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  1. RH: Complete Signed Certificates and Canonical Null SynthesisScott SchubrEdition 12 · 2026-11-01 Public
  2. Polynomial Recovery and Masking under Weak Exponential TailsScott SchubrEdition 4 · 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. Positive Operator Cocycles in Shrinking CorridorsScott SchubrEdition 2 · 2026-10-31 Public
  6. Spectral escape for interacting and coalescing signed potential formsScott SchubrEdition 5 · 2026-10-30 Public
  7. Large negative subspaces for positive Euler deformationsScott SchubrEdition 3 · 2026-10-30 Public
  8. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 3 · 2026-10-30 Public
  9. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 4 · 2026-10-30 Public
  10. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  11. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  12. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  13. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  14. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  15. Mean ergodic convergence from near-diagonal subadditivityScott SchubrEdition 2 · 2026-10-27 Public
  16. Quantitative Null-Space Compression for a Weighted Weil OperatorScott SchubrEdition 2 · 2026-10-27 Public
  17. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  18. Typical-value anchors for polynomial approximation and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  19. Polynomial synthesis and zero ideals for the Riemann xi-functionScott SchubrEdition 2 · 2026-10-27 Public
  20. Finite certificates for the lower edge of a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  21. Sharp regularity criteria for arithmetic cutoff functionalsScott SchubrEdition 1 · 2026-10-26 Public
  22. Optimal energy for Dirichlet repairs in divisor bandsScott SchubrEdition 1 · 2026-10-26 Public
  23. Certified negative-band approximation for odd Weil formsScott SchubrEdition 1 · 2026-10-26 Public
PublicEdition 1

Sharp regularity criteria for arithmetic cutoff functionals

Scott Schubr

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Abstract

We classify the coefficient penalties that control point evaluation and absolute coefficient moments of finite arithmetic cutoff certificates. In divisor coordinates, let W_ω = Σ_{r≥2} ω(r)(J₄(r) + 10J₂(r))|v_r|²/180, where ω(r) ≥ 1 is arbitrary. Every fixed integer Bernoulli cutoff value is bounded in this norm if and only if Σ_r ω(r)^(−1) < ∞. For every integer R ≥ 1, the absolute moment Σ_d d^R |c_d| is bounded if and only if Σ_r r^(2R−2)/ω(r) < ∞. Both classifications persist after any fixed finite collection of bounded homogeneous constraints. A full-divisor lower bound supplies necessity and settles the critical logarithmic exponents. Applications give an exact constrained point capacity, a norm-controlled compensated-mean remainder, and an explicit native approximation floor. At the critical moment penalties, the floor gives a quantitative logarithmic lower bound on the energy required for a given native error.

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