Theorem: The calibrated scalar is a projection, not a lift

The constructed free word satisfies

Neither projection defines ${\mathsf{TO}}_2$, ${\mathsf{T}}_2$, ${\mathsf{Ret}}_1$, or a higher retarded map.

Proof. Every nonconstant term in (eq:word) has positive field degree and vanishes at zero configuration. The displayed identities follow.

The projection has a large kernel: ${\Pi }_{3,0}(\hslash F)=0$ for every $\hslash$-independent $F$, and ${\mathrm{ev}}_0({\hslash }^{j}F)=0$ whenever $F[0,0]=0$. It loses nonconstant coefficient information and has no supplied rule assigning missing binary coefficients, ordered restrictions, or old causal overlaps. A change in a nonconstant coefficient may leave the projection unchanged. This is information loss, not permission to change any locked free coefficient.