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  1. Divisor tests and coefficient transfers for sextic character momentsScott SchubrEdition 1 · 2026-10-28 Public
  2. Strong Self-Permanent Inequalities for Complex Four-Row Bipartite SupportsScott SchubrEdition 3 · 2026-10-28 Public
  3. The Riemann Hypothesis through Arithmetic Weil PositivityScott SchubrEdition 4 · 2026-10-28 Public
  4. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  5. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 1 · 2026-10-27 Public
  6. Resolving Goldreich's Open Problem 4.1: Linear Lower Bounds for Cubic Graph Isomorphism TestingScott SchubrEdition 6 · 2026-10-27 Public
  7. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  8. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 4 · 2026-10-27 Public
  9. Source-Resolved Resolvent Growth under Reciprocal-Theta ConfinementScott SchubrEdition 1 · 2026-10-27 Public
  10. Distributional traces and central moment tests for Vámos quarticsScott SchubrEdition 1 · 2026-10-27 Public
  11. Diffusion budgets for contact-freezing lattice ellipsoidsScott SchubrEdition 1 · 2026-10-27 Public
  12. Exact-rank quadratic correlation: a phase-compatible Clique reductionScott SchubrEdition 1 · 2026-10-27 Public
  13. Sharp output ranges and bias frontiers for stabilizer purity estimationScott SchubrEdition 1 · 2026-10-27 Public
  14. Certified resolvent detection of the third Weyl-blind twisting harmonicScott SchubrEdition 2 · 2026-10-27 Public
  15. Degree-eight positivity and polynomial obstructions for monotone Riemann theta averagesScott SchubrEdition 7 · 2026-10-27 Public
  16. Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codesScott SchubrEdition 2 · 2026-10-27 Public
  17. Independent Squares and Average-Radius Obstructions for Linear CodesScott SchubrEdition 2 · 2026-10-27 Public
  18. An explicit quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
  19. A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
  20. Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theoremScott SchubrEdition 3 · 2026-10-27 Public
  21. Polynomial Recovery and Masking under Weak Exponential TailsScott SchubrEdition 2 · 2026-10-27 Public
  22. Finite positivity and correction inertia for the Riemann theta formScott SchubrEdition 2 · 2026-10-27 Public
  23. Minimum-Degree Obstructions in the Riemann Theta Product: Classification, transition bounds and robust Gram certificatesScott SchubrEdition 3 · 2026-10-27 Public
  24. Collision and cancellation spectra for concentrated energy formsScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 1

Diffusion budgets for contact-freezing lattice ellipsoids

Scott Schubr

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Abstract

We study bounded-covariance matrix martingales whose ellipsoids acquire and retain lattice contacts. On a common set of Haar lattices of probability tending to one, we bound the total nonnegative gain in a heat-occupation frame by the time-averaged square-root diffusion cost. A cost of o(log d) forces this gain to vanish at the horizon (16 log d + 8 log log d + O(1))/d². The bound is uniform over admissible policies on each selected lattice and also gives an averaged-budget theorem. Its proof combines deterministic pair envelopes, radial and angular Haar estimates, same-noise coupling and a potential-weighted restart. Applications include every fixed-strength normalized curvature-preserving tilt and rotating low-rank feedback. We also solve the instantaneous curvature-preserving optimization problem with the same diffusion cost, including noncommuting curvature and occupation operators.

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