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Under these assumptions, we see that there exists the Cannon-Thurston map for $W$, that is, the $W$-equivariant continuous surjection from the Gromov boundary of $W$ to the limit set of $W$. To see this we construct an isometric action of $W$ on an ellipsoid with the Hilbert metric. As a consequence, we see th"},"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":"1312.3174","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-11T14:09:00Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e8ae7368dab8be6fe77224424d4b4b0c9508fee4ad83ad85a353a3ed97995f30","abstract_canon_sha256":"6e31db55e7838dd21dbfdac885668204e350f17e8f904d507d07d55f93683361"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:55.915687Z","signature_b64":"gKxseAnezG9NWLVHraKtAptnqbNcugEDQqnvJ3RQywqaB3+d3X0/klz23hvqGLaIDIJef2IqaAemwXx6AZl7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72662d6800102bc698d139063436171d8fd925a510a18bb3f1f524c08b535457","last_reissued_at":"2026-05-18T02:54:55.915035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:55.915035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cannon-Thurston maps for Coxeter groups with signature $(n-1,1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Ryosuke Mineyama","submitted_at":"2013-12-11T14:09:00Z","abstract_excerpt":"For a Coxeter group $W$ we have an associating bi-linear form $B$ on suitable real vector space. 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