Slot 2, the decision place: Chandrupatla's own acceptance band, put inside our step rule as an instrument, does NOT close the gap - CHA 3066 (project) / 2899 (credit) against his 2423, while APS doubles 2806 -> 5432, and the band is not idle (63.6% refusals). The fifth independent test of one conclusion: the remaining gap is the ORDER of the model the step is built on, not the place the similarity is read in. By the declared stop rule (M1 and M2 both false) the 'where is the similarity read' line is closed: all four places measured.

Not empty-handed: our own parameter-free reading 'defect' - refuse when |phi - xi| > min(xi, 1 - xi) - sets a new canonical best, APS 2523 at 153/154 (previous 2527, Chandrupatla 2785), guarantee intact (0 of 135 family cells), refusing on 7.0% of steps. It is a second point on the same trade, not a replacement: 5733 over both sets against 5511, because CHA gives back 3210. Also: _shape_ratios crashed on a missing third point, which evaluate would have turned into a silent sweep of zeros; the slope-gate pin was anchored on line spelling; and the server copy had drifted (stale relax/sor.py, test_relaxation.py absent - 746 tests instead of 755). All synced, 92/92 files identical by content, 755 pass on the server.

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

tests/test_decision_place.py

@@ -0,0 +1,86 @@
+"""Pins for PREREG 2026-09-21 slot 2: the reading in the DECISION place."""
+from __future__ import annotations
+
+import math
+
+import pytest
+
+from simroot.pure import (PURE_SIMS, _decide_refuse, _shape_defect, _shape_ratios,
+                          pure_root)
+
+PROBS = (
+    (lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0),
+    (lambda t: math.exp(t) - 2.0, 0.0, 3.0),
+    (lambda t: (t - 1.0) ** 3, 0.0, 10.0),
+    (lambda t: math.sin(t) - 0.5, 0.0, 1.5),
+)
+S = PURE_SIMS["ratio"]
+
+
+def test_one_definition_of_the_triple():
+    """The step place and the decision place must not disagree about the configuration."""
+    args = (2.0, 8.0, 1.0, 1.0, 3.0, 27.0)
+    xi, ph = _shape_ratios(*args)
+    assert _shape_defect(*args) == pytest.approx(abs(ph - xi))
+
+
+def test_a_linear_configuration_is_never_refused():
+    """For a linear f, xi == phi, so every reading must trust the model."""
+    f = lambda t: 3.0 * t - 6.0            # noqa: E731
+    args = (1.0, f(1.0), 0.0, f(0.0), 4.0, f(4.0))
+    for mode in ("band", "defect", "simpair"):
+        assert _decide_refuse(mode, S, 0.5, *args) is False
+
+
+def test_band_is_chandrupatlas_rule_verbatim():
+    """Pinned against the published inequality, not against our own restatement."""
+    for xi, ph in ((0.5, 0.5), (0.25, 0.3), (0.9, 0.2), (0.1, 0.9)):
+        # build a triple realising exactly these ratios: u=0, v=1, fu=0, fv=1
+        args = (xi, ph, 0.0, 0.0, 1.0, 1.0)
+        want = not (1.0 - math.sqrt(1.0 - xi) < ph < math.sqrt(xi))
+        assert _decide_refuse("band", S, 0.5, *args) is want
+
+
+def test_a_degenerate_triple_allows_the_step():
+    """No information is not a reason to refuse; the safeguard carries the bound."""
+    for mode in ("band", "defect", "simpair"):
+        assert _decide_refuse(mode, S, 0.5, 1.0, 2.0, 0.0, 5.0, 0.0, 5.0) is False
+        assert _decide_refuse(mode, S, 0.5, 1.0, 2.0, 3.0, 5.0, 3.0, 9.0) is False
+
+
+def test_readings_actually_decide_somewhere():
+    """M5 in miniature: a reading that never fires or always fires is a relabelling."""
+    fired = {m: 0 for m in ("band", "defect", "simpair")}
+    total = 0
+    for xi in (0.05, 0.2, 0.4, 0.6, 0.8, 0.95):
+        for ph in (0.02, 0.15, 0.45, 0.7, 0.98):
+            total += 1
+            for m in fired:
+                fired[m] += _decide_refuse(m, S, 0.5, xi, ph, 0.0, 0.0, 1.0, 1.0)
+    for m, k in fired.items():
+        assert 0 < k < total, (m, k, total)
+
+
+@pytest.mark.parametrize("f,a,b", PROBS)
+@pytest.mark.parametrize("mode", ("band", "defect", "simpair"))
+def test_every_reading_still_solves_with_the_guarantee(f, a, b, mode):
+    x, n, conv = pure_root(f, a, b, 1e-10, 300, similarity="ratio", scale="derived3",
+                           guard="safe", prestep=mode)
+    assert conv
+    assert min(a, b) <= x <= max(a, b)
+    bound = 2 * math.ceil(math.log2(abs(b - a) / 1e-10)) + 4
+    assert n <= bound
+
+
+@pytest.mark.parametrize("f,a,b", PROBS)
+def test_default_untouched_by_slot_two(f, a, b):
+    assert (pure_root(f, a, b, 1e-12, 200, similarity="ratio", scale="derived3",
+                      guard="safe")
+            == pure_root(f, a, b, 1e-12, 200, similarity="ratio", scale="derived3",
+                         guard="safe", prestep="none"))
+
+
+def test_two_point_scale_refuses_a_triple_reading():
+    for mode in ("band", "defect", "simpair"):
+        with pytest.raises(ValueError):
+            pure_root(lambda t: t, 0.0, 1.0, 1e-9, 50, scale="derived", prestep=mode)