Astra's asymmetric word $(0,1,-1,5,3,2,-15,-11,-5,-99,-115,-55)$ is tree-safe, with $3$ before $2$

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 $\theta$. The twelve-letter word

is SAFE, and it lists $3$ before $2$. It extends the prefix $(0,1,-1)$ and contains the target $2$ with the compulsory witness $3$ before it. Its support is not symmetric under any reflection, and $H$ is not a true root release. It is built by two fourth-term repair blocks. In the tree-witness approach to Erdős Problem 195 it shows that a finite SAFE extension of $(0,1,-1)$ containing $3\prec2$ exists, which settles a question that symmetric completions cannot answer.

Formalization note: treeLt θ is from Definitions.Def_Erdos195_tree, and Safe is from Definitions.Def_Erdos195_defs. Positions are List.idxOf, and $\nu_2$ is padicValInt 2.