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An admissible partition $\\mathcal{P}$ determines a quotient Coxeter graph $\\Gamma/\\mathcal{P}$. We prove that, if $\\Gamma/\\mathcal{P}$ is either a forest or an even triangle free Coxeter graph and $A_X$ is residually finite for all $X \\in \\mathcal{P}$, then $A$ is residually finite."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.08538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-25T15:09:01Z","cross_cats_sorted":[],"title_canon_sha256":"4987d03e26a434039605d25484c2e666c9578a8387543285ebe46da508acba12","abstract_canon_sha256":"96053db2ac1b323616fe8e971215d179107f9ccb75cfee3fa8947bf97c60a3d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:25.360214Z","signature_b64":"PXxC6pWNMBi6xEhhooDRCEVBG/VhubaakqoipGHyhKH31adJTLIUXgZ3qfCGlFFvSteMkTtkTZ/mJIR7HnZzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85b1351849b48144de58d9ef8e31144daff7860038cf5e0e3cb7dda0933d4fc5","last_reissued_at":"2026-05-18T00:34:25.359706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:25.359706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Note on residual finiteness of Artin groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Arye Juhasz, Luis Paris (IMB), Ruben Blasco-Garcia","submitted_at":"2017-09-25T15:09:01Z","abstract_excerpt":"Let $A$ be an Artin group. A partition $\\mathcal{P}$ of the set of standard generators of $A$ is called admissible if, for all $X,Y \\in \\mathcal{P}$, $X \\neq Y$, there is at most one pair  $(s,t) \\in X \\times Y$ which has a relation. An admissible partition $\\mathcal{P}$ determines a quotient Coxeter graph $\\Gamma/\\mathcal{P}$. 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