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Let an irrational $\\alpha$ be such that $|\\alpha-p_n/q_n|<c q_n^{-\\varkappa}$, where $p_n/q_n$, $n=1,2,\\dots$ are the convergents to $\\alpha$, and $c$, $\\varkappa$ are positive absolute constants, $\\varkappa<56$. Assuming certain conditions on the parity of the coefficients of the continued fraction of $\\alpha$, we show that the central gaps of $H_{p_n/q_n}$, $n=1,2,\\dots$, are inherited as spectral gaps of $H_\\alpha$ of length at least $c'q_n^{-\\varkappa/2}$, $c"},"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":"1602.08624","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-27T18:43:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ec05be884a5b2feda3f8a4c898b639302d3900622413b99a19f2ffbf3330a886","abstract_canon_sha256":"0f949b7759404230a5c734e8e5522677488ba4885e5903e1cb6a8f35f5c25f94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:31.331772Z","signature_b64":"wLpLOSpewSPatYTvixHgn8tWN+Kt6xmaop07OYwHQqVmdlogTf/6YGs7RMXC1IVrSgvzWwDSQpir2nrOlnExCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7e0941d4eaa2e2b05a223eb75d5357a6db9f7e4cf915e8ea61037eb9a7523e4","last_reissued_at":"2026-05-18T00:57:31.331364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:31.331364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central spectral gaps of the almost Mathieu operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"I. 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