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This extends a theorem of Conway and Coxeter that classifies such solutions subject to a total positivity restriction."},"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":"1710.02996","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-09T08:59:11Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"3659021fdb99bf48d66330222d9234affabebf313765263fa3d8c6329bd99b3a","abstract_canon_sha256":"6da5ac563c77b10d166c93bbf09fe49188889d0d1c5619e21867dbed1e8a09fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:30.514673Z","signature_b64":"5af7J/Sp1a9CbQ7FBkgMteExaXbpOlGziDtIJGmulTFm/8/7pY5PJUFwqMcIAmlgUebtsIgQLI0avXaqBl8UAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cceedbef32eae674c7c3b21e57eee5cd97c94ed9f1343d1ee57258d02f0d8f1","last_reissued_at":"2026-05-18T00:15:30.514021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:30.514021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partitions of unity in $\\mathrm{SL}(2,\\mathbb Z)$, negative continued fractions, and dissections of polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Valentin Ovsienko","submitted_at":"2017-10-09T08:59:11Z","abstract_excerpt":"We characterize sequences of positive integers $(a_1,a_2,\\ldots,a_n)$ for which the $2\\times2$ matrix $\\left( \\begin{array}{cc} a_n&-1 1&0 \\end{array} \\right) \\left( \\begin{array}{cc} a_{n-1}&-1 1&0 \\end{array} \\right) \\cdots \\left( \\begin{array}{cc} a_1&-1 1&0 \\end{array} \\right) $ is either the identity matrix $\\mathrm Id$, its negative $-\\mathrm Id$, or square root of $-\\mathrm Id$. 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