Research Article · Preprint Mathematics
Uniform Resolvent Asymptotics for Growing Theta-Null Source Families
- Primary subject
- Mathematics
- Subject subfields
- Functional Analysis · Complex Analysis · Number Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
Abstract
We prove a relative matrix asymptotic for growing families of derivative-null sources in a reciprocal-theta realization of the Weil form. Writing U = log(1/ε), the actual constrained inverse Gram converges relatively to its explicit outer-Hardy/Cauchy leading matrix uniformly when the source count is o(log U). A finite exponential coefficient budget gives an eventual sufficient schedule and effective absolute, but unevaluated, onset constants. The proof combines a gapped positive inverse-factor kernel, logarithmic model-space plateau leverage, exact polar recovery and complete dual-leakage estimates. Separately, a logarithmically displaced physical wall gives a literal normalized inverse upper 2²³ n I for every U ≥ 64n², replacing a factorial source-count price. Its composition with the original physical null Gram sharpens a signed null-elimination resource bound. The resulting estimates quantify the positive archimedean reference and its exact-null elimination resources.
Keywords theta-null sources · uniform resolvent asymptotics · Hardy spaces · Cauchy matrices · Stieltjes factors · null elimination
Scope of the work
Uniform relative whole-matrix convergence for growing actual-source families under explicit exponential-budget admissions, a complete finite-U thin-wall upper bound, and exact-null elimination resource estimates on the original polar-constrained domain.
Reproduction notes
The package contains complete editable analytical proofs and portable exact/Arb finite controls for atom bounds, wall admissions and Cauchy/exponential budgets. All 10,834 controls pass identically in normal and optimized Python; the effective absolute recovery constants are specified analytically.
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Cite this edition
Scott Schubr. (2026). Uniform Resolvent Asymptotics for Growing Theta-Null Source Families (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/uniform-resolvent-asymptotics-growing-theta-null-source-families/v/1
BibTeX
@techreport{luminary_uniform_resolvent_asymptotics_growing_theta_null_source_families_v1,
title = {Uniform Resolvent Asymptotics for Growing Theta-Null Source Families},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/uniform-resolvent-asymptotics-growing-theta-null-source-families/v/1}
}Loading discussion…