Certified complementary bounds for an odd Weil receiver
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Abstract
We certify the complete positive exterior of a theta-weighted odd Weil receiver on the orthogonal complement of its finite phase space. For the arithmetic prefix through nine, the exterior beyond frequency 2400 has complementary norm below 1/5, uniformly for regularization alpha at least 1e-14, on the existing 4080-dimensional odd phase span. A positive-block Schur estimate pays every exterior mixed term through a finite joint covariance and yields an explicit sufficient signed matrix inequality with exact rows retained. The same exterior has a unique ambient norm-one transition in (4.46, 4.47) times 1e-13. A direct-density rule with 352 positive carriers encloses the actual operator in norm; complete root, quadrature, physical-tail and finite-arithmetic bounds certify both conclusions. The argument organizes receiving estimates around the full complement of the phase span and supplies portable reproducing code and data.
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- main.pdf107.1 KiB · pdf
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38b50702f41ed4ba616360a97167c3f3dfdcdd3c36f8684ef3091807700b8b1a - Certified-complementary-bounds-odd-Weil-receiver.zip1161.2 KiB · package
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183f0b0310c5f6f2a5317ed30d5a4d6f496c4485d9ccc26c4c3a7330fd0b4243
Available editions
- Edition 1 · 2026-10-27 · public
Research details
- Subjects
- Mathematics · Number Theory and Special Functions · Analysis and Spectral Theory
- Keywords
- Weil forms, spectral theory, complementary bounds, Schur complement, validated numerics
- Manuscript date
- 2026-10-26
- Reader reuse
- No additional permission granted
Scope
Uniform complete complementary-space bound for the arithmetic-prefix-nine odd Weil receiver, a positive-block Schur reduction with exact rows, and a certified ambient norm-one transition.
Disclosures
AI assistants supported derivation, programming and verification. The author is responsible for the statements and exposition. The mathematical arguments and complete reproducing code specify the computational evidence.
Reproduction
The source package includes the complete interval cover, density rule, complementary data, threshold endpoint data, portable producers, reproduce.py and build.py. See README.md for dependencies and commands.