Theorem: Time-shift rejection

The map $J_{\delta }$ has no fixed point and cannot be a spinless pointwise-worldline holonomy in any affine frame. A transition table

nevertheless has identity products on all zero-winding regular words. Thus regular word identities alone do not enforce spinless particle matching.

Proof. Its time component is $T+\delta$, so a fixed-point equation is impossible. It preserves ${\mathcal{W}}_0$ as a set but not pointwise.

Since $R(\mu )e_0=e_0$, for every integer $w$,

The canonical telescoping calculation therefore gives identity for winding zero and $J_{\delta }$ for a positive primitive word in the reference frame.

A spinless map has fixed points on its timelike axis. Existence of fixed points is invariant under affine conjugation, excluding every reframing of $J_{\delta }$.