Angular Emergence Of The Spectrum Under The Lilborn Framework

Introduction

This document demonstrates how the Lilborn Framework resolves the phenomenon of spectral color emergence through a prism, not as a dispersion of preexisting wavelengths, but as a structural alignment between the universal light field (ℓ) and the internal geometry of the prism’s electromagnetic field (F).

Coherence Gate Function

We use the function:

f(x) = A · exp[−(1−x)² / (2ε²)], where x = cos(θ) = (F · ∇ℓ) / (|F||∇ℓ|)

This function governs the resolution of energy from the field, enabling angular exposure to determine which frequencies emerge at specific angles from a prism’s structure.

Angular Prism Geometry

The prism is modeled as a triangular body with a uniform internal field F oriented perpendicular to its base. As coherent light potential ℓ enters and exits the prism, each angle of exit selectively satisfies the Coherence Gate Function for a different energy band, resulting in color emergence.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams