01 / Problem
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Paper 014 / June 13, 2026
Topological Boundary Conditions for Edge-Localized Projection Electromagnetism
From hypersurface flux terms to homology-aware null observables
01 / Abstract
Abstract
Boundary-flux projection models suggest that effective electromagnetic residuals may localize near edges, apertures, guards, seams, and dielectric interfaces. This paper proposes a topology-aware version of that idea. Instead of treating edge sensitivity as a geometry anecdote, it classifies conductor-dielectric assemblies by boundary components, oriented seams, guard surfaces, and homology classes. The result is a research program for null observables that distinguish ordinary field concentration from projection-style boundary flux.
02 / Frame
Research Frame
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\[
Q_{\mathrm{eff}}(\Omega)=\int_{\partial\Omega} \Pi\cdot n\,dA
+\sum_{\ell\in \mathcal{E}(\Omega)} \int_{\ell} \beta_\ell(E,\epsilon,K)\,ds .
\]
\[
R_{\mathrm{edge}}=\frac{F(\Omega)-F(\Omega_{\mathrm{smoothed}})}{U_E},
\qquad
R_{\mathrm{seam}}=\frac{F(\Omega_{\mathrm{seam\;rotated}})-F(\Omega)}{U_E}.
\]
03 / Structure
Paper Structure
The manuscript follows the JMP0X1B discipline: state the problem, formalize the model, name the claims, and publish enough source material for review and revision.
02 / Model
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03 / Claims
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04 / Evidence Plan
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04 / Files
Paper Files
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