paper: interim directionality fig (app:directionality) + confound TODO

route2 deploy hack collapses for ANY v_grad (real/placebo/Haar) but solve tracks
direction (real>placebo>Haar). TODO names the load-bearing confound: full-teacher
runs force-route all teacher rows by label (hack_anchor), so the hack-axis collapse
is direction-free force-routing not the cosine gate; clean test = A5 run_tests-only
regime (pending). n=1 interim.

Co-Authored-By: Claudypoo <288921227+claudypoo@users.noreply.github.com>

docs/writeup/main.tex

@@ -994,6 +994,49 @@ live teacher grad) decays $\sim$0.28$\to$0.07 by step 10 on frozen-V; refresh-2
 holds the second-half cosine $\sim$1.43$\times$ higher. Include the
 \texttt{basis\_overlap\_with\_prev} check for route refresh.}
 
+\section{Directionality of route2: what does \texorpdfstring{$v_\mathrm{grad}$}{v\_grad} actually buy?}
+\label{app:directionality}
+% PROVENANCE: data/directionality.csv (final knob-off deploy hack+solve from the
+% FINAL EVAL log line of each route2 run, n=64 T=0.7); figure by
+% figs/plot_directionality.py. real_v = nofloor route2 job (20260601T115713);
+% placebos = jobs 86/115/117; haar_d0 = job 114; vanilla = keynote n=3.
+We test whether route2's suppression needs $v_\mathrm{grad}$ to point at the hack
+(H4: alignment) or works for any direction (H2: mechanical absorption), by swapping
+$v_\mathrm{grad}$ for a semantic-placebo direction (\texttt{null\_city},
+\texttt{vampire}) or a Haar-random out-of-subspace direction.
+Figure~\ref{fig:directionality} reads in two axes. On the hack axis every routing
+arm collapses to $\sim$0 regardless of direction; only vanilla sits out at 0.32. On
+the solve axis the real hack direction recovers the most solve (0.625), placebos sit
+mid ($\sim$0.53--0.58), and out-of-subspace Haar is lowest (0.516).
+
+% FIXME / TODO: more coming, and a load-bearing caveat. These runs use the FULL
+% four-mode teacher pool, so EVERY mode (incl. the ones held out of v_grad) has
+% teacher hack demos -- and route2 force-routes all teacher rows by label
+% (hack_anchor, train.py:352), independent of v_grad. So the hack-axis collapse here
+% is mostly direction-free force-routing, NOT the cosine gate finding the hack; with
+% a random v_grad the gate's tau collapses to ~0 and cos_b>tau is a ~50/50 coin flip.
+% The CLEAN directionality test is the A5 regime (teacher = run_tests only): held-out
+% modes have no teacher to force-route, so their suppression can only come from the
+% v_grad cosine gate -- that is where real-vs-random should diverge if direction
+% matters. Pending: (a) Haar seed replicates (jobs 118/122) + null_city s43 (121) to
+% put error bars on the solve gap; (b) the erase arm (jobs 127/128), whose projection
+% magnitude is proportional to cos(g,v) so direction must matter there if anywhere;
+% (c) random-V/placebo variants in the A5 run_tests-only-teacher regime (not yet
+% queued). n=1 per placebo/draw; the ~0.11 solve gaps are ~1.5--2 SEM at n=64.
+\begin{figure}[h]
+  \centering
+  \includegraphics[width=0.62\linewidth,alt={Scatter of deploy hack vs deploy solve
+  for route2 with different v_grad directions. All routing arms collapse to near-zero
+  hack regardless of direction; the real hack direction recovers the most solve, Haar
+  random the least.}]{figs/directionality.pdf}
+  \caption{route2 deploy hack vs solve as $v_\mathrm{grad}$ is varied. Hack
+  suppression is direction-agnostic (every arm at hack$\approx$0); solve recovery
+  tracks how well the direction points at the hack (real $>$ placebo $>$ Haar). See
+  the source comment for the full-teacher confound and the clean test still pending.
+  Data: \texttt{data/directionality.csv}. \emph{Interim, n=1 per arm.}}
+  \label{fig:directionality}
+\end{figure}
+
 \section{Teacher-off control: the teacher seeds, it does not sustain}
 \label{app:teacher}
 % PROVENANCE: deploy-hack trajectories parsed from the DEPLOY-eval log lines of