diff --git a/results_estimated.txt b/results_estimated.txt
new file mode 100644
index 0000000..18aaaee
--- /dev/null
+++ b/results_estimated.txt
@@ -0,0 +1,23 @@
+E1 - corpus 4 (decisive): K3 total vs A' total; A' w/t/l against K3, p
+  k3_lag: 7526 vs A' 3656   A' 199/24/17 p=1.5e-40  -> stands
+  k3_analogy: 3806 vs A' 3656   A' 126/38/76 p=0.00053  -> stands
+  outcome for the claim of 6.6: stands
+
+E2 - six corpora totals (violations of the 2x bound in brackets)
+  K3L              APS 7215(0) CHA 2188(0) NEW 6618(0) RJL 3167(0) APP 4277(0) D 7526(0)  | all 30991
+  K3A              APS 3453(0) CHA 952(0) NEW 4433(0) RJL 1416(0) APP 1673(0) D 3806(0)  | all 15733
+  A'               APS 2259 CHA 1074 NEW 3290 RJL 1371 APP 1382 D 3656  | all 13032
+  Chandrupatla(f)  APS 2595 CHA 1505 NEW 3716 RJL 1566 APP 1382 D 5717  | all 16481
+
+E3 - multiple/fractional roots (group of Table 11): K3L / K3A / A' / oracle (Chandrupatla on g)
+  CHA: n=20  k3_lag 1062 (closes -73% of A'->oracle)  k3_analogy 322 (closes +59% of A'->oracle)  A' 654  oracle 96
+  NEW: n=40  k3_lag 1699 (closes -54% of A'->oracle)  k3_analogy 721 (closes +58% of A'->oracle)  A' 1229  oracle 358
+  D: n=88  k3_lag 3280 (closes -89% of A'->oracle)  k3_analogy 1766 (closes +31% of A'->oracle)  A' 2159  oracle 901
+
+E4 - the other problems: K3 against Chandrupatla on f (cost of false readings)
+  CHA: k3_lag 1126  k3_analogy 630  Chandrupatla(f) 437  A' 420
+  NEW: k3_lag 4919  k3_analogy 3712  Chandrupatla(f) 1924  A' 2061
+  D: k3_lag 4246  k3_analogy 2040  Chandrupatla(f) 1566  A' 1497
+  k3_lag vs Chandrupatla(f), APS: 7215 vs 2595
+  k3_analogy vs Chandrupatla(f), APS: 3453 vs 2595
+estimated done
diff --git a/simroot/transformed.py b/simroot/transformed.py
new file mode 100644
index 0000000..54be67b
--- /dev/null
+++ b/simroot/transformed.py
@@ -0,0 +1,113 @@
+"""PREREG_estimated_transform_2026-09-22 (control K3): Chandrupatla's method on
+g = sign(f)|f|^(1/m_hat), with m_hat estimated during the run.
+
+The solver is simroot.baselines.chandrupatla line for line (it matches scipy's
+elementwise.find_root on all 199 problems); it keeps the TRUE values of f at its three points, so
+signs, the best point and the stopping rule are those of f, and only the acceptance band's
+(xi, phi) and the inverse quadratic interpolation read G(v) = sign(v)|v|^(1/m_hat), recomputed
+from the stored f whenever m_hat changes - no extra evaluation.  m_hat starts at 1 and is
+replaced by an order read from the last three evaluations only when it lies on a branch of
+section 6.1 (m >= 2 or 0 < m <= 2/3); there is no reset.  With estimator="none" the method is
+the original, bit for bit (tested).
+"""
+from __future__ import annotations
+
+import math
+
+from .baselines import Counter, _Budget
+from .pure import _analogy_order, _config3, _lagouanelle_raw
+
+ESTIMATORS = ("none", "lag", "analogy")
+
+
+def _G(v, inv):
+    if inv == 1.0:
+        return v
+    if v == 0.0:
+        return 0.0
+    try:
+        return math.copysign(abs(v) ** inv, v)
+    except OverflowError:
+        # 1/m_hat > 1 on the fractional branch: a huge |f| overflows; the interpolation that
+        # reads it is then not finite and the step halves, as the method does for any such t
+        return math.copysign(math.inf, v)
+
+
+def chandrupatla_transformed(f, a, b, xtol, maxfev, estimator="none", stats=None):
+    if estimator not in ESTIMATORS:
+        raise ValueError(f"unknown estimator {estimator!r}")
+    g = Counter(f, maxfev)
+    x1, x2 = b, a
+    f1 = f2 = 0.0
+    m_hat = 1.0
+    hist = []             # evaluations in order: (x, f)
+    configs = []          # analogy memory (estimator "analogy")
+
+    def observe(x, fx):
+        nonlocal m_hat
+        hist.append((x, fx))
+        if estimator == "none" or len(hist) < 3:
+            return
+        (xp2, fp2), (xp, fp), (xc, fc) = hist[-3], hist[-2], hist[-1]
+        if estimator == "lag":
+            m = _lagouanelle_raw(xc, fc, xp, fp, xp2, fp2)
+        else:
+            cur = _config3(xc, fc, xp, fp, xp2, fp2)
+            m = _analogy_order(cur, configs, translation=True)
+            if cur is not None:
+                configs.append(cur)
+        if m is not None and (m >= 2.0 or 0.0 < m <= 2.0 / 3.0):
+            if stats is not None and m != m_hat:
+                stats["updates"] = stats.get("updates", 0) + 1
+            m_hat = m
+            if stats is not None:
+                stats["m_hat"] = m_hat      # diagnostic only: the order last held
+
+    try:
+        f1 = g(x1)
+        observe(x1, f1)
+        f2 = g(x2)
+        observe(x2, f2)
+        if f1 == 0.0:
+            return x1, g.n, True
+        if f2 == 0.0:
+            return x2, g.n, True
+        x3, f3 = x2, f2
+        t = 0.5
+        while True:
+            x = x1 + t * (x2 - x1)
+            fx = g(x)
+            observe(x, fx)
+            if (fx > 0.0) == (f1 > 0.0):
+                x3, f3 = x1, f1
+                x1, f1 = x, fx
+            else:
+                x3, f3 = x2, f2
+                x2, f2 = x1, f1
+                x1, f1 = x, fx
+            xm, fm = (x1, f1) if abs(f1) < abs(f2) else (x2, f2)
+            if fm == 0.0:
+                return xm, g.n, True
+            tol = 2.0 * 2.22e-16 * abs(xm) + 0.5 * xtol
+            span = abs(x2 - x1)
+            if span == 0.0:
+                return xm, g.n, True
+            tl = tol / span
+            if tl > 0.5:
+                return xm, g.n, True
+            inv = 0.0 if math.isinf(m_hat) else 1.0 / m_hat
+            G1, G2, G3 = _G(f1, inv), _G(f2, inv), _G(f3, inv)
+            t = 0.5
+            if x3 != x2 and G3 != G2:
+                xi = (x1 - x2) / (x3 - x2)
+                ph = (G1 - G2) / (G3 - G2)
+                if 0.0 < xi < 1.0 and 1.0 - math.sqrt(1.0 - xi) < ph < math.sqrt(xi):
+                    d1, d2, d3 = G1 - G2, G1 - G3, G2 - G3
+                    if d1 != 0.0 and d2 != 0.0 and d3 != 0.0:
+                        t = (G1 / d1) * (G3 / (-d3)) + \
+                            ((x3 - x1) / (x2 - x1)) * (G1 / d2) * (G2 / d3)
+            if not math.isfinite(t):
+                t = 0.5
+            t = min(max(t, tl), 1.0 - tl)
+    except _Budget:
+        return (x1 if abs(f1) < abs(f2) else x2), g.n, False
diff --git a/sweep_estimated.json b/sweep_estimated.json
new file mode 100644
index 0000000..7d54a83
--- /dev/null
+++ b/sweep_estimated.json
@@ -0,0 +1 @@
+{"k3_lag": {"APS": {"aps.01.00": [9, true, false], "aps.02.00": [11, true, false], "aps.02.01": [46, true, false], "aps.02.02": [11, true, false], "aps.02.03": [11, true, false], "aps.02.04": [12, true, false], "aps.02.05": [47, true, false], "aps.02.06": [47, true, false], "aps.02.07": [47, true, false], "aps.02.08": [48, true, false], "aps.02.09": [48, true, false], "aps.03.00": [59, true, false], "aps.03.01": [16, true, false], "aps.03.02": [16, true, false], "aps.04.00": [13, true, false], "aps.04.01": [53, true, false], "aps.04.02": [14, true, false], "aps.04.03": [72, true, false], "aps.04.04": [54, true, false], "aps.04.05": [53, true, false], "aps.04.06": [12, true, false], "aps.04.07": [13, true, false], "aps.04.08": [13, true, false], "aps.04.09": [13, true, false], "aps.04.10": [12, true, false], "aps.04.11": [12, true, false], "aps.04.12": [50, true, false], "aps.04.13": [51, true, false], "aps.05.00": [8, true, false], "aps.06.00": [8, true, false], "aps.06.01": [9, true, false], "aps.06.02": [58, true, false], "aps.06.03": [48, true, false], "aps.06.04": [80, true, false], "aps.06.05": [47, true, false], "aps.06.06": [46, true, false], "aps.06.07": [47, true, false], "aps.06.08": [47, true, false], "aps.06.09": [74, true, false], "aps.07.00": [49, true, false], "aps.07.01": [48, true, false], "aps.07.02": [44, true, false], "aps.08.00": [3, true, false], "aps.08.01": [9, true, false], "aps.08.02": [11, true, false], "aps.08.03": [81, true, false], "aps.08.04": [75, true, false], "aps.09.00": [9, true, false], "aps.09.01": [46, true, false], "aps.09.02": [42, true, false], "aps.09.03": [42, true, false], "aps.09.04": [42, true, false], "aps.09.05": [42, true, false], "aps.09.06": [42, true, false], "aps.10.00": [8, true, false], "aps.10.01": [11, true, false], "aps.10.02": [43, true, false], "aps.10.03": [50, true, false], "aps.10.04": [44, true, false], "aps.11.00": [9, true, false], "aps.11.01": [10, true, false], "aps.11.02": [55, true, false], "aps.11.03": [50, true, false], "aps.12.00": [61, true, false], "aps.12.01": [66, true, false], "aps.12.02": [53, true, false], "aps.12.03": [59, true, false], "aps.12.04": [56, true, false], "aps.12.05": [59, true, false], "aps.12.06": [61, true, false], "aps.12.07": [61, true, false], "aps.12.08": [59, true, false], "aps.12.09": [69, true, false], "aps.12.10": [72, true, false], "aps.12.11": [92, true, false], "aps.12.12": [91, true, false], "aps.12.13": [10, true, false], "aps.12.14": [10, true, false], "aps.12.15": [9, true, false], "aps.12.16": [9, true, false], "aps.12.17": [9, true, false], "aps.12.18": [9, true, false], "aps.13.00": [8, true, false], "aps.14.00": [57, true, false], "aps.14.01": [57, true, false], "aps.14.02": [57, true, false], "aps.14.03": [57, true, false], "aps.14.04": [57, true, false], "aps.14.05": [57, true, false], "aps.14.06": [57, true, false], "aps.14.07": [57, true, false], "aps.14.08": [57, true, false], "aps.14.09": [57, true, false], "aps.14.10": [57, true, false], "aps.14.11": [57, true, false], "aps.14.12": [57, true, false], "aps.14.13": [57, true, false], "aps.14.14": [57, true, false], "aps.14.15": [57, true, false], "aps.14.16": [57, true, false], "aps.14.17": [57, true, false], "aps.14.18": [57, true, false], "aps.14.19": [57, true, false], "aps.14.20": [57, true, false], "aps.14.21": [57, true, false], "aps.14.22": [57, true, false], "aps.14.23": [57, true, false], "aps.14.24": [57, true, false], "aps.14.25": [57, true, false], "aps.14.26": [57, true, false], "aps.14.27": [57, true, false], "aps.14.28": [57, true, false], "aps.14.29": [57, true, false], "aps.14.30": [57, true, false], "aps.14.31": [57, true, false], "aps.14.32": [57, true, false], "aps.14.33": [57, true, false], "aps.14.34": [57, true, false], "aps.14.35": [57, true, false], "aps.14.36": [57, true, false], "aps.14.37": [57, true, false], "aps.14.38": [57, true, false], "aps.14.39": [57, true, false], "aps.15.00": [51, true, false], "aps.15.01": [56, true, false], "aps.15.02": [58, true, false], "aps.15.03": [58, true, false], "aps.15.04": [56, true, false], "aps.15.05": [56, true, false], "aps.15.06": [57, true, false], "aps.15.07": [56, true, false], "aps.15.08": [50, true, false], "aps.15.09": [56, true, false], "aps.15.10": [63, true, false], "aps.15.11": [60, true, false], "aps.15.12": [60, true, false], "aps.15.13": [62, true, false], "aps.15.14": [65, true, false], "aps.15.15": [60, true, false], "aps.15.16": [61, true, false], "aps.15.17": [63, true, false], "aps.15.18": [62, true, false], "aps.15.19": [60, true, false], "aps.15.20": [62, true, false], "aps.15.21": [56, true, false], "aps.15.22": [66, true, false], "aps.15.23": [56, true, false], "aps.15.24": [62, true, false], "aps.15.25": [60, true, false], "aps.15.26": [56, true, false], "aps.15.27": [56, true, false], "aps.15.28": [56, true, false], "aps.15.29": [55, true, false], "aps.15.30": [57, true, false]}, "CHA": {"fun1.1": [8, true, false], "fun1.2": [48, true, false], "fun1.3": [58, true, false], "fun1.4": [59, true, false], "fun1.5": [130, true, false], "fun2.1": [9, true, false], "fun2.2": [64, true, false], "fun2.3": [70, true, false], "fun2.4": [83, true, false], "fun2.5": [93, true, false], "fun3.1": [45, true, false], "fun3.2": [47, true, false], "fun3.3": [58, true, false], "fun3.4": [45, true, false], "fun3.5": [93, true, false], "fun4.1": [45, true, false], "fun4.2": [47, true, false], "fun4.3": [56, true, false], "fun4.4": [65, true, false], "fun4.5": [95, true, false], "fun5.1": [45, true, false], "fun5.2": [45, true, false], "fun5.3": [46, true, false], "fun5.4": [48, true, false], "fun5.5": [49, true, false], "fun6.1": [45, true, false], "fun6.2": [45, true, false], "fun6.3": [46, true, false], "fun6.4": [48, true, false], "fun6.5": [49, true, false], "fun7.1": [8, true, false], "fun7.2": [8, true, false], "fun7.3": [11, true, false], "fun7.4": [18, true, false], "fun7.5": [19, true, false], "fun8.1": [83, true, false], "fun8.2": [11, true, false], "fun8.3": [13, true, false], "fun8.4": [84, true, false], "fun8.5": [85, true, false], "fun9.1": [8, true, false], "fun9.2": [9, true, false], "fun9.3": [69, true, false], "fun9.4": [64, true, false], "fun9.5": [14, true, false]}, "NEW": {"C0.00": [54, true, false], "C0.01": [8, true, false], "C0.02": [9, true, false], "C0.03": [43, true, false], "C0.04": [43, true, false], "C0.05": [45, true, false], "C1.00": [47, true, false], "C1.01": [9, true, false], "C1.02": [50, true, false], "C1.03": [55, true, false], "C1.04": [12, true, false], "C1.05": [90, true, false], "C1.06": [8, true, false], "C1.07": [55, true, false], "C1.08": [7, true, false], "C1.09": [53, true, false], "C1.10": [9, true, false], "C1.11": [50, true, false], "C1.12": [49, true, false], "C1.13": [7, true, false], "C1.14": [10, true, false], "C1.15": [9, true, false], "C1.16": [14, true, false], "C1.17": [62, true, false], "C1.18": [15, true, false], "C1.19": [49, true, false], "C1.20": [16, true, false], "C1.21": [7, true, false], "C1.22": [46, true, false], "C1.23": [7, true, false], "C1.24": [10, true, false], "C1.25": [41, true, false], "C1.26": [55, true, false], "C1.27": [85, true, false], "C1.28": [46, true, false], "C1.29": [45, true, false], "C1.30": [10, true, false], "C1.31": [8, true, false], "C1.32": [56, true, false], "C1.33": [45, true, false], "C1.34": [85, true, false], "C1.35": [68, true, false], "C1.36": [50, true, false], "C1.37": [7, true, false], "C1.38": [10, true, false], "C1.39": [49, true, false], "C2.00": [13, true, false], "C2.01": [8, true, false], "C2.02": [50, true, false], "C2.03": [9, true, false], "C2.04": [61, true, false], "C2.05": [7, true, false], "C2.06": [7, true, false], "C2.07": [61, true, false], "C2.08": [64, true, false], "C2.09": [8, true, false], "C2.10": [66, true, false], "C2.11": [8, true, false], "C2.12": [61, true, false], "C2.13": [10, true, false], "C2.14": [8, true, false], "C2.15": [7, true, false], "C2.16": [6, true, false], "C2.17": [11, true, false], "C2.18": [10, true, false], "C2.19": [49, true, false], "C2.20": [68, true, false], "C2.21": [63, true, false], "C2.22": [60, true, false], "C2.23": [41, true, false], "C2.24": [64, true, false], "C2.25": [8, true, false], "C2.26": [62, true, false], "C2.27": [60, true, false], "C2.28": [7, true, false], "C2.29": [9, true, false], "C2.30": [8, true, false], "C2.31": [15, true, false], "C2.32": [57, true, false], "C2.33": [53, true, false], "C2.34": [68, true, false], "C2.35": [9, true, false], "C2.36": [7, true, false], "C2.37": [9, true, false], "C2.38": [10, true, false], "C2.39": [62, true, false], "C3.00": [42, true, false], "C3.01": [48, true, false], "C3.02": [41, true, false], "C3.03": [18, true, false], "C3.04": [40, true, false], "C3.05": [63, true, false], "C3.06": [43, true, false], "C3.07": [48, true, false], "C3.08": [46, true, false], "C3.09": [44, true, false], "C3.10": [46, true, false], "C3.11": [46, true, false], "C3.12": [37, 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"f90": [12, true, false], "f91": [10, true, false]}, "APP": {"G.sin[3,4]": [8, true, false], "G.sin[-4,-3]": [8, true, false], "G.sin[-1/3,1]": [9, true, false], "G.cos[0,3]": [9, true, false], "G.cos[-3,0]": [9, true, false], "G.x^20-1": [43, true, false], "G.sqrt|x|sgn": [4, true, false], "G.x^2-1e-8": [28, true, false], "G.x*exp(-x)": [10, true, false], "G.(x-1)^7": [7, true, false], "P.kepler.e0.1.M0.001": [6, true, false], "P.kepler.e0.1.M0.01": [7, true, false], "P.kepler.e0.1.M0.1": [7, true, false], "P.kepler.e0.1.M0.5": [7, true, false], "P.kepler.e0.1.M1.0": [7, true, false], "P.kepler.e0.1.M2.0": [7, true, false], "P.kepler.e0.1.M3.0": [8, true, false], "P.kepler.e0.5.M0.001": [7, true, false], "P.kepler.e0.5.M0.01": [8, true, false], "P.kepler.e0.5.M0.1": [8, true, false], "P.kepler.e0.5.M0.5": [9, true, false], "P.kepler.e0.5.M1.0": [8, true, false], "P.kepler.e0.5.M2.0": [9, true, false], "P.kepler.e0.5.M3.0": [8, true, false], "P.kepler.e0.9.M0.001": [10, true, false], "P.kepler.e0.9.M0.01": [11, true, false], "P.kepler.e0.9.M0.1": [11, true, false], "P.kepler.e0.9.M0.5": [11, true, false], "P.kepler.e0.9.M1.0": [10, true, false], "P.kepler.e0.9.M2.0": [9, true, false], "P.kepler.e0.9.M3.0": [9, true, false], "P.kepler.e0.99.M0.001": [45, true, false], "P.kepler.e0.99.M0.01": [39, true, false], "P.kepler.e0.99.M0.1": [11, true, false], "P.kepler.e0.99.M0.5": [11, true, false], "P.kepler.e0.99.M1.0": [9, true, false], "P.kepler.e0.99.M2.0": [9, true, false], "P.kepler.e0.99.M3.0": [9, true, false], "P.kepler.e0.999.M0.001": [43, true, false], "P.kepler.e0.999.M0.01": [42, true, false], "P.kepler.e0.999.M0.1": [11, true, false], "P.kepler.e0.999.M0.5": [10, true, false], "P.kepler.e0.999.M1.0": [9, true, false], "P.kepler.e0.999.M2.0": [9, true, false], "P.kepler.e0.999.M3.0": [9, true, false], "P.colebrook.Re4e+03.e0.0": [10, true, false], "P.colebrook.Re4e+03.e1e-06": [11, true, false], "P.colebrook.Re4e+03.e0.0001": [10, true, false], "P.colebrook.Re4e+03.e0.001": [10, true, false], "P.colebrook.Re4e+03.e0.01": [10, true, false], "P.colebrook.Re4e+03.e0.05": [10, true, false], "P.colebrook.Re1e+04.e0.0": [11, true, false], "P.colebrook.Re1e+04.e1e-06": [11, true, false], "P.colebrook.Re1e+04.e0.0001": [11, true, false], "P.colebrook.Re1e+04.e0.001": [11, true, false], "P.colebrook.Re1e+04.e0.01": [11, true, false], "P.colebrook.Re1e+04.e0.05": [10, true, false], "P.colebrook.Re1e+05.e0.0": [12, true, false], "P.colebrook.Re1e+05.e1e-06": [12, true, false], "P.colebrook.Re1e+05.e0.0001": [12, true, false], "P.colebrook.Re1e+05.e0.001": [12, true, false], "P.colebrook.Re1e+05.e0.01": [10, true, false], "P.colebrook.Re1e+05.e0.05": [10, true, false], "P.colebrook.Re1e+06.e0.0": [13, true, false], "P.colebrook.Re1e+06.e1e-06": [13, true, false], "P.colebrook.Re1e+06.e0.0001": [11, true, false], "P.colebrook.Re1e+06.e0.001": [11, true, false], "P.colebrook.Re1e+06.e0.01": [10, true, false], "P.colebrook.Re1e+06.e0.05": [10, true, false], "P.colebrook.Re1e+07.e0.0": [13, true, false], "P.colebrook.Re1e+07.e1e-06": [13, true, false], "P.colebrook.Re1e+07.e0.0001": [13, true, false], "P.colebrook.Re1e+07.e0.001": [10, true, false], "P.colebrook.Re1e+07.e0.01": [10, true, false], "P.colebrook.Re1e+07.e0.05": [10, true, false], "P.colebrook.Re1e+08.e0.0": [13, true, false], "P.colebrook.Re1e+08.e1e-06": [13, true, false], "P.colebrook.Re1e+08.e0.0001": [12, true, false], "P.colebrook.Re1e+08.e0.001": [11, true, false], "P.colebrook.Re1e+08.e0.01": [10, true, false], "P.colebrook.Re1e+08.e0.05": [10, true, false], "P.lambert.y1e-06": [6, true, false], "P.lambert.y0.001": [7, true, false], "P.lambert.y0.1": [9, true, false], "P.lambert.y1.0": [9, true, false], "P.lambert.y10.0": [10, true, false], "P.lambert.y1000.0": [12, true, false], "P.lambert.y1000000.0": [12, true, false], "P.planck.n2": [10, true, false], "P.planck.n3": [10, true, false], "P.planck.n4": [10, true, false], "P.planck.n5": [10, true, false], "P.planck.n6": [10, true, false], "P.planck.n8": [9, true, false], "P.planck.n10": [9, true, false], "P.vdw.T280.P1": [7, true, false], "P.vdw.T280.P10": [8, true, false], "P.vdw.T280.P40": [12, true, false], "P.vdw.T280.P73": [13, true, false], "P.vdw.T280.P100": [44, true, false], "P.vdw.T304.P1": [7, true, false], "P.vdw.T304.P10": [8, true, false], "P.vdw.T304.P40": [10, true, false], "P.vdw.T304.P73": [13, true, false], "P.vdw.T304.P100": [13, true, false], "P.vdw.T350.P1": [6, true, false], "P.vdw.T350.P10": [8, true, false], "P.vdw.T350.P40": [9, true, false], "P.vdw.T350.P73": [12, true, false], "P.vdw.T350.P100": [11, true, false], "P.vdw.T500.P1": [6, true, false], "P.vdw.T500.P10": [7, true, false], "P.vdw.T500.P40": [8, true, false], "P.vdw.T500.P73": [9, true, false], "P.vdw.T500.P100": [10, true, false], "P.irr.c5.n5": [14, true, false], "P.irr.c5.n10": [15, true, false], "P.irr.c5.n30": [45, true, false], "P.irr.c10.n5": [14, true, false], "P.irr.c10.n10": [14, true, false], "P.irr.c10.n30": [45, true, false], "P.irr.c20.n5": [12, true, false], "P.irr.c20.n10": [14, true, false], "P.irr.c20.n30": [52, true, false], "P.irr.c50.n5": [13, true, false], "P.irr.c50.n10": [13, true, false], "P.irr.c50.n30": [46, true, false], "P.well.z01": [8, true, false], "P.well.z03": [9, true, false], "P.well.z05": [9, true, false], "P.well.z010": [9, true, false], "P.well.z020": [9, true, false]}, "D": {"D1.00": [46, true, false], "D1.01": [46, true, false], "D1.02": [8, true, false], "D1.03": [44, true, false], "D1.04": [7, true, false], "D1.05": [10, true, false], "D1.06": [10, true, false], "D1.07": [12, true, false], "D1.08": [9, true, false], "D1.09": [10, true, false], "D1.10": [10, true, false], "D1.11": [47, true, false], "D1.12": [15, true, false], "D1.13": [12, true, false], "D1.14": [8, true, false], "D1.15": [7, true, false], "D1.16": [9, true, false], "D1.17": [47, true, false], "D1.18": [15, true, false], "D1.19": [10, true, false], "D1.20": [8, true, false], "D1.21": [7, true, false], "D1.22": [7, true, false], "D1.23": [9, true, false], "D1.24": [9, true, false], "D1.25": [9, true, false], "D1.26": [8, true, false], "D1.27": [12, true, false], "D1.28": [10, true, false], "D1.29": [8, true, false], "D1.30": [7, true, false], "D1.31": [9, true, false], "D1.32": [12, true, false], "D1.33": [11, true, false], "D1.34": [49, true, false], "D1.35": [11, true, false], "D1.36": [10, true, false], "D1.37": [9, true, false], "D1.38": [44, true, false], "D1.39": [8, true, false], "D2.00": [22, true, false], "D2.01": [21, true, false], "D2.02": [20, true, false], "D2.03": [18, true, false], "D2.04": [17, true, false], "D2.05": [19, true, false], "D2.06": [20, true, false], "D2.07": [22, true, false], "D2.08": [19, true, false], "D2.09": [19, true, false], "D2.10": [16, true, false], "D2.11": [18, true, false], "D2.12": [16, true, false], "D2.13": [16, true, false], "D2.14": [18, true, false], "D2.15": [13, true, false], "D2.16": [17, true, false], "D2.17": [20, true, false], "D2.18": [18, true, false], "D2.19": [16, true, false], "D2.20": [16, true, false], "D2.21": [16, true, false], "D2.22": [16, true, false], "D2.23": [21, true, false], "D2.24": [19, true, false], "D2.25": [20, true, false], "D2.26": [21, true, false], "D2.27": [20, true, false], "D2.28": [18, true, false], "D2.29": [17, true, false], "D2.30": [17, true, false], "D2.31": [21, true, false], "D2.32": [17, true, false], "D2.33": [14, true, false], "D2.34": [18, true, false], "D2.35": [21, true, false], "D2.36": [17, true, false], "D2.37": [15, true, false], "D2.38": [19, true, false], "D2.39": [16, true, false], "D3.00": [24, true, false], "D3.01": [16, true, false], "D3.02": [22, true, false], "D3.03": [22, true, false], "D3.04": [16, true, false], "D3.05": [38, true, false], "D3.06": [23, true, false], "D3.07": [15, true, false], "D3.08": [23, true, false], "D3.09": [21, true, false], "D3.10": [27, true, false], "D3.11": [24, true, false], "D3.12": [16, true, false], "D3.13": [35, true, false], "D3.14": [31, true, false], "D3.15": [45, true, false], "D3.16": [21, true, false], "D3.17": [17, true, false], "D3.18": [30, true, false], "D3.19": [19, true, false], "D3.20": [23, true, false], "D3.21": [22, true, false], "D3.22": [34, true, false], "D3.23": [22, true, false], "D3.24": [21, true, false], "D3.25": [20, true, false], "D3.26": [24, true, false], "D3.27": [17, true, false], "D3.28": [26, true, false], "D3.29": [24, true, false], "D3.30": [29, true, false], "D3.31": [30, true, false], "D3.32": [20, true, false], "D3.33": [19, true, false], "D3.34": [19, true, false], "D3.35": [23, true, false], "D3.36": [31, true, false], "D3.37": [17, true, false], "D3.38": [21, true, false], "D3.39": [12, true, false], "D4.00": [10, true, false], "D4.01": [7, true, false], "D4.02": [7, true, false], "D4.03": [8, true, false], "D4.04": [8, true, false], "D4.05": [8, true, false], "D4.06": [10, true, false], "D4.07": [7, true, false], "D4.08": [8, true, false], "D4.09": [10, true, false], "D4.10": [9, true, false], "D4.11": [8, true, false], "D4.12": [9, true, false], "D4.13": [7, true, false], "D4.14": [10, true, false], "D4.15": [9, true, false], "D4.16": [13, true, false], "D4.17": [7, true, false], "D4.18": [8, true, false], "D4.19": [8, true, false], "D4.20": [9, true, false], "D4.21": [6, true, false], "D4.22": [9, true, false], "D4.23": [9, true, false], "D4.24": [8, true, false], "D4.25": [7, true, false], "D4.26": [6, true, false], "D4.27": [8, true, false], "D4.28": [8, true, false], "D4.29": [9, true, false], "D4.30": [7, true, false], "D4.31": [7, true, false], "D4.32": [7, true, false], "D4.33": [8, true, false], "D4.34": [10, true, false], "D4.35": [7, true, false], "D4.36": [9, true, false], "D4.37": [6, true, false], "D4.38": [8, true, false], "D4.39": [9, true, false], "D5.00": [8, true, false], "D5.01": [8, true, false], "D5.02": [21, true, false], "D5.03": [21, true, false], "D5.04": [8, true, false], "D5.05": [20, true, false], "D5.06": [21, true, false], "D5.07": [21, true, false], "D5.08": [12, true, false], "D5.09": [31, true, false], "D5.10": [9, true, false], "D5.11": [15, true, false], "D5.12": [10, true, false], "D5.13": [9, true, false], "D5.14": [9, true, false], "D5.15": [10, true, false], "D5.16": [46, true, false], "D5.17": [8, true, false], "D5.18": [7, true, false], "D5.19": [20, true, false], "D5.20": [6, true, false], "D5.21": [7, true, false], "D5.22": [19, true, false], "D5.23": [11, true, false], "D5.24": [7, true, false], "D5.25": [25, true, false], "D5.26": [9, true, false], "D5.27": [16, true, false], "D5.28": [7, true, false], "D5.29": [11, true, false], "D5.30": [23, true, false], "D5.31": [10, true, false], "D5.32": [6, true, false], "D5.33": [10, true, false], "D5.34": [21, true, false], "D5.35": [47, true, false], "D5.36": [7, true, false], "D5.37": [23, true, false], "D5.38": [21, true, false], "D5.39": [10, true, false], "D6.00": [8, true, false], "D6.01": [7, true, false], "D6.02": [7, true, false], "D6.03": [47, true, false], "D6.04": [7, true, false], "D6.05": [9, true, false], "D6.06": [7, true, false], "D6.07": [8, true, false], "D6.08": [7, true, false], "D6.09": [9, true, false], "D6.10": [7, true, false], "D6.11": [7, true, false], "D6.12": [7, true, false], "D6.13": [6, true, false], "D6.14": [9, true, false], "D6.15": [9, true, false], "D6.16": [7, true, false], "D6.17": [7, true, false], "D6.18": [10, true, false], "D6.19": [11, true, false], "D6.20": [9, true, false], "D6.21": [9, true, false], "D6.22": [50, true, false], "D6.23": [7, true, false], "D6.24": [9, true, false], "D6.25": [7, true, false], "D6.26": [7, true, false], "D6.27": [11, true, false], "D6.28": [7, true, false], "D6.29": [8, true, false], "D6.30": [43, true, false], "D6.31": [11, true, false], "D6.32": [8, true, false], "D6.33": [7, true, false], "D6.34": [46, true, false], "D6.35": [12, true, false], "D6.36": [56, true, false], "D6.37": [11, true, false], "D6.38": [7, true, false], "D6.39": [45, true, false]}}}
\ No newline at end of file
diff --git a/sweep_estimated.py b/sweep_estimated.py
new file mode 100644
index 0000000..9463e4e
--- /dev/null
+++ b/sweep_estimated.py
@@ -0,0 +1,114 @@
+"""PREREG_estimated_transform_2026-09-22 (control K3): Chandrupatla on sign(f)|f|^(1/m_hat), m_hat
+estimated during the run by Lagouanelle (K3L) or by A's analogy order (K3A), on the six corpora with
+the harness of sweep_fourth.py (same problems, seeding, charging, uniform criterion).  Report E1-E4.
+
+    python -u sweep_estimated.py            run -> sweep_estimated.json, then the report
+    python -u sweep_estimated.py --report
+"""
+from __future__ import annotations
+
+import functools
+import json
+import sys
+from multiprocessing import Pool
+
+import sweep_fourth
+import sweep_full
+from simroot.transformed import chandrupatla_transformed
+from sweep_controls import nonsimple
+from sweep_oos import sign_p
+
+for _name, _est in (("k3_lag", "lag"), ("k3_analogy", "analogy")):
+    sweep_full.EXTRA_BASELINES[_name] = functools.partial(chandrupatla_transformed, estimator=_est)
+    sweep_fourth.CONFIGS[_name] = ("base", _name)
+NAMES = ("k3_lag", "k3_analogy")
+SETS = ("APS", "CHA", "NEW", "RJL", "APP", "D")
+
+
+def job(j):
+    name, which = j
+    return name, sweep_fourth.evaluate((name, which))[1]
+
+
+def cost(v):
+    return v[0] if v[1] else 200
+
+
+def tot(r, keep=None):
+    return sum(cost(v) for p, v in r.items() if keep is None or keep(p))
+
+
+def h2h(a, b, keep=None):
+    ps = [p for p in a if keep is None or keep(p)]
+    w = sum(cost(a[p]) < cost(b[p]) for p in ps)
+    l = sum(cost(a[p]) > cost(b[p]) for p in ps)
+    return w, len(ps) - w - l, l
+
+
+def report(R):
+    seen = json.load(open("sweep_fourth_seen.json", encoding="utf8"))
+    four = json.load(open("sweep_fourth_fourth.json", encoding="utf8"))
+    ref = {}
+    for k in ("Aprime", "chandrupatla"):
+        ref[k] = dict(seen[k])
+        ref[k].update(four[k])
+    ap, ch = ref["Aprime"], ref["chandrupatla"]
+    K1 = json.load(open("sweep_controls.json", encoding="utf8"))["K1"]
+    print("E1 - corpus 4 (decisive): K3 total vs A' total; A' w/t/l against K3, p")
+    verdict = []
+    for k in NAMES:
+        w, t, l = h2h(ap["D"], R[k]["D"])
+        k3_not_worse = tot(R[k]["D"]) <= tot(ap["D"])
+        k3_wins = l > w and sign_p(w, l) < 0.05
+        a_wins = tot(ap["D"]) < tot(R[k]["D"]) and w > l and sign_p(w, l) < 0.05
+        verdict.append("withdraw" if (k3_not_worse or k3_wins) else ("stands" if a_wins else "intermediate"))
+        print(f"  {k}: {tot(R[k]['D'])} vs A' {tot(ap['D'])}   A' {w}/{t}/{l} p={sign_p(w, l):.2g}  -> {verdict[-1]}")
+    overall = "withdraw" if "withdraw" in verdict else ("stands" if all(v == "stands" for v in verdict)
+                                                        else "intermediate")
+    print(f"  outcome for the claim of 6.6: {overall}")
+    print("\nE2 - six corpora totals (violations of the 2x bound in brackets)")
+    for k, r in (("K3L", R["k3_lag"]), ("K3A", R["k3_analogy"]), ("A'", ap), ("Chandrupatla(f)", ch)):
+        cells = " ".join(f"{s} {tot(r[s])}" + (f"({sum(v[2] for v in r[s].values())})" if k.startswith("K3") else "")
+                         for s in SETS)
+        print(f"  {k:<16} {cells}  | all {sum(tot(r[s]) for s in SETS)}")
+    print("\nE3 - multiple/fractional roots (group of Table 11): K3L / K3A / A' / oracle (Chandrupatla on g)")
+    for s in ("CHA", "NEW", "D"):
+        m = K1[s]["mstar"]
+        keep = lambda p, _m=m: nonsimple(_m[p])  # noqa: E731
+        orc = tot(K1[s]["chandrupatla_g"], keep)
+        a_ = tot(ap[s], keep)
+        row = []
+        for k in NAMES:
+            v = tot(R[k][s], keep)
+            share = (a_ - v) / (a_ - orc) if a_ != orc else float("nan")
+            row.append(f"{k} {v} (closes {100 * share:+.0f}% of A'->oracle)")
+        print(f"  {s}: n={sum(1 for p in m if keep(p))}  " + "  ".join(row) + f"  A' {a_}  oracle {orc}")
+    print("\nE4 - the other problems: K3 against Chandrupatla on f (cost of false readings)")
+    for s in ("CHA", "NEW", "D"):
+        m = K1[s]["mstar"]
+        keep = lambda p, _m=m: not nonsimple(_m[p])  # noqa: E731
+        print(f"  {s}: " + "  ".join(f"{k} {tot(R[k][s], keep)}" for k in NAMES)
+              + f"  Chandrupatla(f) {tot(ch[s], keep)}  A' {tot(ap[s], keep)}")
+    for k in NAMES:
+        keep = lambda p: True  # noqa: E731
+        print(f"  {k} vs Chandrupatla(f), APS: {tot(R[k]['APS'])} vs {tot(ch['APS'])}")
+
+
+def main():
+    if "--report" not in sys.argv:
+        jobs = [(n, w) for n in NAMES for w in ("seen", "fourth")]
+        with Pool(len(jobs)) as pool:
+            out = pool.map(job, jobs)
+        R = {}
+        for name, res in out:
+            R.setdefault(name, {}).update(res)
+        with open("sweep_estimated.json", "w", encoding="utf8") as fh:
+            json.dump(R, fh)
+    with open("sweep_estimated.json", encoding="utf8") as fh:
+        R = json.load(fh)
+    report(R)
+    print("estimated done")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tests/test_transformed.py b/tests/test_transformed.py
new file mode 100644
index 0000000..157a3ea
--- /dev/null
+++ b/tests/test_transformed.py
@@ -0,0 +1,60 @@
+"""PREREG_estimated_transform_2026-09-22: the control K3 must be Chandrupatla's method itself when
+no order is estimated, and must stay a bracketing method when one is."""
+from __future__ import annotations
+
+import math
+
+import pytest
+
+from simroot.baselines import chandrupatla
+from simroot.transformed import chandrupatla_transformed
+from sweep_full import load_problems
+
+PROBS = load_problems()
+
+
+def test_without_an_estimate_it_is_chandrupatla_bit_for_bit():
+    bad = []
+    for s, pid, f, a, b, _r in PROBS:
+        r1 = chandrupatla(f, a, b, 1e-12, 200)
+        r2 = chandrupatla_transformed(f, a, b, 1e-12, 200, estimator="none")
+        if (float(r1[0]).hex(), r1[1], r1[2]) != (float(r2[0]).hex(), r2[1], r2[2]):
+            bad.append(pid)
+    assert not bad, bad[:5]
+
+
+@pytest.mark.parametrize("estimator", ("lag", "analogy"))
+def test_with_an_estimate_it_still_brackets(estimator):
+    for s, pid, f, a, b, _r in PROBS:
+        x, n, ok = chandrupatla_transformed(f, a, b, 1e-12, 200, estimator=estimator)
+        assert min(a, b) <= x <= max(a, b), pid
+        assert n <= 200
+
+
+def test_the_estimate_is_read_and_used_on_a_pure_power():
+    """The analogy estimator must reach m_hat on (t - 1)^9 and pay.  Lagouanelle's is NOT asserted:
+    on Chandrupatla's iterates, which alternate sides of the root, its three-point parabola reads
+    m ~ 1 at every step - an outcome of the experiment, reported by the run, not a property
+    to pin here."""
+    f = lambda t: (t - 1.0) ** 9  # noqa: E731
+    plain = chandrupatla_transformed(f, -2.0, 5.0, 1e-12, 200, estimator="none")[1]
+    st = {}
+    x, n, ok = chandrupatla_transformed(f, -2.0, 5.0, 1e-12, 200, estimator="analogy", stats=st)
+    assert ok and abs(x - 1.0) < 1e-6
+    assert st.get("updates", 0) >= 1
+    assert n < plain, (n, plain)
+    x, n, ok = chandrupatla_transformed(f, -2.0, 5.0, 1e-12, 200, estimator="lag")
+    assert ok and abs(x - 1.0) < 1e-6
+
+
+def test_an_overflowing_transform_halves_instead_of_raising():
+    """Found 2026-09-22: on the fractional branch 1/m_hat > 1 and |f|^(1/m_hat) overflowed with
+    an OverflowError that escaped the solver.  Now it is inf, the interpolation is refused, and
+    the step halves."""
+    from simroot.transformed import _G
+    assert _G(1e300, 3.0) == math.inf and _G(-1e300, 3.0) == -math.inf
+
+
+def test_unknown_estimator_is_refused():
+    with pytest.raises(ValueError):
+        chandrupatla_transformed(math.sin, 3.0, 4.0, 1e-12, 200, estimator="guess")