{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KGVQP52CAIY2DTJG6LZSEMSFQI","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":"e0053238d33ffdc8105ff53b6b0676c92c3951853e16599ab9d35a1afbcbd800","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-30T18:08:32Z","title_canon_sha256":"188a005ef7c4c54d11c755149411f9bc15bc988ff8ae9fcf75561c62ab98815e"},"schema_version":"1.0","source":{"id":"1109.6917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6917","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6917v1","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6917","created_at":"2026-05-18T04:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"KGVQP52CAIY2","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KGVQP52CAIY2DTJG","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KGVQP52C","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:0431543b66c293aabc1e9972ece5b3aaf3e9fa86dfa10e888a19c99d6ecb3a04","target":"graph","created_at":"2026-05-18T04:11:52Z","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":"In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.","authors_text":"F. W. Lemire, J. Patera, M. Larouche","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-30T18:08:32Z","title":"Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6917","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":"sha256:1836d42ab64392ef875044f44f14dac48e2db304d959295a391bd7ce6ef9b7aa","target":"record","created_at":"2026-05-18T04:11:52Z","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":"e0053238d33ffdc8105ff53b6b0676c92c3951853e16599ab9d35a1afbcbd800","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-30T18:08:32Z","title_canon_sha256":"188a005ef7c4c54d11c755149411f9bc15bc988ff8ae9fcf75561c62ab98815e"},"schema_version":"1.0","source":{"id":"1109.6917","kind":"arxiv","version":1}},"canonical_sha256":"51ab07f7420231a1cd26f2f3223245823f7e458b5570bd7acd20eaa7ed10f796","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51ab07f7420231a1cd26f2f3223245823f7e458b5570bd7acd20eaa7ed10f796","first_computed_at":"2026-05-18T04:11:52.211294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:52.211294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SrL8uoP+9d7en/h+pW8R6/BU0h2GIQ6BzZk7JfPLObD1XA3FdL0Y4XclydnR5HzTnX1ts4yCthvIrzWjMPxrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:52.211805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1836d42ab64392ef875044f44f14dac48e2db304d959295a391bd7ce6ef9b7aa","sha256:0431543b66c293aabc1e9972ece5b3aaf3e9fa86dfa10e888a19c99d6ecb3a04"],"state_sha256":"3a334771b537912b6fd612fa64de96a49c66defb4fab7c1cbb83c114524b2d7f"}