":"graph","created_at":"2026-05-18T02:38:17Z","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 use topological K-theory to study non-singular varieties with quadratic entry locus. We thus obtain a new proof of Russo's Divisibility Property for locally quadratic entry locus manifolds. In particular we obtain a K-theoretic proof of Zak's theorem that the dimension of a Severi variety must be 2, 4, 8 or 16 and so resolve a conjecture of Atiyah and Berndt. We also show how the same methods applied to dual varieties recover the Landman parity theorem.","authors_text":"Oliver Nash","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-05T11:45:40Z","title":"K-theory, LQEL manifolds and Severi varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0949","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:dd89cf80d8dde07d60c769ce262bffd04f4ccd55b0d242a975316ea1398c082a","target":"record","created_at":"2026-05-18T02:38:17Z","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":"91bf68e807a6705b12966af0123254b5312856b7758b2e1052f69fdc5e95ad66","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-05T11:45:40Z","title_canon_sha256":"1bb3fca0b9e14b6401bbfc70ca509601e83688b70bf14ceabf197f5a7460be02"},"schema_version":"1.0","source":{"id":"1308.0949","kind":"arxiv","version":2}},"canonical_sha256":"d273c1c72c7c9f760bd9e27b3d8b7ea61630d2bb6d676d75a9edd7200078b6e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d273c1c72c7c9f760bd9e27b3d8b7ea61630d2bb6d676d75a9edd7200078b6e1","first_computed_at":"2026-05-18T02:38:17.125685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:17.125685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o3ktLYv2G/J1Hs5hHcEKN93W+FMJM/pn8FgWoFXzPoOr3rdqsYxBcGEfxAEtzWSmQ/4mPDTalEToY0kAVl69Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:17.126296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0949","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd89cf80d8dde07d60c769ce262bffd04f4ccd55b0d242a975316ea1398c082a","sha256:ba9ec31caac065e66f33c43ed6b91b06be3674af412a8173f27a7eb5faaa2782"],"state_sha256":"a5029bf8e1921aafe6d0ff09d231e6e1bcbeec36cbce775664f252d6f4f8277d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ii1cCqNImtXGr6Q8VDY5a2sD4PGAmG+fNbaKKgvfGBRh5cxU0tFCv/VPKHfFMlfLNTwpuifcpsac5h++ux9kBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:35:17.411390Z","bundle_sha256":"523f717ab017eb40b7c9747d9ef08f3d473999bd470b4f804b14d86fd7df749b"}}