{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CJ6JHJLHH2ZWSJDNYE6CJFJV6W","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":"2a709536932bdbd90acf67f09f3b2e2674f18754097b1ffa19864605a663d470","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-05-16T18:53:23Z","title_canon_sha256":"a2d2ac62d904a2fec5124b2a619680ee7884603063853d594281b4f61d6bb295"},"schema_version":"1.0","source":{"id":"1005.2769","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2769","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2769v6","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2769","created_at":"2026-05-18T02:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"CJ6JHJLHH2ZW","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CJ6JHJLHH2ZWSJDN","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CJ6JHJLH","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:85ea0ec45c4920828c51e6c3570e94996995e192f479f21dc4622c1cdeca468a","target":"graph","created_at":"2026-05-18T02:23:59Z","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 1972, R. Carter introduced admissible diagrams to classify conjugacy classes in a finite Weyl group W. We say that an admissible diagram \\Gamma is a Carter diagram if any edge {\\alpha, \\beta} with inner product (\\alpha, \\beta) > 0 (resp. (\\alpha, \\beta) < 0) is drawn as dotted (resp. solid) edge. We construct an explicit transformation of any Carter diagram containing long cycles (with the number of vertices l > 4) into another Carter diagram containing only 4-cycles. Thus, all Carter diagrams containing long cycles can be eliminated from the classification list. There exist diagrams determ","authors_text":"Rafael Stekolshchik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-05-16T18:53:23Z","title":"Root systems and diagram calculus. I. Regular extensions of Carter diagrams and the uniqueness of conjugacy classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2769","kind":"arxiv","version":6},"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":"sha256:5d3d623ae5b070f8879f17048447cc5db864ae474548f36a1d9cf95165d743e0","target":"record","created_at":"2026-05-18T02:23:59Z","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":"2a709536932bdbd90acf67f09f3b2e2674f18754097b1ffa19864605a663d470","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-05-16T18:53:23Z","title_canon_sha256":"a2d2ac62d904a2fec5124b2a619680ee7884603063853d594281b4f61d6bb295"},"schema_version":"1.0","source":{"id":"1005.2769","kind":"arxiv","version":6}},"canonical_sha256":"127c93a5673eb369246dc13c249535f5ab4aaaf773ed1c530a661d342661cece","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"127c93a5673eb369246dc13c249535f5ab4aaaf773ed1c530a661d342661cece","first_computed_at":"2026-05-18T02:23:59.552638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:59.552638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S6wKLzDNDQ+YKhoDfOI2gpeodO+NXvTQcIUc3IpGDzLI/4U0GaKuGHmx53KIOwCO1sj8UckkxCb9nERBD7IOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:59.553226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2769","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d3d623ae5b070f8879f17048447cc5db864ae474548f36a1d9cf95165d743e0","sha256:85ea0ec45c4920828c51e6c3570e94996995e192f479f21dc4622c1cdeca468a"],"state_sha256":"d059bf019ce86d8c2f7aae73033001a66b99c84361b0eed16711113f9560b4ad"}