Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

135 papers
Browse papers
  1. A square-integral threshold for subadditivity on shrinking corridorsScott SchubrEdition 3 · 2026-10-27 Public
  2. Small-ball estimates for Hölder centers of the Kloosterman processScott SchubrEdition 2 · 2026-10-27 Public
  3. Fekete convergence from balanced integer predecessors in shrinking corridorsScott SchubrEdition 2 · 2026-10-27 Public
  4. A sharp lower bound for adjacent-edge correlations in random subtreesScott SchubrEdition 2 · 2026-10-27 Public
  5. Sharp trace-degree certificates for rank-two permanent-derivative compensationScott SchubrEdition 2 · 2026-10-27 Public
  6. Residual Certificates and Empirical Sharpness for Entropic Self-Transport ScoresScott SchubrEdition 2 · 2026-10-27 Public
  7. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  8. Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-TransportScott SchubrEdition 2 · 2026-10-27 Public
  9. Statistical inference for empirical heat-kernel Sinkhorn metricsScott SchubrEdition 3 · 2026-10-27 Public
  10. Sharp collision criteria for frozen color histogramsScott SchubrEdition 2 · 2026-10-27 Public
  11. Finite-spectral recovery of Weyl-blind twisting modesScott SchubrEdition 2 · 2026-10-27 Public
  12. Local comparison counting for linear extensions and a bounded-range balance refinementScott SchubrEdition 2 · 2026-10-27 Public
  13. An explicit hyperbolicity threshold for xi Jensen polynomialsScott SchubrEdition 2 · 2026-10-27 Public
  14. A quantitative Chollet inequality for rank-four matrices of order sevenScott SchubrEdition 2 · 2026-10-27 Public
  15. Single-copy learning of stabilizers with correlated diagonal noiseScott SchubrEdition 2 · 2026-10-27 Public
  16. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 3 · 2026-10-27 Public
  17. Relative finite optimization of arithmetic approximation distancesScott SchubrEdition 2 · 2026-10-27 Public
  18. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  19. Covariance confidence bounds and parity certificates for stable count lawsScott SchubrEdition 2 · 2026-10-27 Public
  20. Frequency Localization for Weil Operator CertificatesScott SchubrEdition 3 · 2026-10-27 Public
  21. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  22. Local and eventual mixing-weight entropy concavity under Gaussian smoothingScott SchubrEdition 2 · 2026-10-27 Public
  23. Joint Cutoffs and Negative-Spectrum Decay for Weighted Weil OperatorsScott SchubrEdition 3 · 2026-10-27 Public
  24. First-Hit Stopping and Bias-Corrected Score Inference in Dimension ThreeScott SchubrEdition 3 · 2026-10-27 Public
PublicEdition 3

A square-integral threshold for subadditivity on shrinking corridors

Scott Schubr

Original PDF · First-page preview

Loading original first page…

Abstract

Let w:[T,∞)→[0,1] be measurable and nonincreasing. For exact eventual subadditivity on the integer corridor n≤m≤n+n w(log n), we identify a square-integral threshold. If ∫_T^∞ w(s)² ds diverges, normalized slopes converge for nondecreasing nonnegative linearly bounded sequences, without continuity or an adjacent-pair assumption. In this divergent-integral case, if adjacent integer pairs are eventually admissible, a prefix-envelope and dyadic-record argument removes all monotonicity, sign and growth hypotheses: every real sequence satisfying the corridor inequality has a normalized limit in ℝ∪{−∞}. In particular, n/√log n is a sufficient sublinear corridor for arbitrary real sequences. If the integral is finite, a shifted-tail correction gives strictly increasing integer submultiplicative and supermultiplicative counterexamples with logarithmic growth endpoints 1.99 and 2.01. Thus the criterion is an exact dichotomy in the monotone counting class, and also for arbitrary real sequences when the adjacent-pair condition holds. Without monotonicity, adjacent-pair legality cannot simply be omitted: we construct a positive nonincreasing width for which every finite positive-power integral diverges, yet an integer-valued linearly bounded subadditive sequence has normalized lower and upper limits zero and one.

Read the full paper in the original PDF.