{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:HXLZWFUR4IJGEVAJ3Q74HUHWWL","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":"502851cea806a129330f87e43c96e731a6b0673c834e7f8089e2cafc649bf529","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2002-02-18T15:14:09Z","title_canon_sha256":"d45cb5dd3dc22eca71fd38a66f9b2e3b9aabd48efaea8a2cf1380214d963f70b"},"schema_version":"1.0","source":{"id":"math/0202174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0202174","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0202174v1","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202174","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"HXLZWFUR4IJG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"HXLZWFUR4IJGEVAJ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"HXLZWFUR","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:891013a3fd0c55e0732ea281190acaa8d461a3c6a3b7a3c199d6ccfbb7359f4e","target":"graph","created_at":"2026-05-18T01:05:29Z","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 $(A_S,S)$ be an Artin-Tits and $X$ a subset of $S$ ; denote by $A_X$ the subgroup of $A_S$ generated by $X$. When $A_S$ is of spherical type, we prove that the normalizer and the commensurator of $A_X$ in $A_S$ are equal and are the product of $A_X$ by the quasi-centralizer of $A_X$ in $A_S$. Looking to the associated monoids $A_S^+$ and $A_X^+$, we describe the quasi-centralizer of $A_X^+$ in $A_S^+$ thanks to results in Coxeter groups. These two results generalize earlier results of Paris. Finaly, we compare, in the spherical case, the normalizer of a parabolic subgroup in the Artin-Tits","authors_text":"Eddy Godelle","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2002-02-18T15:14:09Z","title":"Normalisateurs et groupes d'Artin-Tits de type sph\\'erique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202174","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:a227825160dbe3c2cc59970cb39bfddc28525c972b33e5a04dae7e03ed9d1864","target":"record","created_at":"2026-05-18T01:05:29Z","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":"502851cea806a129330f87e43c96e731a6b0673c834e7f8089e2cafc649bf529","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2002-02-18T15:14:09Z","title_canon_sha256":"d45cb5dd3dc22eca71fd38a66f9b2e3b9aabd48efaea8a2cf1380214d963f70b"},"schema_version":"1.0","source":{"id":"math/0202174","kind":"arxiv","version":1}},"canonical_sha256":"3dd79b1691e212625409dc3fc3d0f6b2e0d767ddb5c4831dc68c49ed258b4ed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dd79b1691e212625409dc3fc3d0f6b2e0d767ddb5c4831dc68c49ed258b4ed4","first_computed_at":"2026-05-18T01:05:29.770128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:29.770128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z86e8vQB5o9Rn4W8Fo02P0dttGiR7RCQ+zwAbc2ajRt3KxiheWk7Eii+Evu7dvXshC/YxPWbYYjZ+aEuyBJwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:29.770620Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0202174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a227825160dbe3c2cc59970cb39bfddc28525c972b33e5a04dae7e03ed9d1864","sha256:891013a3fd0c55e0732ea281190acaa8d461a3c6a3b7a3c199d6ccfbb7359f4e"],"state_sha256":"a67e07aad61182a7e5dfb634f6274672d4dd5b53c2353ae33abdb5bebb2930e1"}