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Paris, 337 (2003), pp. 409--414","work_id":"89a71bad-a326-4897-9b45-1a7d59510f08","year":2003}],"snapshot_sha256":"91eb3a8d3cdfbb7438508659745754f3d1c093a695b41d160b604b025a145228"},"source":{"id":"2605.16624","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T21:06:14.201810Z","id":"0cdeaa76-bbd9-48f1-b98c-c080935db166","model_set":{"reader":"grok-4.3"},"one_line_summary":"Small solutions of the nonlinear Maryland model remain O(ε) in polynomially weighted ℓ² norm for times |t| ≤ ε^{-1} ε^{-M_*} under small ε and Diophantine conditions on ϖ for almost all x.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"For almost every phase, small solutions to the nonlinear Maryland model remain of size order epsilon for times up to any negative power of epsilon.","strongest_claim":"Given any M_* ∈ N^*, for phase parameters x belonging to an almost full-measure subset of R/Z, if |ε| is sufficiently small, then solutions q(t) of the nonlinear Maryland model with sufficiently small initial weighted norm ε satisfy ||q(t)||_s = O(ε) for all |t| ≤ ε^{-1} ε^{-M_*}.","weakest_assumption":"The frequency vector ϖ ∈ R^d satisfies a suitable Diophantine condition (as required for the Birkhoff normal form procedure to control resonances), together with the restriction to an almost full-measure set of phases x; if this condition fails, the normal form reduction and resulting stability bound may not hold."}},"verdict_id":"0cdeaa76-bbd9-48f1-b98c-c080935db166"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0c9da3f9d49456a2e12065499928938f212042c2d392ece23ca2f95b638981a7","target":"record","created_at":"2026-05-20T00:02:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ae1b57c5a16dc462f1370905eeadf32497eeec7401a4665658c0c9bdca814619","cross_cats_sorted":["math.DS","math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2026-05-15T20:45:16Z","title_canon_sha256":"b228f3dfde306a36e1bbd7f4c2df4a3f318f9da3dcd3199056a0e0d583f87986"},"schema_version":"1.0","source":{"id":"2605.16624","kind":"arxiv","version":1}},"canonical_sha256":"77a8229184b2dac1812f2da4979e7d74cac32de68e040c05790c03109a5651ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77a8229184b2dac1812f2da4979e7d74cac32de68e040c05790c03109a5651ee","first_computed_at":"2026-05-20T00:02:33.042830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:33.042830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fdtulvp2MCKatNsEZbTckj0sDNd990SMwIKPjCav+GcTCQikHEEvl8MnFsXudxO6DsVxqMtoAe5NaeDncPtjAg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:33.043663Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c9da3f9d49456a2e12065499928938f212042c2d392ece23ca2f95b638981a7","sha256:a9298ac015e19adbcbe18113ff0c48ee2ed6be137d0f823aa8bfd64e30974953"],"state_sha256":"7925af0bf043e30da9341bf9044818f3fe1fd61b33ef70cf4deb4e4f3e5a18be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIJffNwWcLl8kZfmAqMBL8gecg3eoTXTd4tQPk4hUseaugUzi1Y3eKFNc+eglkJuAOMdkythYEgJBu+QT7TuDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T14:45:38.836236Z","bundle_sha256":"c63c55448554b4308b986ce4ca45597febcdeb5f6350df3bc087d214196de38e"}}