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  1. Critical-tail localization and growing theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  2. Pure-Point Dirichlet Spectrum in an Enlarging Cube TowerScott SchubrEdition 2 · 2026-10-27 Public
  3. Sharp permanent-derivative compensation on the flat equal-spectrum conjugate-disjoint Gram stratumScott SchubrEdition 2 · 2026-10-27 Public
  4. Geometric Blind Modes in the Weyl Asymptotics of Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  5. Variance cancellation and two-direction bounds for six-row permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  6. Heat-Trace Recovery of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  7. Real-section permanent-derivative compensation and quadratic phase controlScott SchubrEdition 2 · 2026-10-27 Public
  8. Full-phase permanent-derivative compensation under real-part spectral pinchingScott SchubrEdition 2 · 2026-10-27 Public
  9. Phase-boundary reduction and low-rank compensation for permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  10. Typical-value anchors for polynomial approximation and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  11. All-depth root-Laguerre positivity with nonreal Fourier zerosScott SchubrEdition 3 · 2026-10-27 Public
  12. Polynomial synthesis and zero ideals for the Riemann xi-functionScott SchubrEdition 2 · 2026-10-27 Public
  13. Sharp degree exponents for polynomial detection of isolated negative atomsScott SchubrEdition 2 · 2026-10-27 Public
  14. A sixth-order obstruction to total positivity of an arithmetic theta trace kernelScott SchubrEdition 2 · 2026-10-27 Public
  15. Sharp collision laws and subexponential masking for polynomial certificatesScott SchubrEdition 2 · 2026-10-27 Public
  16. Collision geometry and concentration in polynomial sign recoveryScott SchubrEdition 2 · 2026-10-27 Public
  17. Left-Sector Mellin Certification of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  18. Growing-Index Recovery and Tail Scales for Signed MeasuresScott SchubrEdition 2 · 2026-10-27 Public
  19. A Positive Corner Limit for Inverse Half-Powers of Vámos QuarticsScott SchubrEdition 2 · 2026-10-27 Public
  20. A counterexample and corrected translation-density criterion for correlation kernelsScott SchubrEdition 2 · 2026-10-27 Public
  21. Asymptotically optimal bounds for permanental cofactor matricesScott SchubrEdition 2 · 2026-10-27 Public
  22. Exact minimax estimation of homogeneous complex Gaussian energiesScott SchubrEdition 2 · 2026-10-27 Public
  23. An explicit global lower certificate for a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  24. Odd Weil-form bounds by positive exterior eliminationScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

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. For fixed instantaneous operators, matching two-sided bounds give the sharp square-root small-budget law with an explicit linear error.

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