Article: the similarity in the step is earned, not scaffolding; literature in place.

S-ablation of A' (server): A' with each of the nine similarity functions in the step - tent 4443 on the paper protocol (13032 over 855 problems), the nearest other function e^-|z| 4988 (+12%; +9% over six corpora), quadratic ones 18410-18422 (+315%); ranking as the contraction law predicts; guarantee held with every S. The audit of section 7 rerun on the regenerated sweeps (APS unchanged: triple by shape -493 with the tent, +250 with 1/sqrt(1+z^2); defect -283 vs +215).

Text: abstract and section 3 no longer call the similarity scaffolding - the tent making the step Newton's is a property of the similarity chosen; a paragraph in section 7 on the audit; Table 9a; new 8.6 'What is known, and what is new' - Lagouanelle (the order estimate of 7.1 / 10.5), Rall and Hansen-Patrick (8.1), the log-log slope / COC / ACOC (8.2, formula 6), Schroeder and Traub (the split 7 = false position on sign(f)|f|^(1/m)), Brent's acceptance condition (half), Dekker/Brent (tolerance step); what we found no counterpart for is the decision layer by similarity and analogy and the step set by a similarity whose form is decisive. References 13-19. verify_article: Table 9a, the percentages and the audit numbers added; server 446 OK, 0 BAD; regression x2 1226 passed, 0 failed.

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

sweep_full.py

@@ -352,6 +352,14 @@ def build_grid_aprime(smoke):
     return specs
 
 
+def build_grid_aprime_s(smoke):
+    """A' with each of the nine similarity functions in the step (the S-ablation of the
+    proposed method, on the paper's own protocol); the tent ('ratio') row is A' itself."""
+    sims = ["ratio", "sqrt"] if smoke else sorted(PURE_SIMS)
+    return [("pure", s, "derived3", "project", "x", APRIME, "recent", "distance", "none",
+             "pattern") for s in sims]
+
+
 def build_grid_extrap2(smoke):
     """PREREG_extrapolation_gates_2026-09-21: the same cells as build_grid_extrap, every
     one in all five modes (none, A, G1, G2, G3)."""
@@ -534,10 +542,12 @@ def main():
     expmode = "--explimit" in sys.argv     # the translation limit of the analogy, m = inf
     halfmode = "--half" in sys.argv        # the half promised by the step vs the bracket
     apmode = "--aprime" in sys.argv        # the paper's proposed rule A' and its ablations
+    apsmode = "--aprimeS" in sys.argv      # A' with each of the nine S in the step
     combomode = "--combo" in sys.argv      # modes A and B together
     pointsmode = "--points" in sys.argv    # mode A: triple by shape
     dirmode = "--direction" in sys.argv    # mode B: far end by dissimilarity
-    specs = (build_grid_aprime(smoke) if apmode else
+    specs = (build_grid_aprime_s(smoke) if apsmode else
+             build_grid_aprime(smoke) if apmode else
              build_grid_half(smoke) if halfmode else
              build_grid_explimit(smoke) if expmode else
              build_grid_orderpt(smoke) if ptmode else
@@ -576,8 +586,9 @@ def main():
 
     # the published sweep_full.json is what verify_article.py checks the paper
     # against, so the log grid never writes into it
-    if apmode or halfmode or expmode or ptmode or dcmode or memmode or analogmode or judgemode or exitmode or stickmode or creepmode or flat2mode or flatmode or ext2mode or extmode or decmode or ordermode or capmode or combomode or pointsmode or dirmode:
-        base = ("sweep_aprime" if apmode else
+    if apsmode or apmode or halfmode or expmode or ptmode or dcmode or memmode or analogmode or judgemode or exitmode or stickmode or creepmode or flat2mode or flatmode or ext2mode or extmode or decmode or ordermode or capmode or combomode or pointsmode or dirmode:
+        base = ("sweep_aprime_s" if apsmode else
+                "sweep_aprime" if apmode else
                 "sweep_half" if halfmode else
                 "sweep_explimit" if expmode else
                 "sweep_orderpt" if ptmode else