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Applying this algorithm to \"tagged\" indefinite integral binary Hermitian forms demonstrates the existence of entire circles in $\\mathbb{C}$ whose points are badly approximable over $K$, with effective constants.\n  By other methods (the Dani correspondence), we prove the e"},"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":"1707.07231","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-22T23:34:31Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"44a0513e3fff64cbeaed54ec51a649d21e181dc2998daaca429e1841ced0c8e5","abstract_canon_sha256":"bd0799f56412bfef53b2b8fd435c25b06ede67955dfeac57e63eab3b13e315b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:19.728554Z","signature_b64":"SzA1ZrSL1NfJVMWIQHt81JVDd8IwmpvWl3C9aeDa1B+V/QukvHO6uzu/h9CJvCB1CKFE5AysK0REqKlcz4drDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"187addfd9e728b63f97188d37ca923f10b87c4823528f5aec5aa1e809f21ca32","last_reissued_at":"2026-05-18T00:05:19.727943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:19.727943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Badly approximable numbers over imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Robert Hines","submitted_at":"2017-07-22T23:34:31Z","abstract_excerpt":"We recall the notion of nearest integer continued fractions over the Euclidean imaginary quadratic fields $K$ and characterize the \"badly approximable\" numbers, ($z$ such that there is a $C(z)>0$ with $|z-p/q|\\geq C/|q|^2$ for all $p/q\\in K$), by boundedness of the partial quotients in the continued fraction expansion of $z$. 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