{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OD7GLIPYRPZWKBC5RZIQ6CYCCH","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":"fd17d7aa05e8740db71bed0de311d7d3658104ecc37b489435f47d734b9459a0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-06T05:05:38Z","title_canon_sha256":"3bd0171a0b92e9e24a03e8fb0fa45072b82e00fefaa4484bfa6ac6ded4647629"},"schema_version":"1.0","source":{"id":"0910.0923","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.0923","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"0910.0923v4","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.0923","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"OD7GLIPYRPZW","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OD7GLIPYRPZWKBC5","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OD7GLIPY","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:667c96288452956c01de2bbefc1fb26541bd242304c330f4bceb5998c3322128","target":"graph","created_at":"2026-05-18T00:26:52Z","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":"Let $(W,S)$ be a Coxeter system and suppose that $w \\in W$ is fully commutative (in the sense of Stembridge) and has a reduced expression beginning (respectively, ending) with $s \\in S$. If there exists $t\\in S$ such that $s$ and $t$ do not commute and $tw$ (respectively, $wt$) is no longer fully commutative, we say that $w$ is left (respectively, right) weak star reducible by $s$ with respect to $t$. In this paper, we classify the fully commutative elements in Coxeter groups of types $B$ and affine $C$ that are irreducible under weak star reductions. In a sequel to this paper, the classificat","authors_text":"Dana C. Ernst","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-06T05:05:38Z","title":"Non-cancellable elements in type affine $C$ Coxeter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0923","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:c8f405b52a0dd5b7d0875acd89718c34235027c88d331f74b2d9cb1945136452","target":"record","created_at":"2026-05-18T00:26:52Z","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":"fd17d7aa05e8740db71bed0de311d7d3658104ecc37b489435f47d734b9459a0","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-06T05:05:38Z","title_canon_sha256":"3bd0171a0b92e9e24a03e8fb0fa45072b82e00fefaa4484bfa6ac6ded4647629"},"schema_version":"1.0","source":{"id":"0910.0923","kind":"arxiv","version":4}},"canonical_sha256":"70fe65a1f88bf365045d8e510f0b0211f37b2ad152f4158b47a99a166b6020d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70fe65a1f88bf365045d8e510f0b0211f37b2ad152f4158b47a99a166b6020d7","first_computed_at":"2026-05-18T00:26:52.342747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:52.342747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qzw6Fs7CL4qjRz1SaFsqZL78RP4iBlRYx4Z/7a9Kd252bub6Cizrgy2/SSpk5vO0jSMUZfTI/D4MWyleOBCXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:52.343375Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.0923","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8f405b52a0dd5b7d0875acd89718c34235027c88d331f74b2d9cb1945136452","sha256:667c96288452956c01de2bbefc1fb26541bd242304c330f4bceb5998c3322128"],"state_sha256":"986bd27d115f8f0f5a2f2992bd60bf75399326d598af58c098c071fd48b484a5"}