Valeri's objection measured: the principle is right (a similarity step should be large far away and small near), and our sigma = |f'|D defeats it — at x=1e4 on a 2e4 bracket the normalised residual is 0.167, so S=0.833 'similar' and the step is small five thousand step-lengths from the root. Selecting sigma = min(|f'|D, max|f| at the ends) — no new constant — improves 403 to 390 on eight hand-picked wide problems but is WORSE over the grid: APS 3288 vs 2726, CHA 3111 vs 2683, so the mode is rejected by its pre-registered rule. Its extra solves are two fun7 problems landing inside the flat zero region, i.e. the scoring artefact and not a capability. Written into Negative results as the answer to the natural objection

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

sweep_full.py

@@ -198,6 +198,15 @@ def build_grid_log(smoke):
             for sim in sims for sc in ("derived", "derived3") for gu in guards]
 
 
+def build_grid_cap(smoke):
+    """Scale as a SELECTION between the two computed ones (PREREG 2026-09-21): identical to
+    the slope+dissimilar configuration except scale = derived3_cap, so one thing changes."""
+    sims = ["ratio", "sqrt"] if smoke else sorted(PURE_SIMS)
+    guards = ("credit", "safe") if smoke else GUARD_MODES
+    return [("pure", sim, "derived3_cap", gu, "x", "slope", "recent", "dissimilar")
+            for sim in sims for gu in guards]
+
+
 def build_grid_combo(smoke):
     """A+B together (PREREG 2026-09-21 §2: licensed only because each mode alone improved
     APS — A 2527 and B 2726 against the published 2806)."""
@@ -264,10 +273,12 @@ def main():
     logmode = "--log" in sys.argv          # the u-space grid, written to its OWN file
     gatemode = "--gate" in sys.argv        # the pre-step gate grid, likewise
     slopemode = "--slope" in sys.argv      # the slope-stability gate grid
+    capmode = "--cap" in sys.argv          # scale selected between the two computed ones
     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_combo(smoke) if combomode else
+    specs = (build_grid_cap(smoke) if capmode else
+             build_grid_combo(smoke) if combomode else
              build_grid_points(smoke) if pointsmode else
              build_grid_direction(smoke) if dirmode else
              build_grid_slope(smoke) if slopemode else
@@ -288,8 +299,9 @@ 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 combomode or pointsmode or dirmode:
-        base = ("sweep_combo" if combomode else
+    if capmode or combomode or pointsmode or dirmode:
+        base = ("sweep_cap" if capmode else
+                "sweep_combo" if combomode else
                 "sweep_points" if pointsmode else "sweep_direction")
         out = f"{base}_smoke.json" if smoke else f"{base}.json"
         with open(out, "w", encoding="utf8") as fh: