paper: de-meta the captions (humanizer/paper-writing)

Captions describe the data and state the finding, not the figure's role in
the paper. Drop 'Headline result' / 'the companion to the 60-step headline' /
'(keynote)' meta-narration; lead with what is plotted. Also: 'headline
direction' -> 'the v_hack direction'; move the 'Source: docs/results.md'
provenance from body text into a comment.

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

docs/writeup/main.tex

@@ -104,13 +104,13 @@ the three claims C1/C2/C3.}
 \begin{figure}[!ht]
   \centering
   \includegraphics[width=0.72\linewidth]{figs/dyn_sub4_hack_overlay.png}
-  \caption{\textbf{Headline result.} Deploy hack rate (top) and solve rate
-  (bottom) over 60 GRPO steps, route (ours, $n{=}3$ seeds) vs vanilla ($n{=}3$);
-  thick line = mean, thin = per seed. EMA-5, knob-off deploy eval, $n{=}64$,
-  $T{=}0.7$. Vanilla hack emerges to ${\sim}0.4$ while route stays near zero, and
-  route reaches a higher solve rate (${\sim}0.6$ vs ${\sim}0.4$). The arms differ
-  only in the gradient policy (Section~\ref{sec:method}). Persistence to 200 steps
-  is Figure~\ref{fig:longrun}. \TODO{interp prose -- author.}}
+  \caption{Deploy hack rate (top) and solve rate (bottom) over 60 GRPO steps for
+  route (ours) and vanilla GRPO, three seeds each; thick line is the mean, thin
+  lines per seed (EMA-5). Deploy evaluation is knob-off at $n{=}64$, $T{=}0.7$.
+  Vanilla acquires the hack, rising to ${\sim}0.4$, while route stays near zero and
+  reaches a higher solve rate (${\sim}0.6$ vs ${\sim}0.4$). The arms differ only in
+  the gradient policy (Section~\ref{sec:method}); the gap persists to 200 steps
+  (Figure~\ref{fig:longrun}).}
   \label{fig:keynote}
 \end{figure}
 
@@ -239,7 +239,7 @@ deploy-eval = knob-off, $n=64$ prompts$\times$group, $T=0.7$, per env\_mode.}
 % ===================================================================
 \section{Results}
 
-\subsection{C1: route vs vanilla deploy hack/solve (keynote)}
+\subsection{C1: route vs vanilla deploy hack and solve}
 
 Over three seeds at the 60-step preset, route holds deploy hack near zero while
 vanilla GRPO acquires it, and route also raises the solve rate
@@ -382,19 +382,15 @@ at zero while vanilla acquires the hack and then collapses
 \begin{figure}[t]
   \centering
   \includegraphics[width=0.95\linewidth]{../../out/figs/dyn_longrun_200.png}
-  \caption{\textbf{Long-horizon convergence (200 steps, $n{=}1$).} The companion
-  to the 60-step headline (Figure~\ref{fig:keynote}): same arms, single seed, run
-  to convergence. Deploy hack (red) vs solve (green), seed 41, deploy-eval
-  $n{=}64$, $T{=}0.7$, EMA-5. \textbf{route} (right) holds
-  deploy hack at exactly $0$ for all 200 steps ($\text{hack}\equiv 0$ label) while
-  solve climbs to ${\sim}0.61$ and plateaus. \textbf{vanilla} (left) learns the
-  cheat (hack rises from the first-hack step to ${\sim}0.55$ by step~80), then the
-  policy \emph{collapses} around step~88 (student logp craters, reward $\to 0$,
-  grad-norm spikes ${\sim}75\times$ with no KL anchor), dragging both hack and
-  solve down: the late-vanilla descent is degeneration, not hack suppression. The
-  valid comparison window is steps 0--85, where vanilla acquires the hack and
-  route never does. The gap that opens by step~60 persists to convergence:
-  route's deploy hack stays at $0$ through all 200 steps.}
+  \caption{Deploy hack (red) and solve (green) over 200 GRPO steps for the same
+  two arms, seed 41 (deploy evaluation $n{=}64$, $T{=}0.7$, EMA-5). route (right)
+  holds deploy hack at $0$ for all 200 steps while solve climbs to ${\sim}0.61$
+  and plateaus. vanilla (left) acquires the hack (${\sim}0.55$ by step~80), then
+  collapses around step~88: student log-prob craters, reward falls to $0$, and the
+  pre-clip gradient norm spikes ${\sim}75\times$ with no KL anchor, dragging hack
+  and solve down together. That late descent is degeneration, not hack
+  suppression, so the valid comparison window is steps 0--85; within it vanilla
+  acquires the hack and route never does.}
   \label{fig:longrun}
 \end{figure}
 
@@ -419,7 +415,7 @@ extraction set, not only the in-distribution mode (Table~\ref{tab:generalisation
   \caption{Per-mode deploy hack, route $n{=}3$. ``held-out'' = mode's pairs
   absent from the extraction set (\texttt{in\_dist=false}). \TODO{the clean
   2-of-4 held-out design (A5 / jobs G2/G3) is not yet queued; these per-mode
-  numbers are an opportunistic read of the keynote runs, not the designed test.}}
+  numbers are an opportunistic read of the $n{=}3$ runs, not the designed test.}}
   \label{tab:generalisation}
   \begin{tabular}{lccc}
     \toprule
@@ -756,8 +752,8 @@ The erase and route gradient policies at the optimizer step
 % were AI-authored (Claude, prompted to write a correct solution paired with the
 % same solution wrapped in each loophole). We show one pair rather than claim the
 % direction is "label-free"; the reader can see exactly what supervision built it.
-The headline direction is extracted from $\sim$10--21 such pairs (full set:
-\texttt{out/pairsets/prog\_wide.json}). Each pair holds the \emph{same} prompt
+The $v_{\text{hack}}$ direction is extracted from $\sim$10--21 such pairs (full
+set: \texttt{out/pairsets/prog\_wide.json}). Each pair holds the \emph{same} prompt
 and the \emph{same} solve code; only the grading-facing scaffold differs, so the
 paired difference $g_{\text{hack}}-g_{\text{clean}}$ isolates the loophole, not
 the algorithm. One \texttt{run\_tests}-mode pair (\texttt{twoSum}):
@@ -797,10 +793,10 @@ holds the second-half cosine $\sim$1.43$\times$ higher. Include the
 These runs predate the deploy-eval harness and the current route arm; they use the last-5-step
 \emph{training} hack rate (student rollouts flagged) on the one-sided erase arm
 at the fast 20-step preset. Treat as context for the design choices, not as
-deploy numbers. Source: \texttt{docs/results.md} (curated 2026-05-30, each row
-citing its logs). They cover the erase arm (Table~\ref{tab:ctx-erase}), teacher
+deploy numbers. They cover the erase arm (Table~\ref{tab:ctx-erase}), teacher
 density (Table~\ref{tab:ctx-mix}), pair-set content (Table~\ref{tab:ctx-pairset}),
 and basis strength (Table~\ref{tab:ctx-basis}).
+% Source: docs/results.md (curated 2026-05-30, each row citing its logs).
 
 % results.md Q2 (mix=0.5, v_hack_21pairs, one_sided, k=5, n=4 seeds 41-44).
 \begin{table}[h]