From 51ee43577a0f157506b47e478d43d517d56ed8f6 Mon Sep 17 00:00:00 2001
From: wassname <1103714+wassname@users.noreply.github.com>
Date: Wed, 3 Jun 2026 11:05:20 +0000
Subject: [PATCH] paper: tab:ablation interp -- weak vector fails to erase but
 routes (SGTM absorption)

Fill the \TODO{interp} in tab:ablation caption: post-hoc erase exposes how weak v_hack is
(weight-erase 0.39->0.30; act-erase zeroes hack only by collapsing solve), yet the same
direction drives route to 0 deploy hack because routing only needs to discriminate hack
rollouts, not span the hack subspace -- absorption (cloud2024/sgtm2025) localises into the
discarded knob. 'A detector too weak to erase a trained hack is still strong enough to route
one as it forms.'

Co-Authored-By: Claudypoo <288921227+claudypoo@users.noreply.github.com>
---
 docs/writeup/main.tex | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/docs/writeup/main.tex b/docs/writeup/main.tex
index 6264a84..8edffd9 100644
--- a/docs/writeup/main.tex
+++ b/docs/writeup/main.tex
@@ -245,7 +245,16 @@ $+0.024$ while a mechanism-contrasting pairset moved it $-0.226$
   \caption{Ablation: deploy hack/solve per arm, seed 41, matched preset.
   Controls (random-V, placebo) should sit at the vanilla hack level if the
   effect is directional rather than generic adapter regularization.
-  \TODO{interp -- author.}}
+  The post-hoc rows expose how weak the extracted direction is on its own:
+  erasing along it after training barely moves the hack (weight-erase,
+  $0.39{\to}0.30$), and activation ablation removes hacking only by collapsing
+  solve to zero. The same weak direction still drives the train-time route arm
+  to zero deploy hack at $0.625$ solve, because routing needs the direction only
+  to \emph{discriminate} hack rollouts, not to \emph{span} the hack subspace in
+  weight space; the absorption property of gradient routing
+  \citep{cloud2024gradientrouting, sgtm2025localization} then localises the
+  capability into the discarded knob. So a detector too weak to erase a trained
+  hack is still strong enough to route one as it forms.}
   \label{tab:ablation}
   \begin{tabular}{lccl}
     \toprule