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  1. Spectral Crowding and Compression Limits for Arithmetic Covariance OperatorsScott SchubrEdition 2 · 2026-11-02 Public
  2. RH: Complete Signed Certificates and Canonical Null SynthesisScott SchubrEdition 12 · 2026-11-01 Public
  3. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 5 · 2026-11-01 Public
  4. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 2 · 2026-10-31 Public
  5. Large negative subspaces for positive Euler deformationsScott SchubrEdition 3 · 2026-10-30 Public
  6. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 4 · 2026-10-30 Public
  7. Divisor tests and coefficient transfers for sextic character momentsScott SchubrEdition 1 · 2026-10-28 Public
  8. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  9. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  10. Degree-eight positivity and polynomial obstructions for monotone Riemann theta averagesScott SchubrEdition 7 · 2026-10-27 Public
  11. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  12. An explicit hyperbolicity threshold for xi Jensen polynomialsScott SchubrEdition 2 · 2026-10-27 Public
  13. Relative finite optimization of arithmetic approximation distancesScott SchubrEdition 2 · 2026-10-27 Public
  14. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  15. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  16. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  17. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  18. Finite certificates for the lower edge of a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  19. Finite theta interpolation and eventual Laguerre failureScott SchubrEdition 2 · 2026-10-27 Public
  20. Sharp regularity criteria for arithmetic cutoff functionalsScott SchubrEdition 1 · 2026-10-26 Public
  21. Optimal energy for Dirichlet repairs in divisor bandsScott SchubrEdition 1 · 2026-10-26 Public
  22. Certified negative-band approximation for odd Weil formsScott SchubrEdition 1 · 2026-10-26 Public
PublicEdition 1

Optimal energy for Dirichlet repairs in divisor bands

Scott Schubr

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Abstract

We construct finite arithmetic corrections that impose an exact complex Dirichlet value using a prescribed band of divisor coordinates. For q = 1/2 − a + iT, 0 < a < 1/2, and the critical Bernoulli penalty ω(r) = r log²(er), the minimum energy for value t on N < r ≤ 2N is of order |t|² N^(3−2a) log²(eN), with explicit constants and onset independent of T. The minimizing correction has complete native norm O_a(|t| N^(−a)) and first absolute coefficient moment O_a(|t| N^(3/2−a)). Applied to native approximants at a smaller scale, it gives actual finite anchored and q-null trials with energy O_a(N^(3−a) log²(eN)) and an explicit approximation bound relative to the best native trial at the smaller scale. At a specified height-dependent cutoff, their complete compensated mean, including its boundary term, is O_a(N^(−3/2−5a/2)). The approximation limit is the optimal native distance, uniformly in T.

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