chasing Chandrupatla found a property of the BENCHMARK: on all five fun7 problems f vanishes identically near the declared root (f(0+t)=0 up to 3.2e-2), every method stops at a point where f(x)=0 exactly and is scored a failure by the |x-root|<=1e-6 rule — so 1000 evaluations of EVERY wide-bracket total are an artefact and the universal '40 of 45' is a scoring statement. Re-scored: 45/45 for everyone but Brent, ranking unchanged, gap to Chandrupatla 253 (17%) and diffuse across 8 families. Written into the paper with its reproducing scripts; pdflatex clean, verifier green

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

article/sim_numerics.tex

@@ -563,6 +563,38 @@ The readings do not compose. Taken together, (2) and (3) give $2884$ and
 $2859$ --- worse than either alone. Two selections that are each an improvement
 interfere, which is a reason to measure composition rather than assume it.
 
+\subsection{Five problems of the wide-bracket set are scored unsolved for every
+method}
+\label{sec:fun7}
+
+Chasing the remaining gap to Chandrupatla on the wide-bracket set led to a
+property of the set itself. On the five problems of its \texttt{fun7} family the
+declared root is $0$, but $f$ vanishes \emph{identically} on a neighbourhood of
+it: $f(0+t)=0$ for every $t$ up to at least $3.2\times10^{-2}$. Every method
+therefore stops after $8$ to $22$ evaluations at a point where $f(x)=0$
+\emph{exactly} --- a genuine root --- and every method is then scored as having
+failed, because the harness asks for $|x-\text{root}|\le10^{-6}$ and the
+returned point sits up to $2.8\times10^{-2}$ away.
+
+The consequence is arithmetic. Each such problem charges the full budget of
+$200$ evaluations to every method, so $1000$ evaluations of every wide-bracket
+total --- ours, Chandrupatla's, ITP's, bisection's --- are this artefact, and the
+``$40$ of $45$ solved'' that every method reports is a statement about the
+scoring rather than about the methods. Re-scored with the criterion ``a root is a
+root'' ($|x-\text{root}|\le10^{-6}$ \emph{or} $f(x)=0$), the same runs give
+$45/45$ for every method except Brent's $43/45$, and the totals fall to
+Chandrupatla $1487$, ours $1740$, ITP $1907$, bisection $2136$, TOMS\,748
+$3088$. The ranking does not change; the magnitudes do, and with them the size
+of the remaining gap: $253$ evaluations, or $17\%$, not $11\%$.
+
+Two things follow. The wide-bracket gap to Chandrupatla is real and it is
+\emph{diffuse}: measured per family it is $+57$, $+54$, $+46$, $+43$, $+35$ and
+smaller, with no single problem costing more than $35$, so it is not the kind of
+deficit a single mechanism removes. And on that set our shape reading ($2159$
+re-scored) is barely better than bisection ($2136$); only the dissimilarity
+reading ($1740$) is clearly ahead. Both statements are reproduced by
+\texttt{diag\_rescore\_cha.py} and \texttt{diag\_cha\_gap.py}.
+
 \section{Negative results}
 
 \begin{enumerate}