Certified negative-band approximation for odd Weil forms
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Abstract
We construct certified finite approximations to the complete negative Fourier observation of an odd Weil form in its reciprocal-theta norm. Weighted Chebyshev features on a rigorous negative-symbol cover give a positive remainder with an explicit trace bound after exact orthogonal constraints. Discrete cosine orthogonality provides a degree-independent ridge charge. At arithmetic cutoff eleven, a 1366-feature construction admits ridge parameter 10^-17 with complete trace error below 1.121 × 10^-14. A support-sensitive paired arithmetic-tail estimate yields a nonnegative addition to the localized positive reference while preserving the same negative observation. We derive the corresponding finite inverse conditions and a compact physical-to-weighted certificate transfer, retaining the complete covariance and tail costs.
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Available editions
- Edition 1 · 2026-10-26 · public
Research details
- Subjects
- Mathematics · Number Theory · Functional Analysis · Numerical Analysis
- Keywords
- Weil forms, Chebyshev interpolation, ridge regularization, certified approximation, trace bounds
- Manuscript date
- 2026-10-26
- Reader reuse
- No additional permission granted
Scope
Certified complete negative-observation approximation on the specified weighted odd Weil space, with degree-independent ridge control, support-sensitive paired tails and conditional finite inverse criteria for original-form lower bounds.
Disclosures
AI assistance supported derivation, literature comparison, manuscript preparation and computational checks. The author is responsible for the mathematical statements and presentation.
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