{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YAN7K6QUFBS75RL4DSTLHZJND5","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":"671ad5cc21b7860ce093a82854c9ce42bba1fdb01b6fef3c585d6855dbc5927d","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T15:19:51Z","title_canon_sha256":"4fda49d54b043dbdcd46542385b6e1909a47c99b390602c1b591780cd2e363c0"},"schema_version":"1.0","source":{"id":"1609.08494","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08494","created_at":"2026-05-18T00:59:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08494v2","created_at":"2026-05-18T00:59:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08494","created_at":"2026-05-18T00:59:41Z"},{"alias_kind":"pith_short_12","alias_value":"YAN7K6QUFBS7","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YAN7K6QUFBS75RL4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YAN7K6QU","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:33b00bea14400af13bda6e9c0abb40d10df7651a7164edf3b81bf132dfa1374d","target":"graph","created_at":"2026-05-18T00:59:41Z","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 $\\ast$ be an automorphism of $W$ with order $\\leq 2$ such that $s^{\\ast}\\in S$ for any $s\\in S$. Let $I_{\\ast}$ be the set of twisted involutions relative to $\\ast$ in $W$. In this paper we consider the case when $\\ast=\\text{id}$ and study the braid $I_\\ast$-transformations between the reduced $I_\\ast$-expressions of involutions. If $W$ is the Weyl group of type $B_n$ or $D_n$, we explicitly describe a finite set of basic braid $I_\\ast$-transformations for all $n$ simultaneously, and show that any two reduced $I_\\ast$-expressions for a given involution can b","authors_text":"Jing Zhang, Jun Hu","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T15:19:51Z","title":"On involutions in Weyl groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08494","kind":"arxiv","version":2},"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:aa8964fc847dc2217a92ece2041eceed12523803db4409a0aa0d8e003a5a3573","target":"record","created_at":"2026-05-18T00:59:41Z","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":"671ad5cc21b7860ce093a82854c9ce42bba1fdb01b6fef3c585d6855dbc5927d","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-27T15:19:51Z","title_canon_sha256":"4fda49d54b043dbdcd46542385b6e1909a47c99b390602c1b591780cd2e363c0"},"schema_version":"1.0","source":{"id":"1609.08494","kind":"arxiv","version":2}},"canonical_sha256":"c01bf57a142865fec57c1ca6b3e52d1f52d99d660bf82ed2e1236b4fa090fb91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c01bf57a142865fec57c1ca6b3e52d1f52d99d660bf82ed2e1236b4fa090fb91","first_computed_at":"2026-05-18T00:59:41.576112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:41.576112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2PIVB7nM7yiS4MwxKU8p8ZrraO+RyxT5MSjo23mMjfGkavIBN/zfo1y425HG/h5ucJ4/bVZ+oIH9LRtAkBxvAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:41.576951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08494","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa8964fc847dc2217a92ece2041eceed12523803db4409a0aa0d8e003a5a3573","sha256:33b00bea14400af13bda6e9c0abb40d10df7651a7164edf3b81bf132dfa1374d"],"state_sha256":"3dc2be710ce95c6b0b0e8ccd3785a174aaacd22ed2612bd174a9bd6619bc52c7"}