The new sections move into the canonical text, article/sim_numerics.md (Valeri's decision): section 7 'Where the similarity is read' with 7.1 per-place similarity, 7.2 the decision place, 7.3 the fun7 scoring artefact, 7.4 the gap decomposition; negative results 8-11 appended so items 1-7 keep their numbers; abstract paragraph; Future work rewritten (the refuted log transform removed); item 6 now says aps.13.00 is a scoring artefact, not a method failure. Translated into the .md's revised names: code 'ratio' = the tent max(0,1-|z|), code 'rational' = the ratio similarity 1/(1+|z|); the proposed method stays the .md's (tent, 3-point, projection).

Found on the way: negative item 'log change of variable' compared 3474 with 4516, the total of a DIFFERENT configuration; the honest pair is the same configuration in x, CHA 3643 -> 3474, APS 5822 -> 6940. Fixed in both texts. The gap-decomposition numbers were only traced to saved logs; they are now RECOMPUTED by verify_article.py from fresh runs of the diagnosis scripts (which return their values): 216 checks OK on Linux, 762 tests pass twice.

Open, for Valeri: the .md still says the projection's doubling is 'not a tuning constant', which simroot/pure.py (project_credit) refutes and which is why the .tex proposes credit; the .md's Tables 2-3 predate Chandrupatla's own method as a baseline (2785 APS, first place), so its 'parity' abstract is out of date; Brent 2890/4101 in the .md against 2889/4099 in the current sweep.

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

article/sim_numerics.tex

@@ -852,9 +852,11 @@ the same algorithm --- our iterate starts at the midpoint of the bracket, plain
 false position at an end --- and the two must not be differenced.
 \item \textbf{A logarithmic change of variable does not buy the wide brackets.}
 Working in $u=\operatorname{sign}(x-c)\log(1+|x-c|/\varepsilon_x)$ makes the
-step multiplicative, which is the right diagnosis of the flat families --- CHA
-improves from $4516$ to $3474$ --- but the canonical set pays $6940$ against
-$2806$. A march needs a \emph{ratio} of distances while an identity on narrow
+step multiplicative, which looked like the right diagnosis of the flat families
+--- for the same similarity, scale and safeguard CHA improves from $3643$ to
+$3474$ --- but the canonical set gets worse, $5822$ to $6940$, against the $2806$
+of the projection variant. An earlier version compared the $3474$ with $4516$,
+the total of a different configuration. A march needs a \emph{ratio} of distances while an identity on narrow
 brackets needs an \emph{absolute} unit, and no parameter-free unit provides
 both.
 \item \textbf{The prototype-aggregation form of the method loses.} A richer