Garfield's Light Conjecture

 

Lemma 1 (Redshift as an Observer-Dependent Quantity)

Lemma.
If $\Phi(v_o)$ is continuous and monotonic in $v_o$, then the redshift parameter

$$z = \frac{\lambda_{\text{obs}} - \lambda_0}{\lambda_0}$$

is fully determined by observer motion and does not require the assumption of light propagation or expanding space.

Proof (Direct Substitution).
Substituting the conjectured relation into the definition of redshift yields:

$$z = \frac{\lambda_0 \cdot \Phi(v_o) - \lambda_0}{\lambda_0} = \Phi(v_o) - 1$$

Thus, $z$ is a direct function of observer motion alone. No dependence on distance, travel time, or transmission medium is required.