Six-entry absorption family from $(0,1,-1)$ for every nonzero $s\equiv 0\pmod 4$

A tree witness is a function $\theta(k,r)\in\{0,1\}$ on the nodes $(k,r)$, $0\le r<2^k$, of the binary tree of residues. For distinct integers $x,y$ with $k=\nu_2(y-x)$, put $x\prec_\theta y$ iff $\mathrm{bit}_k(x)=\theta(k,\,x\bmod 2^k)$. A finite word $Q$ of integers is $\theta$-safe if the sequence "the letters of $Q$ in order, then all remaining integers in $\prec_\theta$-order" contains no monotone $4$-term arithmetic progression. $Q$ is SAFE if it is $\theta$-safe for some tree witness $\theta$. For every nonzero integer $s$ with $s\equiv0\pmod4$, the word

is SAFE. So the prefix $(0,1,-1)$ absorbs each such target $s$ with six new entries, three of them before $s$. This is GPT Astra's six-entry absorption family. It is not an instance of the mod-32 restricted absorption theorem (that would need $s\equiv8\pmod{16}$).