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  1. Divisor tests and coefficient transfers for sextic character momentsScott SchubrEdition 1 · 2026-10-28 Public
  2. The Riemann Hypothesis through Arithmetic Weil PositivityScott SchubrEdition 4 · 2026-10-28 Public
  3. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  4. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 1 · 2026-10-27 Public
  5. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  6. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 4 · 2026-10-27 Public
  7. Degree-eight positivity and polynomial obstructions for monotone Riemann theta averagesScott SchubrEdition 7 · 2026-10-27 Public
  8. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  9. An explicit hyperbolicity threshold for xi Jensen polynomialsScott SchubrEdition 2 · 2026-10-27 Public
  10. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 3 · 2026-10-27 Public
  11. Relative finite optimization of arithmetic approximation distancesScott SchubrEdition 2 · 2026-10-27 Public
  12. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  13. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  14. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  15. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  16. Finite certificates for the lower edge of a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  17. Finite theta interpolation and eventual Laguerre failureScott SchubrEdition 2 · 2026-10-27 Public
  18. Sharp regularity criteria for arithmetic cutoff functionalsScott SchubrEdition 1 · 2026-10-26 Public
  19. Optimal energy for Dirichlet repairs in divisor bandsScott SchubrEdition 1 · 2026-10-26 Public
  20. Certified negative-band approximation for odd Weil formsScott SchubrEdition 1 · 2026-10-26 Public
PublicEdition 2

Observation norms under double-exponential confinement

Scott Schubr

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Abstract

We determine the small-regularization norm of a weighted observation of a positive Fourier-energy operator under double-exponential spatial confinement. The leading term is the logarithm of the logarithm of the inverse regularization, with an explicit constant given by the quadratic part of the symbol and a constrained Dirichlet eigenvalue on an interval. Finitely many fixed nonzero polynomial-exponential constraint chains leave this constant unchanged; zero-exponent moment chains survive in the limiting problem. In particular a mean-zero constraint halves the leading observation norm. For the original two-row theta-weighted reference, the result gives the exact constant together with finite explicit bounds. Applications include a full factored-residual covariance enclosure and a complete-arithmetic sandwich bound. The proofs retain the specified compact-core closure and all mixed residual terms.

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