01 / Problem
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PAPER-014 / June 13, 2026 / corrected September 18, 2026
Topology-Aware Boundary Manifests for Edge-Localized Projection Electromagnetism Tests
Separating homology invariants from constitutive edge-response proxies
01 / Abstract
Abstract
This proposal distinguishes genuine homology invariants, which require a closed differential form on a source-free domain, from weighted edge-response functionals that depend on fields, materials, and ordinary spatial curvature. It does not call every boundary integral topological, and no geometry atlas or measurement is released.
02 / Frame
Research Frame
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\[
\Phi[C]=\int_C\omega,\qquad
\mathrm d\omega=0,\qquad
C_1\sim C_2\Longrightarrow\Phi[C_1]=\Phi[C_2].
\]
\[
C_{\mathrm{edge}}=\frac{F(\Omega)-F(\Omega_{\mathrm{smoothed}})}{F_{\rm cal}},
\qquad
C_{\mathrm{seam}}=\frac{F(\Omega_{\mathrm{seam\;rotated}})-F(\Omega)}{F_{\rm cal}}.
\]
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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