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  1. Source-Resolved Resolvent Growth under Reciprocal-Theta ConfinementScott SchubrEdition 1 · 2026-10-27 Public
  2. Distributional traces and central moment tests for Vámos quarticsScott SchubrEdition 1 · 2026-10-27 Public
  3. Certified resolvent detection of the third Weyl-blind twisting harmonicScott SchubrEdition 2 · 2026-10-27 Public
  4. Finite positivity and correction inertia for the Riemann theta formScott SchubrEdition 2 · 2026-10-27 Public
  5. Collision and cancellation spectra for concentrated energy formsScott SchubrEdition 2 · 2026-10-27 Public
  6. Finite-spectral recovery of Weyl-blind twisting modesScott SchubrEdition 2 · 2026-10-27 Public
  7. Frequency Localization for Weil Operator CertificatesScott SchubrEdition 3 · 2026-10-27 Public
  8. Joint Cutoffs and Negative-Spectrum Decay for Weighted Weil OperatorsScott SchubrEdition 3 · 2026-10-27 Public
  9. Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentrationScott SchubrEdition 2 · 2026-10-27 Public
  10. Sharp all-times heat-content comparison and concentration on compact metric graphsScott SchubrEdition 2 · 2026-10-27 Public
  11. Phase transitions and effective curvature bounds in Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  12. Energy-Filtered Dynamical Localization in Constructive Dirichlet TowersScott SchubrEdition 2 · 2026-10-27 Public
  13. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  14. A Weyl Law for Rapidly Twisted Polar-Strip TubesScott SchubrEdition 2 · 2026-10-27 Public
  15. Weyl Laws and Angular Stability for Rapidly Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  16. Pure-Point Dirichlet Spectrum in an Enlarging Cube TowerScott SchubrEdition 2 · 2026-10-27 Public
  17. Geometric Blind Modes in the Weyl Asymptotics of Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  18. Heat-Trace Recovery of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  19. Polynomial inertia of signed measures with negative intervalsScott SchubrEdition 2 · 2026-10-27 Public
  20. Left-Sector Mellin Certification of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  21. Audibility of all odd blind modes in rapidly twisted polar-strip tubesScott SchubrEdition 2 · 2026-10-27 Public
  22. A Positive Corner Limit for Inverse Half-Powers of Vámos QuarticsScott SchubrEdition 2 · 2026-10-27 Public
  23. Polynomial Certificates for the Vámos Riesz ObstructionScott SchubrEdition 3 · 2026-10-27 Public
  24. An explicit global lower certificate for a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 1

Source-Resolved Resolvent Growth under Reciprocal-Theta Confinement

Scott Schubr

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Abstract

We prove two-sided bounds for the complete inverse-energy Gram of prescribed theta-derivative sources in the original polar-constrained archimedean realization of the Weil form. For every finite source size d + 1, diagonal normalization by explicit powers of U = log(1/ε) gives positive degree-dependent lower and upper bounds whenever U ≥ 64(d + 2)². For each fixed family the normalized Gram is bounded above and below by constants, and source i has exact logarithmic exponent 4i + 13/2. The upper estimate uses exact half-line polar cancellation and a uniformly priced Fourier primitive, retaining the complete exterior polar tail. The lower estimate combines an exact polynomial coefficient map, all-atom theta bounds and a common-weight shell covariance with exact polar shorting. A two-metric residual theorem receives non-square-integrable divided sources, and explicit finite receiving bounds accompany the analytic estimates.

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