Research Article · Preprint Mathematics
Quantitative Null-Space Compression for a Weighted Weil Operator
- Primary subject
- Mathematics
- Subject subfields
- Functional Analysis · Number Theory and Special Functions
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
Abstract
We study a fixed minimal weighted realization H = A + B of the constrained Weil form, with nonnegative logarithmic reference A and the complete bounded paired arithmetic perturbation B. For every 0 < τ ≤ 1, explicit Fourier-band moments cut out a finite-codimensional subspace of the entire operator kernel on which both A and A^(1/2) have norm at most τ. The number n(τ) of observations satisfies log n(τ) = O(√(1 + log(1/τ)) log(3 + log(1/τ))). Consequently AΠ_Y and A^(1/2)Π_Y belong to every Schatten class for every closed Y ⊆ ker H. The proof combines two complete phase-space tails, a finite-rank real-phase Taylor approximation, and the exact null equation. We also give norm estimates for finite null deflation, a full residual-Gram receiving certificate, an explicit weighted bound H ≥ −99I/100, and a multiplicity obstruction to identifying the derivative-null closure with the whole kernel. The observations are explicit; the projection inside the unknown kernel is not computationally constructed.
Keywords Weil quadratic form · null space · Schatten classes · finite-rank approximation · resolvent residuals · spectral theory
Scope of the work
A fixed minimal weighted Weil realization with the complete paired arithmetic perturbation; quantitative entire-kernel observation and reference-output bounds, norm deflation and a conditional signed finite-matrix receiver.
Reproduction notes
The supplement contains all editable LaTeX sections, a portable Tectonic build helper and three standard-library Python controls. Run python build.py with Tectonic, or compile main.tex with pdfLaTeX twice. Run verify_lower.py, verify_gram.py and verify_compression.py normally and with python -O. These check exact finite arithmetic and residual examples and supplement the analytic proofs.
The manuscript
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Author disclosures
AI systems assisted with mathematical exploration, literature comparison, proof checking and manuscript preparation. These checks are not external human refereeing or formal verification of this manuscript. The author takes responsibility for its statements, proofs, citations and limitations.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Quantitative Null-Space Compression for a Weighted Weil Operator (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/quantitative-null-space-compression-weighted-weil-operator/v/1
BibTeX
@techreport{luminary_quantitative_null_space_compression_weighted_weil_operator_v1,
title = {Quantitative Null-Space Compression for a Weighted Weil Operator},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/quantitative-null-space-compression-weighted-weil-operator/v/1}
}Loading discussion…