Slot 2, the decision place: Chandrupatla's own acceptance band, put inside our step rule as an instrument, does NOT close the gap - CHA 3066 (project) / 2899 (credit) against his 2423, while APS doubles 2806 -> 5432, and the band is not idle (63.6% refusals). The fifth independent test of one conclusion: the remaining gap is the ORDER of the model the step is built on, not the place the similarity is read in. By the declared stop rule (M1 and M2 both false) the 'where is the similarity read' line is closed: all four places measured.

Not empty-handed: our own parameter-free reading 'defect' - refuse when |phi - xi| > min(xi, 1 - xi) - sets a new canonical best, APS 2523 at 153/154 (previous 2527, Chandrupatla 2785), guarantee intact (0 of 135 family cells), refusing on 7.0% of steps. It is a second point on the same trade, not a replacement: 5733 over both sets against 5511, because CHA gives back 3210. Also: _shape_ratios crashed on a missing third point, which evaluate would have turned into a silent sweep of zeros; the slope-gate pin was anchored on line spelling; and the server copy had drifted (stale relax/sor.py, test_relaxation.py absent - 746 tests instead of 755). All synced, 92/92 files identical by content, 755 pass on the server.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

article/sim_numerics.tex

@@ -624,6 +624,45 @@ the \emph{slope} reading the same exponent is harmful, $2806\to2854$, which is
 the same statement read from the other side --- a function that does not belong
 to a place does not become right by being applied there.
 
+\subsection{The decision place, and the one test that settles the gap}
+\label{sec:decision}
+
+Three places have now been measured: the step length, the far end, and the
+points the model is built on. The fourth is the \emph{decision} --- whether the
+local model deserves this evaluation or halving is the better use of it.
+Chandrupatla's method is strong exactly there: it refuses its model on most
+steps by the acceptance band $1-\sqrt{1-\xi}<\varphi<\sqrt{\xi}$, where
+$\xi=(x-u)/(v-u)$ and $\varphi=(f(x)-f(u))/(f(v)-f(u))$ are ratios of positions
+and of values, equal for a linear $f$. Our method has no similarity in this
+place at all: a sign gate and a projection that repairs \emph{after} the step.
+
+Three readings of that place were measured, each on quantities already in hand
+and each without a constant. Two are ours: refuse when the configuration is
+less like a linear one than the iterate is off-centre,
+$|\varphi-\xi|>\min(\xi,1-\xi)$ (``defect''); and refuse when the
+configuration's similarity to linear falls below the iterate's similarity to
+the root, $S(|\varphi-\xi|)<S(z)$, with the \emph{same} $S$ in both places
+(``simpair''). The third is \emph{Chandrupatla's own band}, placed inside our
+step rule. It is not a proposal; it is an instrument, and it answers the only
+question that matters here --- whether the remaining gap lives in this place.
+
+It does not. With Chandrupatla's band in our step, the wide-bracket set costs
+$3066$ under the projection guard and $2899$ under credit, against his $2423$,
+while the canonical set rises from $2806$ to $5432$. The band is not idle ---
+it refuses $63.6\%$ of steps --- so this is a decision that was taken and did
+not pay. That is the fifth independent test of the same conclusion: the gap is
+the \emph{order of the model} the step is built on, not the place where the
+similarity is read.
+
+Our own readings do not close it either (best $2868$ on the wide-bracket set),
+but ``defect'' sets a new best on the canonical set: $\mathbf{2523}$ at
+$153/154$, below the $2527$ of reading~(2) and below every method measured,
+with the guarantee intact and no constant. It refuses only $7.0\%$ of steps,
+the fewest of the three. Over both sets it costs $5733$ against the $5511$ of
+reading~(3), because it gives back on the wide brackets ($3210$) what it gains
+on the canonical problems --- so it is a second point on the same trade, not a
+replacement.
+
 \subsection{Six problems of the two sets are scored unsolved for every method}
 \label{sec:fun7}