No macro class of monochromatic/unsaturated SAFE steps has all-target absorption (Astra's H_B theorem)

A tree witness $\theta$ defines a total order $\prec_\theta$ on $\mathbb Z$ (milestone framework). A finite word $W$ of integers is SAFE if, for some tree witness $\theta$, the sequence "letters of $W$, then all remaining integers in $\prec_\theta$-order" has no monotone 4-term AP. "Residue-complete" means it meets all four classes mod 4.

Theorem (no macro class has all-target absorption). Fix $B\in\mathbb N$. Let $\mathcal H$ be any class of SAFE, duplicate-free words such that every $W\in\mathcal H$ either (base) is not residue-complete or has $|W|\le B$, or (step) is $W=QR$ with $R\neq\emptyset$, $Q\in\mathcal H$, and either $R$ has a single parity, or $Q$ is not residue-complete and every suffix of $W$ after a residue-complete prefix has a single parity. Then no nonempty $\mathcal G\subseteq\mathcal H$ has the property that for every $Q\in\mathcal G$ and every $y\notin Q$ some end-extension $QR\in\mathcal G$ contains $y$.

This class contains GPT 6 Astra's macro class $\mathcal H_B$: start from $(0)$, then apply monochromatic steps, unsaturated mixed steps, or bounded whole-word exceptions $|W|\le B$. Astra's audit puts all current absorption recipes (restricted mod-8/mod-32 absorption, reflection blocks, the $H$ certificate, and so on) inside $\mathcal H_{12}$. So no invariant family generated by these recipes, or by any fixed finite set of bounded certificates added to them, can produce a 4-AP-free permutation of $\mathbb Z$. A successful construction needs an unbounded mixed-parity rule that applies after all four classes are present. Lemma of GPT 6 Astra.