{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MS7MPL43GAL3JYLSTR5EDAJB6M","short_pith_number":"pith:MS7MPL43","canonical_record":{"source":{"id":"1007.4614","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-27T04:05:25Z","cross_cats_sorted":[],"title_canon_sha256":"ff7f1ef4af59655c1f2e80ab215d43b41aadd58bd8a16d4e0bc7c001bb668b48","abstract_canon_sha256":"5d697bbf01a335426825235a4468e2d8aaa27f85345e01ff959a1d28ae62bdec"},"schema_version":"1.0"},"canonical_sha256":"64bec7af9b3017b4e1729c7a418121f302dad991dee65c87eb2aaf6c05262821","source":{"kind":"arxiv","id":"1007.4614","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4614","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4614v4","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4614","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"MS7MPL43GAL3","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MS7MPL43GAL3JYLS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MS7MPL43","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MS7MPL43GAL3JYLSTR5EDAJB6M","target":"record","payload":{"canonical_record":{"source":{"id":"1007.4614","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-27T04:05:25Z","cross_cats_sorted":[],"title_canon_sha256":"ff7f1ef4af59655c1f2e80ab215d43b41aadd58bd8a16d4e0bc7c001bb668b48","abstract_canon_sha256":"5d697bbf01a335426825235a4468e2d8aaa27f85345e01ff959a1d28ae62bdec"},"schema_version":"1.0"},"canonical_sha256":"64bec7af9b3017b4e1729c7a418121f302dad991dee65c87eb2aaf6c05262821","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:47.176588Z","signature_b64":"Vberq6LiKskE0Q9XIbl4l4WJLvoijpS9WnW0Fckyu9nDulmVn4Yv5uYxndJovoDDkB2r0gSW60imThDzXg+ZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64bec7af9b3017b4e1729c7a418121f302dad991dee65c87eb2aaf6c05262821","last_reissued_at":"2026-05-18T04:10:47.176150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:47.176150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.4614","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":"2026-05-18T04:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tnKrUlMM5HZups12aGGRNP2K5yRId89vp5WPCB6IbseP3PqiGW3Rv2ZTBML/Ma5HHB87ouG/lZKCrLjOKSMvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:47:01.201541Z"},"content_sha256":"768ea8606569e822ae02ed47c42d558118260dbad54cffde0856d3ea8325bf63","schema_version":"1.0","event_id":"sha256:768ea8606569e822ae02ed47c42d558118260dbad54cffde0856d3ea8325bf63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MS7MPL43GAL3JYLSTR5EDAJB6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Frobenius incidence varieties of linear subspaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ichiro Shimada","submitted_at":"2010-07-27T04:05:25Z","abstract_excerpt":"We define Frobenius incidence varieties by means of the incidence relation of Frobenius images of linear subspaces in a fixed vector space over a finite field, and investigate their properties such as supersingularity, Betti numbers and unirationality. These varieties are variants of the Deligne-Lusztig varieties. We then study the lattices associated with algebraic cycles on them. We obtain a positive-definite lattice of rank 84 that yields a dense sphere packing from a 4-dimensional Frobenius incidence variety in characteristic 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4614","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":"2026-05-18T04:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o10JkuqKIiEzeG1SSAUOFlCKgwOXzs3xfentWRnAc3yejcR+KWDupcKppMbLUw5zAruyEMgFoTwUHX1WxdXCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:47:01.201889Z"},"content_sha256":"61b0d7fa8249d2d315e45205d149ece52197721e8fa05b208038aa8400d8c78b","schema_version":"1.0","event_id":"sha256:61b0d7fa8249d2d315e45205d149ece52197721e8fa05b208038aa8400d8c78b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MS7MPL43GAL3JYLSTR5EDAJB6M/bundle.json","state_url":"https://pith.science/pith/MS7MPL43GAL3JYLSTR5EDAJB6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MS7MPL43GAL3JYLSTR5EDAJB6M/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":"2026-06-23T12:47:01Z","links":{"resolver":"https://pith.science/pith/MS7MPL43GAL3JYLSTR5EDAJB6M","bundle":"https://pith.science/pith/MS7MPL43GAL3JYLSTR5EDAJB6M/bundle.json","state":"https://pith.science/pith/MS7MPL43GAL3JYLSTR5EDAJB6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MS7MPL43GAL3JYLSTR5EDAJB6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MS7MPL43GAL3JYLSTR5EDAJB6M","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":"5d697bbf01a335426825235a4468e2d8aaa27f85345e01ff959a1d28ae62bdec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-27T04:05:25Z","title_canon_sha256":"ff7f1ef4af59655c1f2e80ab215d43b41aadd58bd8a16d4e0bc7c001bb668b48"},"schema_version":"1.0","source":{"id":"1007.4614","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4614","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4614v4","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4614","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"MS7MPL43GAL3","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MS7MPL43GAL3JYLS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MS7MPL43","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:61b0d7fa8249d2d315e45205d149ece52197721e8fa05b208038aa8400d8c78b","target":"graph","created_at":"2026-05-18T04:10:47Z","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 define Frobenius incidence varieties by means of the incidence relation of Frobenius images of linear subspaces in a fixed vector space over a finite field, and investigate their properties such as supersingularity, Betti numbers and unirationality. These varieties are variants of the Deligne-Lusztig varieties. We then study the lattices associated with algebraic cycles on them. We obtain a positive-definite lattice of rank 84 that yields a dense sphere packing from a 4-dimensional Frobenius incidence variety in characteristic 2.","authors_text":"Ichiro Shimada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-27T04:05:25Z","title":"On Frobenius incidence varieties of linear subspaces over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4614","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":"sha256:768ea8606569e822ae02ed47c42d558118260dbad54cffde0856d3ea8325bf63","target":"record","created_at":"2026-05-18T04:10:47Z","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":"5d697bbf01a335426825235a4468e2d8aaa27f85345e01ff959a1d28ae62bdec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-27T04:05:25Z","title_canon_sha256":"ff7f1ef4af59655c1f2e80ab215d43b41aadd58bd8a16d4e0bc7c001bb668b48"},"schema_version":"1.0","source":{"id":"1007.4614","kind":"arxiv","version":4}},"canonical_sha256":"64bec7af9b3017b4e1729c7a418121f302dad991dee65c87eb2aaf6c05262821","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64bec7af9b3017b4e1729c7a418121f302dad991dee65c87eb2aaf6c05262821","first_computed_at":"2026-05-18T04:10:47.176150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:47.176150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vberq6LiKskE0Q9XIbl4l4WJLvoijpS9WnW0Fckyu9nDulmVn4Yv5uYxndJovoDDkB2r0gSW60imThDzXg+ZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:47.176588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4614","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:768ea8606569e822ae02ed47c42d558118260dbad54cffde0856d3ea8325bf63","sha256:61b0d7fa8249d2d315e45205d149ece52197721e8fa05b208038aa8400d8c78b"],"state_sha256":"d2e2c804be414662ce918a7006cc14f6c5bf5966504a90d00555d3d011230b8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gR02VF1iskRnGKhLFJ85hB9z1Hp+LE/9Ib5yKhB8hdtRjgMHTkUxhkD5HPmS+UkHwLhzTv9ZsmICpV7Ac+Q2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:47:01.203813Z","bundle_sha256":"8b344d7e2885c527b9cd9a5201c28b7c81f09861c8ac1fbf8a44be85c22ccb66"}}