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For the particular value $V=1/\\sqrt{2}$, respectively $V=\\sqrt{2}$, we show the existence of additional critical energies "},"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/9907006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1999-07-07T08:32:18Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ba9ddee533f5d8e5831f9e9270cdf29907971b7950de3e0a8fa90d2a212d6186","abstract_canon_sha256":"ebacf6e365e860e65331eb17ab7f75ad5dce26f2f09890156cc99cb0b2b7738e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:30.523781Z","signature_b64":"vHUeAedlCsDDhlG4x5d/UpjQfuYouonUiD3FvLNcZfqehSMP3CpUgCZrQ2Hci3MKpnCLRQ15V9T6DQytWv+TDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fde18a94560239f3c99199c763d465613de54bc399feffb72daa0b354ec66a0","last_reissued_at":"2026-05-18T01:38:30.523106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:30.523106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamical Localization for the Random Dimer Model","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"F. 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