Research Article · Preprint Mathematics
Collision and cancellation spectra for concentrated energy forms
- Primary subject
- Mathematics
- Subject subfields
- Analysis and Spectral Theory
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
Abstract
We study concentrated signed potential forms in the derivative-energy space H_0^1(a,b). An explicit finite matrix retains the complete projected primitive Gram and original spline trace, with bounded norm error independent of center separation, boundary distance and rank loss. If the smallest node or boundary gap h resolves the width epsilon, every spectral pair instead follows the exact primitive-weighted Dirichlet Green matrix with relative error O(log(2+h/epsilon)/sqrt(h/epsilon)). This holds for a fixed number of zero-mean profiles with uniform envelopes and primitive L2 norms bounded below, arbitrary resolved nested geometry and boundary approach. An exact trace factorization and a small shear pay trace entries that can exceed secondary spectral scales. Integrable primitives improve the relative error to O(sqrt(epsilon/h)). Neutral fixed-order stencils give vanishing residual spectrum and critical scale d^p/epsilon^(p+1/2); their explicit rational realizations also distinguish finite, vanishing and escaping secondary channels. Unresolved Cauchy collision and cancellation examples explain why the resolution condition cannot simply be removed. All conclusions concern fixed-order bounded-interval operators, with no full-line theta sign or polynomial-degree assertion.
Keywords concentrated potentials · Dirichlet Green matrix · spectral asymptotics · collision · cancellation · trace factorization
Scope of the work
Fixed-order bounded-interval signed energy forms, resolved multiscale Green spectra and neutral-stencil collision/cancellation laws. No full-line theta sign, polynomial-degree assertion or Riemann hypothesis proof.
Reproduction notes
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Author preprint. AI-assisted mathematical research and internal verification; no external human refereeing or formal verification is claimed.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Collision and cancellation spectra for concentrated energy forms (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/collision-cancellation-spectra-concentrated-energy-forms/v/1
BibTeX
@techreport{luminary_collision_cancellation_spectra_concentrated_energy_forms_v1,
title = {Collision and cancellation spectra for concentrated energy forms},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/collision-cancellation-spectra-concentrated-energy-forms/v/1}
}Loading discussion…