This document confirms the final transformation of the geometric Compton structure equation into a form based on wavelength.

Starting Structure Equation (from Law of Cosines, rearranged):

k_c² = (k – k’)² + 2kk'(1 – cos(θ))

Substituting the spatial frequency terms:

k = 1/λ

k’ = 1/λ’

Resulting equation:
Eq(kc**2, lamp**(-2) – 2*cos(theta)/(lam*lamp) + lam**(-2))

This equation geometrically derives the observed wavelength shift in the Compton Effect without invoking photon momentum or mass–energy conversion.

This marks the final algebraic confirmation that the Compton shift:

Δλ = λ’ – λ = (h / m_e ℓ) (1 – cos θ)

Is a purely geometric result arising from angular coherence interaction, not relativistic mass exchange.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams