Laws of Manifold Theory
For all of humanity and not just the select few among each country with enough money and power to afford it. JTRedmond Laws of Manifold Theory Abstract We present a geometric extension of classical electromagnetism through a manifold-centric framework, incorporating curvature, tensor deformation, and harmonic field resonance. This paper outlines the foundational equations governing manifold electromagnetics, supported by theoretical and visual models. Core Equations Curvature-Augmented Faraday's Law ∇ × E = -∂B/∂t + β∇R Modified Maxwell-Ampère Law with Tensor Flux ∇ × B = μ₀J + μ₀ε₀ ∂E/∂t + γ□T_{μν} Field Propagation Over Harmonic Topography □A = -μ₀J + αΔφ EM Tensor from Manifold Harmonics F_{μν} = ∂_μ A_ν - ∂_ν A_μ + η_{μν}Φ(𝓜) Charge Localization via Curvature Scalar ρ = κ R φ² Holographic Flux Encoding ∮_∂𝓜 E · dA = ∬_𝓜 ∇·E dV + ∫_ℋ H(φ) dS Light Cone Compression via Curvature Tension θ = d/dτ [ln(1/√g)] Figure 1: Curvature-augmented field lines Figure 2...