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We consider a lower spectral band edge of $ \\sigma (H_0) $, say $ E= 0 $, at a gap which is preserved by the perturbation $ V_\\omega $. Assuming that all Floquet eigenvalues of $ H_0$, which reach the spectral edge 0 as a minimum, have there a positive definite Hessian, we conclude that there exists an interval $ I $ containing 0 such that $ H_\\omega $ has only pure poi"},"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":"math-ph/0510063","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-10-17T11:25:41Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"7daecfd2285295efba05330ba690843c75719835b9cdab92d63ee1ad3365556e","abstract_canon_sha256":"43204297dcb789058094775ee845d54cf25f940bde926c586e5e0813da913f9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:17.161776Z","signature_b64":"stqpJeOnod6p4wMXEGKvfBwNxucu3xabJiJhIPXPYVCSuTni43wXAbKiCXhVHnb2TTBqcnsw9iYYRUsl6vwYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85d76bf13d4d1222041e7f0d11995e80836069ee04abed59fc5831f934c4df90","last_reissued_at":"2026-05-18T01:23:17.161009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:17.161009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localization for random perturbations of periodic Schroedinger operators with regular Floquet eigenvalues","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Ivan Veselic'","submitted_at":"2005-10-17T11:25:41Z","abstract_excerpt":"We prove a localization theorem for continuous ergodic Schr\\\"odinger operators $ H_\\omega := H_0 + V_\\omega $, where the random potential $ V_\\omega $ is a nonnegative Anderson-type perturbation of the periodic operator $ H_0$. 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