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We investigate extremality of J\\o{}rgensen type inequalities in ${\\rm SL(2, \\mathbb H)}$. Along the way, we derive J\\o{}rgensen type inequalities for quaternionic M\\\"obius transformations which extend earlier inequalities obtained by Waterman and Kellerhals."},"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":"1503.08802","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-30T19:14:30Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"44f231c6ec825bd6ab9f7b7cb1b73a8eaa0a064d9777bbb1ad38dc358761623f","abstract_canon_sha256":"4346f6bb0ffe929f7bf1059c3d4a9f7ff9c52f1db1d0f5127f0e5fddcdb932b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:27.419247Z","signature_b64":"MqZQWSthZ6E0rWUM3uLnuZNl5k0BI+kqWezzKLhuKcHKMcqXcdP1OnN4hDBflBWCMRAPAB4VAXPk4HS/05wDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b05eeb06a49b04b516171101675d0f9dbb2e6897e5091c5fa41e0a927da274dd","last_reissued_at":"2026-05-18T00:25:27.418579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:27.418579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremality of Quaternionic J{\\o}rgensen Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CV","authors_text":"Abhishek Mukherjee, Krishnendu Gongopadhyay","submitted_at":"2015-03-30T19:14:30Z","abstract_excerpt":"Let ${\\rm SL(2, \\mathbb H)}$ be the group of $2 \\times 2$ quaternionic matrices with Dieudonn\\'e determinant $1$. 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