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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 5

Spectral escape for interacting and coalescing signed potential forms

Scott Schubr ORCID

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Abstract

We determine how the spectrum of a concentrating signed potential form splits between escaping eigenvalues and a bounded remainder as its centers coalesce. Zero profile integrals alone do not rule out escape, and relative leading-order estimates need not determine logarithmic shifts to bounded error. For two unequal asymmetric zero-mean profiles separated by more than their width, we obtain logarithmic formulas with bounded additive remainders on both escaping scales throughout the mesoscopic collision regime. Exact primitive correlations and Green geometry, together with a cancellation in a quadratic spectral pencil, control mixed trace terms that can exceed the slower scale. For a noncancelling cluster at bounded separation-to-width ratios and zero background, we identify the operator remaining after removal of the actual escaping pair. Aggregate inverse-square tails determine its essential and absolutely continuous channels; vanishing aggregate tails give trace-norm convergence. Fixed-threshold eigenvalue counts and signed spectral masses quantify how a bounded bulk balances the escaping pair's logarithmic trace drift. At exact cancellation, a primitive estimate controls the complete operator for measurable profiles. An anchored cusp family exhibits regularity-dependent transition scales and a logarithmic endpoint, with a vanishing rank-two approximation error along every joint path. Identical even profiles supply explicit scalar matching through all collision ratios.

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