\section{Mechanistic studies and ablations}\label{sec:mechanistic}

\paragraph{Where the gains are.}
The variance decomposition of Section~\ref{sec:results-oracle} is the central mechanistic fact of this study:
for the trained editor, whether an edit helps is mostly a property of the \emph{state} (\labelscaliballpos{}\,\%
of audited states have every action helpful, \labelscaliballneg{}\,\% every action harmful), and only
\labelscalibwithin{}\,\% of the variance of gains is attributable to which slot is written. Opportunity is
concentrated in high-loss states, where the spread between the best and a random action is largest
(\labelscalibtopdecoracle{} versus \labelscalibtopdecrandom{} nats in the top decile). A router that can only
detect opportunity but not rank actions therefore edits exactly where editing is riskiest---which is what the
learned controller did.

\paragraph{Harm and overthinking.}
Across fixed schedules the loss is U-shaped in the budget (Table~\ref{tab:seedmatrix}): one or two random
edits help, eight hurt, for both the sparse editor and (less so) the global adapter; the fraction of positive
logged gains falls from 48\,\% at the first edit to 37--40\,\% after three (Figure~\ref{fig:labels}, left). Edits
compound noise faster than they compound signal in the forced-training regime, and nothing in the forced recipe
teaches the editor to leave a good state alone.

\paragraph{Slot usage and fixed pairs.}
In the exhaustive audits no slot or pair is preferred: the best action's identity agrees between consecutive
states 11--12\,\% of the time (uniform guess 4.2\,\%), singles and fixed pairs have indistinguishable mean gains on
the editor-unseen stream, and the round-robin schedule, which visits every slot, matches random selection.
The address embeddings $e_j$ therefore do not induce functional specialisation in 3,000 steps of forced training;
we make no interpretability claim about slots.

\paragraph{Myopia.}
The two-action oracle exceeds the one-step oracle by \oracletwostep{} versus \oracleonestep{} nats, but
``greedy first action, then best second'' recovers nearly all of it; the one-step greedy rule is not what limits
the learned controller.

\paragraph{Cost decomposition.}
Analytically (Section~\ref{sec:compute}), at the 103M configuration and $T=512$ a single-slot edit costs
\costsingle{} and a pair \costpair{} of the backbone's operations per token, of which the slot-key refresh of
all $M$ slots is the largest single term; measured at the tiny scale, host dispatch dominates
(Section~\ref{sec:results-latency}).

\paragraph{Slots, depth and pairing.}
Table~\ref{tab:ablations} varies the workspace size ($M\in\{4,8,16,32\}$), the number of shared editor blocks
($L_w\in\{1,2,4\}$) and the pairing scheme (adjacent $(2i,2i+1)$ versus offset $(i,i+M/2)$) on the v2 backbone with
three adapter seeds each (the reference uses five). Every variant lands within a few thousandths of a nat of the
reference: at budget 2 the loss falls by \ablmfourgainbtwo{}\,\% ($M=4$), \ablmeightgainbtwo{}\,\% ($M=8$),
\ablrefgainbtwo{}\,\% ($M=16$) and \ablmthirtytwogainbtwo{}\,\% ($M=32$); one block gives
\abllonegainbtwo{}\,\% and four blocks \abllfourgainbtwo{}\,\% against \ablrefgainbtwo{}\,\% for two;
offset pairs give \abloffsetgainbtwo{}\,\%. Exact match at budget 2 stays between \ablmfourembtwo{} and
\abllfourembtwo{}\,\% for all variants. Four slots are as good as thirty-two, one block as good as four, and the
pairing is immaterial: the effect of the editor does not depend on the structure that would make spatial routing
meaningful, which is consistent with the null results on routing.
\input{tables/ablations.tex}

\paragraph{Ablations executed.}
Readout initialisation (zero vs $\sigma\in\{0.2,0.5\}$), readout scale, editor width ($w\in\{64,128\}$),
learning rate ($10^{-3}$ vs $3\times10^{-3}$), budget schedule (mixed vs budget-8 only), write locality
(1--2 slots vs all 16), slots $M\in\{4,8,16,32\}$, editor depth $L_w\in\{1,2,4\}$, pairing scheme, global vs
local recurrence, controller features ($z$ vs $\hat h$ + entropy), label stream (editor-seen vs editor-unseen),
ranking losses, penalties ($\lambda,\kappa$). Not executed: joint fine-tuning (one attempt degraded the backbone
and was stopped), distillation, quantisation. All executed runs, including failed ones, are listed in
Appendix~\ref{app:runs}.