{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O7LYLQPWOCYJN5PZQIP6GCPPNM","short_pith_number":"pith:O7LYLQPW","canonical_record":{"source":{"id":"1308.2270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-10T03:13:05Z","cross_cats_sorted":[],"title_canon_sha256":"c467253ee46481893db4de21b66415e7aebd946c92af50e9950e3f16d4828a4d","abstract_canon_sha256":"cf633d38ba7b894ba97b1bc1ce0c70232156e71c933c4c4ae4b3c1a2959b06e9"},"schema_version":"1.0"},"canonical_sha256":"77d785c1f670b096f5f9821fe309ef6b2fe325cdd546fa576f28eb8930be73fa","source":{"kind":"arxiv","id":"1308.2270","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2270","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2270v1","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2270","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"O7LYLQPWOCYJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O7LYLQPWOCYJN5PZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O7LYLQPW","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O7LYLQPWOCYJN5PZQIP6GCPPNM","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-10T03:13:05Z","cross_cats_sorted":[],"title_canon_sha256":"c467253ee46481893db4de21b66415e7aebd946c92af50e9950e3f16d4828a4d","abstract_canon_sha256":"cf633d38ba7b894ba97b1bc1ce0c70232156e71c933c4c4ae4b3c1a2959b06e9"},"schema_version":"1.0"},"canonical_sha256":"77d785c1f670b096f5f9821fe309ef6b2fe325cdd546fa576f28eb8930be73fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:07.980037Z","signature_b64":"50iHDOt6m9BdjnBwDKqI6b/jNIjJvwTHoj7PE8TdGDJa2dRvK6FIKSgC4Qgab2AIrpE5p1GqKBJj1nzZddQ0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77d785c1f670b096f5f9821fe309ef6b2fe325cdd546fa576f28eb8930be73fa","last_reissued_at":"2026-05-18T03:16:07.979504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:07.979504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2270","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xx0WoKg2xBv0wvZQY7t/Ig8vnArdnSuI/YxqYGsOPhUqzquymvUfI3ZpwgWgTbwq5MJoK1PD9Ar4IG65uXiGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:43:56.500732Z"},"content_sha256":"d6a2ab09784eee72c2edb9553394c5ef5b60fcbab7fbeefde6d713fb7dc6ed20","schema_version":"1.0","event_id":"sha256:d6a2ab09784eee72c2edb9553394c5ef5b60fcbab7fbeefde6d713fb7dc6ed20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O7LYLQPWOCYJN5PZQIP6GCPPNM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications of vertex algebra covering procedures to Chevalley groups and modular moonshine","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Ching Hung Lam, Robert L. Griess Jr.","submitted_at":"2013-08-10T03:13:05Z","abstract_excerpt":"A vertex operator algebra of lattice type ADE has a standard integral form which extends a Chevalley basis for its degree 1 Lie algebra. This integral form may be used to define a vertex algebra over a commutative ring $R$ and to get a Chevalley group over $R$ of the same type, acting as automorphisms of this vertex algebra. We define vertex algebras of types BCFG over a commutative ring and certain reduced VAs, then get analogous results about automorphism groups. In characteristics 2 and 3, there are exceptionally large automorphism groups. A covering algebra idea of Frohardt and Griess for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2270","kind":"arxiv","version":1},"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":"2026-05-18T03:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYsWtSgb016eCLP2AjX6SnXQhPzGlhpVy6xxsTS1ZqdqNSp3RqWGjPHSlsbwyG3MYdsAYpdIQ8+NBPsGNbucCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:43:56.501512Z"},"content_sha256":"0a30d358a58bfec1a625e568802dc2ff0a70f81193ed3e58b1b8cfb62d396152","schema_version":"1.0","event_id":"sha256:0a30d358a58bfec1a625e568802dc2ff0a70f81193ed3e58b1b8cfb62d396152"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7LYLQPWOCYJN5PZQIP6GCPPNM/bundle.json","state_url":"https://pith.science/pith/O7LYLQPWOCYJN5PZQIP6GCPPNM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7LYLQPWOCYJN5PZQIP6GCPPNM/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":"2026-06-06T16:43:56Z","links":{"resolver":"https://pith.science/pith/O7LYLQPWOCYJN5PZQIP6GCPPNM","bundle":"https://pith.science/pith/O7LYLQPWOCYJN5PZQIP6GCPPNM/bundle.json","state":"https://pith.science/pith/O7LYLQPWOCYJN5PZQIP6GCPPNM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7LYLQPWOCYJN5PZQIP6GCPPNM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O7LYLQPWOCYJN5PZQIP6GCPPNM","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":"cf633d38ba7b894ba97b1bc1ce0c70232156e71c933c4c4ae4b3c1a2959b06e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-10T03:13:05Z","title_canon_sha256":"c467253ee46481893db4de21b66415e7aebd946c92af50e9950e3f16d4828a4d"},"schema_version":"1.0","source":{"id":"1308.2270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2270","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2270v1","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2270","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"O7LYLQPWOCYJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O7LYLQPWOCYJN5PZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O7LYLQPW","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:0a30d358a58bfec1a625e568802dc2ff0a70f81193ed3e58b1b8cfb62d396152","target":"graph","created_at":"2026-05-18T03:16:07Z","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":"A vertex operator algebra of lattice type ADE has a standard integral form which extends a Chevalley basis for its degree 1 Lie algebra. This integral form may be used to define a vertex algebra over a commutative ring $R$ and to get a Chevalley group over $R$ of the same type, acting as automorphisms of this vertex algebra. We define vertex algebras of types BCFG over a commutative ring and certain reduced VAs, then get analogous results about automorphism groups. In characteristics 2 and 3, there are exceptionally large automorphism groups. A covering algebra idea of Frohardt and Griess for ","authors_text":"Ching Hung Lam, Robert L. Griess Jr.","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-10T03:13:05Z","title":"Applications of vertex algebra covering procedures to Chevalley groups and modular moonshine"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2270","kind":"arxiv","version":1},"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:d6a2ab09784eee72c2edb9553394c5ef5b60fcbab7fbeefde6d713fb7dc6ed20","target":"record","created_at":"2026-05-18T03:16:07Z","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":"cf633d38ba7b894ba97b1bc1ce0c70232156e71c933c4c4ae4b3c1a2959b06e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-10T03:13:05Z","title_canon_sha256":"c467253ee46481893db4de21b66415e7aebd946c92af50e9950e3f16d4828a4d"},"schema_version":"1.0","source":{"id":"1308.2270","kind":"arxiv","version":1}},"canonical_sha256":"77d785c1f670b096f5f9821fe309ef6b2fe325cdd546fa576f28eb8930be73fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77d785c1f670b096f5f9821fe309ef6b2fe325cdd546fa576f28eb8930be73fa","first_computed_at":"2026-05-18T03:16:07.979504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:07.979504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"50iHDOt6m9BdjnBwDKqI6b/jNIjJvwTHoj7PE8TdGDJa2dRvK6FIKSgC4Qgab2AIrpE5p1GqKBJj1nzZddQ0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:07.980037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6a2ab09784eee72c2edb9553394c5ef5b60fcbab7fbeefde6d713fb7dc6ed20","sha256:0a30d358a58bfec1a625e568802dc2ff0a70f81193ed3e58b1b8cfb62d396152"],"state_sha256":"96c56d1f6616ddd7490803c959a68f67f6f8db88cff7857442e9f5985b02553c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nLWaDcfiAenB3dSNQDpMp/KC4QrAxrtYON6BSvLeZBF9YlnzzgCgJsnyuVNtnbEDXb8ClYem7LqghkwIcfr1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:43:56.505824Z","bundle_sha256":"c85bfdcdb331f3c32a47c3123fb67a603e2b4f4b440659196a7099d412564941"}}