I've been developing a theoretical framework that extends conventional field theory by treating modulation depth as a dynamical coordinate rather than a parameter. I'm curious if anyone has encountered similar approaches or can provide insights on this mathematical structure.

The Generalized Modulation-Based Field Equation:

∫[1/2(∂Φ/∂t)² - 1/2(∇Φ)² - V(Φ,η) + Σ(n=1 to 5) Wₙ sin(L/2πn + R)] d⁴x

Key Components:

• Φ(x,t,ε): Field potential across space, time, and modulation dimension ε
• V(Φ,η): Potential incorporating modulation coupling parameter η
• Wₙ: Universal weighting function with precomputed values:W₁ = 0.602, W₂ = -0.172, W₃ = -0.205, W₄ = -0.054, W₅ = 0.019
• Modulation terms: Structured oscillations governing force interactions

Mathematical Features:

The framework appears to naturally reproduce fundamental constants without manual calibration:

• Gravitational constant G emerges from potential curvature terms
• Fine-structure constant α from oscillatory electromagnetic coupling
• Planck constant ℏ from temporal energy quantization
• Speed of light c from spatial-temporal field balance

The equation reduces to established physics under appropriate limits:

• Schrödinger equation (non-relativistic quantum limit)
• Einstein field equations (gravitational limit with modulated G)
• Maxwell equations (electromagnetic sector)
• Standard Model interactions (through weighted oscillatory terms)