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It has been proven that all states are delocalized if $V$ is less than a critical value $V_c=2t$ and localized if $V> V_c$. Here, we show that this result (while correct) is highly misleading, at least in the small $Q$ limit. In particular, for $V<V_c$ there is an abrupt crossover akin to a mobility edge at an energy $E_c$; states with energy $|E|<E_c$ are robustly delocal"},"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":"1504.05205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-04-20T20:03:13Z","cross_cats_sorted":["cond-mat.quant-gas"],"title_canon_sha256":"5f0cbf5461be08c2365ccef8577dc4d5a0c28d823bc08e9cb0612e16e992e10f","abstract_canon_sha256":"f9f684d91e3ee2487e1b6cb73cbd21b61f9ec598af0e770a9888e688d81f05a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:48.868708Z","signature_b64":"BQW+WbcnfLyAIoPE9U2MzFp+tV6L/sxTc6qvjVM/s4LRH6t/L8U+ee0bwEwn3uDSFk7WVphpM23643bGH6LcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4e29ec210c4f0d07a449aea51b99ce6229da11664b9a7baed918712a01266f9","last_reissued_at":"2026-05-18T01:37:48.868278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:48.868278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The almost mobility edge in the almost Mathieu equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas"],"primary_cat":"cond-mat.mes-hall","authors_text":"Akash V. 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