Proposition: What the history does on a fixed host

On a fixed host with ${\mu }_{\mathrm{H}}={\mu }_0$, the nonzero-token word (eq:fiveword) is an implemented history of description registers. Its post-source certificates concern $M_{{\mu }_1}$, not a changed host metric. The zero-token word may instead describe the host's own prescribed family throughout.

Neither history supplies an Einstein evolution or a geometric interpolation between different deficits.

Proof. The host metric is fixed by Definition def:host. Every source and event operation in the word is specified on finite description data; none acts on the metric. The distinct deficits have distinct peripheral rotations by Proposition prop:rejections. The zero-token specialization has $\mu ={\mu }_{\mathrm{H}}$. No common mixed realization has been supplied.