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>

report_uniform.py

@@ -0,0 +1,84 @@
+"""The protocol tables under the single criterion of sweep_uniform.json (revision point 3), next
+to the numbers the paper printed under the published-root criterion.
+
+    python -u report_uniform.py
+"""
+from __future__ import annotations
+
+import json
+
+from rescore_uniform import load_uniform
+
+APRIME = "pure+extP+contra+flatanalogmempt+exp+half+close+sub.ratio.derived3"
+
+
+def rows(path):
+    return {r["label"]: r for r in load_uniform(path)}
+
+
+def old(path):
+    with open(path, encoding="utf8") as fh:
+        return {r["label"]: r for r in json.load(fh)}
+
+
+def cost(v):
+    return v[0] if v[1] else 200
+
+
+def wtl(a, b, s):
+    ps = list(a[s]["per"])
+    w = sum(cost(a[s]["per"][p]) < cost(b[s]["per"][p]) for p in ps)
+    l = sum(cost(a[s]["per"][p]) > cost(b[s]["per"][p]) for p in ps)
+    return w, len(ps) - w - l, l
+
+
+def rank(R, s):
+    return sorted(R.values(), key=lambda r: (r[s]["n"] - r[s]["solved"], r[s]["total"]))
+
+
+def main():
+    U, O = rows("sweep_full.json"), old("sweep_full.json")
+    for s in ("APS", "CHA"):
+        print(f"\n== {s}: top 12 of {len(U)} under the single criterion (old total in brackets)")
+        for i, r in enumerate(rank(U, s)[:12], 1):
+            lb = r["label"]
+            print(f"  {i:2d}. {lb:<34} solved {r[s]['solved']:3d}/{r[s]['n']}  total {r[s]['total']:5d}"
+                  f"  ({O[lb][s]['total']})  over {r[s]['over']}")
+        pos = {r["label"]: i for i, r in enumerate(rank(U, s), 1)}
+        for lb in ("pure.ratio.derived3.project", "chandrupatla", "toms748", "brent",
+                   "itp_oracle", "itp", "bisection"):
+            print(f"     place {pos[lb]:3d}: {lb:<30} {U[lb][s]['total']:5d} ({O[lb][s]['total']})"
+                  f"  solved {U[lb][s]['solved']}")
+    base, ch = U["pure.ratio.derived3.project"], U["chandrupatla"]
+    print("\nbase rule vs Chandrupatla, failures charged:",
+          {s: wtl(base, ch, s) for s in ("APS", "CHA")})
+    A = rows("sweep_aprime.json")
+    ap = A[f"{APRIME}.project"]
+    print(f"\nTable 8 under the single criterion: A' {ap['APS']['total']} / {ap['CHA']['total']}"
+          f"  earned {A[APRIME + '.credit']['APS']['total']} / {A[APRIME + '.credit']['CHA']['total']}")
+    for opp in ("chandrupatla", "toms748", "brent", "itp_oracle", "itp", "bisection"):
+        o = U[opp]
+        print(f"  {opp:<14} {o['APS']['total']:5d} {o['CHA']['total']:5d}  "
+              f"A' vs: APS {wtl(ap, o, 'APS')}  CHA {wtl(ap, o, 'CHA')}")
+    print("\nTable 5 cells (single criterion / old):")
+    for path, lb in (("sweep_full.json", "pure.ratio.derived3.credit"),
+                     ("sweep_slope.json", "slope.ratio.derived3.project"),
+                     ("sweep_points.json", "pure+shape+slope.ratio.derived3.safe"),
+                     ("sweep_direction.json", "pure+dissim+slope.ratio.derived3.project"),
+                     ("sweep_combo.json", "pure+shape+dissim+slope.ratio.derived3.safe")):
+        try:
+            r, o = rows(path)[lb], old(path)[lb]
+            print(f"  {lb:<46} {r['APS']['total']:5d} {r['CHA']['total']:5d}   "
+                  f"({o['APS']['total']} {o['CHA']['total']})  over {r['APS']['over'] + r['CHA']['over']}")
+        except KeyError:
+            print(f"  {lb}: label not in {path}")
+    S = rows("sweep_aprime_s.json")
+    print("\nTable 9a protocol column (single criterion / old):")
+    So = old("sweep_aprime_s.json")
+    for lb, r in S.items():
+        print(f"  {r['spec'][1]:<11} {r['APS']['total'] + r['CHA']['total']:6d} "
+              f"({So[lb]['APS']['total'] + So[lb]['CHA']['total']})")
+
+
+if __name__ == "__main__":
+    main()