Revision 1, step 1: one scoring criterion, the correct order, and the internal inconsistencies.

Point 1. The base step's order is Muller's 1.839, not 2: the derivative of the parabola through
the last three points errs by f'''/6 (x_n - x_{n-1})(x_n - x_{n-2}) = O(e_{n-1} e_{n-2}).
order_high_precision.py (3000 digits, to 1e-2900): 1.840 on cos x - x, e^x - 2, x^3 - x - 2,
sin x - 1/2; 2.000 only on x^2 - 2; two-point 1.618. The double-precision medians (2.000, 1.94)
are removed from the text.

Point 3. Every protocol number is re-scored under the criterion of section 9 - a sign change
within 1e-6 or f(x) == 0. rescore_uniform.py re-runs all 2779 distinct configurations of the 25
protocol sweeps on APS and CHA (the runs did not keep x) -> sweep_uniform.json, same row format;
it reproduces the APS/CHA lines of Table 10 exactly (built-in check). verify_article.py,
audit_similarity_places.py and the gap diagnostics read the re-scored data; the multiplier and
endowment measurements score by the same criterion. Table 7 (two criteria side by side) is gone;
7.3 now explains why the criterion is a sign change. Consequences stated in the text: the base
rule 2634 / 2357 against Chandrupatla 2595 / 1505 (1.5% behind on APS, no longer "level"); A'
2259 / 1074 (12.9% and 28.6% below Chandrupatla); the defect reading 2351 is second to the
shape reading 2337, not the record; the remembered analogy is level with no regime (2633 vs
2634) under this criterion; Table 9a's range is 19% to 425%.

Point 8. report_sweep.head_to_head counts every problem, failures charged (it counted only the
problems both methods solved, which is why Table 8 rows summed to 153 and 40). Family-level
comparisons added (A' vs Chandrupatla 8/1/6 of 15 and 7/0/2 of 9 families, not significant), and
an independence paragraph in section 9.

Point 11. sweep_itp.py: ITP (recommended constants and per-problem oracle) on all six corpora ->
Table 10; behind A' on every corpus, 0 bound violations.

Points 7, 9, 10 and the internals: the 2x bound is ours, not the rivals' promise; the law
predicts the group order only; "outside the proven bracket" explained (narrowest bracket of all
observed signs); 7.4's fun1 paragraph corrected (five costs under safe; the unguarded numbers
belong to fun1.4, fun1.5 and to fun3.1, fun5.1 separately); Table 1's last cell; the corpus-4
composition and odd multiplicities stated, also in the abstract.

build_tex.py: pdflatex output decoded with errors="replace" (a UTF-8 character cut by TeX's log
wrap crashed the build). Table 10 column widths rebalanced.

Checks: verify_article on the server 500 OK / 0 BAD (467 existing with the new values, 33 new);
regression x2 on the server 1232 passed, 0 failed; PDF 28 pages, 0 errors, 0 undefined, 0 overfull.

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

diag_model_order.py

@@ -39,6 +39,8 @@ from simroot.baselines import chandrupatla, chandrupatla_scipy
 from simroot.pure import pure_root
 
 XTOL, MAXFEV, ACC = 1e-12, 200, 1e-6
+# success = the paper's single criterion since 2026-09-22 (revision point 3)
+from corpus_roots_jl import solved  # noqa: E402
 OURS = dict(similarity="ratio", scale="derived3", guard="safe", prestep="slope",
             direction="dissimilar")          # reading (3), CHA 2683 per set
 
@@ -78,7 +80,7 @@ def ch_cost(f, a, b, r):
             x, n, c = impl(f, a, b, XTOL, MAXFEV)
         except Exception:
             continue
-        if c and math.isfinite(float(x)) and abs(float(x) - r) <= ACC:
+        if c and solved(f, float(x)):
             best = int(n) if best is None else min(best, int(n))
     return best
 
@@ -119,7 +121,7 @@ def main():
         r = float(d["root"])
         st = {"trace": []}
         x, n, conv = pure_root(f, a, b, XTOL, MAXFEV, stats=st, **OURS)
-        if not (conv and abs(float(x) - r) <= ACC):
+        if not (conv and solved(f, float(x))):
             continue
         ch = ch_cost(f, a, b, r)
         if ch is None or n <= ch: