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
- 2 · 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 ε, every spectral pair instead follows the exact primitive-weighted Dirichlet Green matrix with relative error O(log(2+h/ε)/√(h/ε)). This holds for a fixed number of zero-mean profiles with uniform envelopes and primitive L^2 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(√(ε/h)). Neutral fixed-order stencils give vanishing residual spectrum and critical scale d^p/ε^(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.
Keywords concentrated potentials · Dirichlet Green matrix · spectral asymptotics · collision · cancellation · trace factorization
Scope of the work
Fixed-order bounded-interval concentrated energy forms admit a collision-uniform finite primitive matrix model and a relative Green spectral law for every resolved channel; signed cancellation stencils give vanishing residuals and explicit unresolved examples.
Reproduction notes
The 17-page manuscript and complete editable LaTeX sources are supplied in this 14-member package. README.md gives the build and reproduction commands. Reproducibility code: verify_beta.py, verify_constants.py, verify_geometry.py. The accompanying manuscript and reader instructions specify the mathematical scope and required dependencies.
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Author disclosures
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 2). Luminary Research Archive. https://research.luminaryoddities.com/collision-cancellation-spectra-concentrated-energy-forms/v/2
BibTeX
@techreport{luminary_collision_cancellation_spectra_concentrated_energy_forms_v2,
title = {Collision and cancellation spectra for concentrated energy forms},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/collision-cancellation-spectra-concentrated-energy-forms/v/2}
}Loading discussion…