Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

154 papers
Browse papers
  1. Spectral Crowding and Compression Limits for Arithmetic Covariance OperatorsScott SchubrEdition 2 · 2026-11-02 Public
  2. Diffusion budgets for contact-freezing lattice ellipsoidsScott SchubrEdition 2 · 2026-11-02 Public
  3. Stable star marginals and strict edge correlations for random forestsScott SchubrEdition 3 · 2026-11-02 Public
  4. Sharp output ranges and bias frontiers for stabilizer purity estimationScott SchubrEdition 2 · 2026-11-02 Public
  5. Covariance confidence bounds and parity certificates for stable count lawsScott SchubrEdition 3 · 2026-11-02 Public
  6. Log-concave polynomial prefix sums: algebraic certificates and a sharp zero sectorScott SchubrEdition 3 · 2026-11-02 Public
  7. Audibility of all odd blind modes in rapidly twisted polar-strip tubesScott SchubrEdition 3 · 2026-11-02 Public
  8. Sharp collision criteria for frozen color histogramsScott SchubrEdition 3 · 2026-11-02 Public
  9. Sharp noise transitions for an adaptive single-copy stabilizer-learning processScott SchubrEdition 3 · 2026-11-02 Public
  10. Leading bias and positive correction of heat-kernel Sinkhorn metricsScott SchubrEdition 3 · 2026-11-02 Public
  11. Chollet's inequality for positive semidefinite matrices of rank at most fourScott SchubrEdition 4 · 2026-11-02 Public
  12. Bose gases in weakly twisted annular-sector waveguidesScott SchubrEdition 3 · 2026-11-02 Public
  13. Optimal concavity powers for lattice counts on smooth toric Fano threefoldsScott SchubrEdition 3 · 2026-11-02 Public
  14. A square-integral threshold for subadditivity on shrinking corridorsScott SchubrEdition 5 · 2026-11-02 Public
  15. Small-ball estimates for Hölder centers of the Kloosterman processScott SchubrEdition 3 · 2026-11-02 Public
  16. Finite-projection holomorphic stabilization of contractible affine manifoldsScott SchubrEdition 4 · 2026-11-02 Public
  17. Power Concavity of Low-Dimensional Unimodular Fiber CountsScott SchubrEdition 5 · 2026-11-02 Public
  18. Positive Eigenfunctions Above the First Eigenvalue of the Affine 2-LaplacianScott SchubrEdition 4 · 2026-11-02 Public
  19. Finite Persistent Memory in Exact Sampling: Countable Rigidity and Algebraic Memory BoundsScott SchubrEdition 3 · 2026-11-02 Public
  20. Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensionsScott SchubrEdition 4 · 2026-11-02 Public
  21. Resolving Goldreich's Open Problem 4.1: Linear Lower Bounds for Cubic Graph Isomorphism TestingScott SchubrEdition 7 · 2026-11-02 Public
  22. Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codesScott SchubrEdition 3 · 2026-11-01 Public
  23. Single-time boundary heat-flux rigidity for smooth domainsScott SchubrEdition 4 · 2026-11-01 Public
  24. RH: Complete Signed Certificates and Canonical Null SynthesisScott SchubrEdition 12 · 2026-11-01 Public
PublicEdition 2

Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentration

Scott Schubr

Original PDF · First-page preview

Loading original first page…

Abstract

On a fixed spherical shell, we determine the last time at which nonnegative initial temperatures can produce one common signed whole-boundary heat flux. Admissible times form (0,τ), with a finite unattained cutoff. The boundary heat-kernel law fixes the shrinking concentration scale. After unit ground-state normalization, every weighted finite-q preparation problem, 1<q<∞, has a unique optimizer described by a scalar moment equation, and the cutoff limit has sharp costs and universal near-minimizer profiles. The conclusions include quantitative ground-weighted probability stability, second-moment control and physical angular rigidity. Separate endpoint arguments give atomic probability concentration at the L^1 endpoint and a filled-layer profile at the cap endpoint. Exactly feasible examples show the limits of higher-moment and strong cap-topology conclusions. An interior convex-hull criterion treats simultaneous finite schedules, and the smooth compatible class has the same norm infima. The shell-dependent boundary law connects feasibility, optimal preparation and concentration throughout the paper.

Read the full paper in the original PDF.