Uniform Resolvent Asymptotics for Growing Theta-Null Source Families
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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.
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Research details
- Subjects
- Mathematics · Number Theory · Complex Analysis · Functional Analysis
- Keywords
- theta-null sources, uniform resolvent asymptotics, Hardy spaces, Cauchy matrices, Stieltjes factors, null elimination
- Manuscript date
- 2026-10-27
- Reader reuse
- No additional permission granted
Scope
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.
Disclosures
AI-assisted mathematical research, computation and manuscript preparation.
Reproduction
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.