Valeri's second point measured: the similarity function belongs to the PLACE it is read in, not to the method. False position's three-century stall is a similarity read at order one on an approach of order m: with sigma = |f(far)| the residual ratio is (e/E)^m, so raising it to the measured 1/m recovers the distance ratio exactly. Paired inside each cell, the correction is cheaper in 7 of 7 safeguards for S = 1/(1+z) - the one function that makes that place exact inverse interpolation - and in only 29 of 60 cells over all nine functions, i.e. a coin. It does NOT beat Chandrupatla (2884 against 2683 and 2423), it HARMS the slope reading (2806 -> 2854), and it does not cure false position: 127/154 and 10676 become 128/154 and 10043, where Illinois buys 153/154 and 7045 with one constant. Estimator bias measured and stated: a pure cube reads 2.830, not 3

Also fixes a real regression from cc2c499: the derived3_cap branch was inserted in front of the derived3_m note and swallowed its division, so derived3_m silently became derived3 (2806 against 2806) and a refutation recorded in the paper stopped being reproducible. The full pin caught it; a cheap pin now guards it too. And \label{sec:method} never existed while the table on page 7 referenced it.

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

verify_article.py

@@ -201,6 +201,7 @@ def main():
         check(f"scale {sc} best", best_by_scale[sc], v)
 
     verify_placement_modes()
+    verify_per_place()
 
     print()
     if FAILS:
@@ -226,6 +227,76 @@ PLACEMENT = {
     "sweep_gate.json":      ("gate.ratio.derived.project",                    4449, 2991),
     "sweep_log.json":       ("log.ratio_soft.derived.safe",                   6940, 3474),
 }
+# The per-place table of section "the similarity function belongs to the place":
+# seven PAIRED comparisons in sweep_order.json.  Checked as pairs, because a pair is
+# what the pre-registration licensed and a single cell would prove nothing.
+ORDER_PAIRS = {
+    # guard      (APS m=1, APS measured, CHA m=1, CHA measured)
+    "both":    (4522, 3675, 3387, 3216),
+    "bracket": (4606, 3542, 3571, 3303),
+    "credit":  (5190, 4686, 3013, 2884),
+    "project": (6932, 6364, 4794, 4559),
+    "safe":    (5987, 5229, 4108, 3923),
+    "step":    (6435, 5551, 4257, 4022),
+    "none":    (10676, 10043, 8265, 7794),
+}
+# the negative item: the order does not cure false position
+ORDER_FALSEPOS = {("rational", "far", "none", "none"): (127, 10676),
+                  ("rational", "far", "none", "order"): (128, 10043)}
+# and the harmful direction, quoted in the same subsection
+ORDER_SLOPE_HARM = {("ratio", "derived3", "none", "none"): 2806,
+                    ("ratio", "derived3", "none", "order"): 2854}
+
+
+def verify_per_place():
+    print("\nThe per-place reading (sweep_order.json):")
+    if not os.path.exists("sweep_order.json"):
+        print("  !!  sweep_order.json absent — section 'belongs to the place' unverifiable")
+        FAILS.append("missing sweep_order.json")
+        return
+    with open("sweep_order.json", encoding="utf8") as fh:
+        rows = json.load(fh)
+
+    def cell(sim, sc, gu, ex):
+        for r in rows:
+            s = r["spec"]
+            if (s[1], s[2], s[3], s[8] if len(s) > 8 else "none") == (sim, sc, gu, ex):
+                return r
+        return None
+
+    cheaper = 0
+    for gu, (a1, a2, c1, c2) in ORDER_PAIRS.items():
+        p = cell("rational", "far", gu, "none")
+        q = cell("rational", "far", gu, "order")
+        if p is None or q is None:
+            FAILS.append(f"order pair {gu} missing from sweep_order.json")
+            print(f"  !!  pair {gu} missing — stale sweep")
+            continue
+        check(f"far+rational {gu} APS m=1", p["APS"]["total"], a1)
+        check(f"far+rational {gu} APS order", q["APS"]["total"], a2)
+        check(f"far+rational {gu} CHA m=1", p["CHA"]["total"], c1)
+        check(f"far+rational {gu} CHA order", q["CHA"]["total"], c2)
+        cheaper += (q["APS"]["total"] + q["CHA"]["total"]
+                    < p["APS"]["total"] + p["CHA"]["total"])
+    check("cheaper in 7 of 7 safeguards", cheaper, 7)
+    for (sim, sc, gu, ex), (solved, total) in ORDER_FALSEPOS.items():
+        r = cell(sim, sc, gu, ex)
+        if r is None:
+            FAILS.append(f"false-position cell {ex} missing")
+            continue
+        check(f"false position {ex} solved", r["APS"]["solved"], solved)
+        check(f"false position {ex} APS", r["APS"]["total"], total)
+    for (sim, sc, gu, ex), want in ORDER_SLOPE_HARM.items():
+        r = cell(sim, sc, gu, ex)
+        if r is None:
+            FAILS.append(f"slope-harm cell {ex} missing")
+            continue
+        check(f"slope reading {ex} APS", r["APS"]["total"], want)
+    fam = [r for r in rows if r["spec"][3] in ("project", "safe", "credit")]
+    check("guarantee family violations", sum(r["APS"]["over"] + r["CHA"]["over"]
+                                            for r in fam), 0)
+
+
 PLACEMENT_PER_SET = {
     "sweep_direction.json": ("CHA", "pure+dissim+slope.ratio.derived3.safe", 2683),
     "sweep_gate.json": ("CHA", "gate.ratio_soft.derived.safe", 2851),