Sign tests by product underflowed: FIXED everywhere (branch, not master - the paper is not yet updated). FA * fnew < 0.0 with FA ~ -1e-200, fnew ~ 1e-150 is -0.0 and '-0.0 < 0.0' is False, so on flat functions (x^19) the bracket update moved the wrong end, the root left the bracket and the run still reported convergence - the proposed rule returned 4.9e-9, bisection 3.5e-9, ITP 1.6e-8 with a claimed 1e-12 bracket; the 1e-6 harness scored them solved. Same defect in our bisection, false-position family, Ridders, Brent, ITP and twelve copies in stage scripts, simroot/sim.py and one test; all replaced by _opposite / _same_sign, pinned by test_sign_underflow.

Impact, every sweep regenerated: the paper's key configurations are unchanged to the evaluation (proposed 2806/3220, credit 3568/3020, Chandrupatla, TOMS 748, Brent, bisection); 46 stated numbers move (ITP CHA 2857 -> 2896, ITP oracle 2611 -> 2647, record CHA figures by 14-18, the grid means by ~1%) and one finding weakens: the measured-order exponent of section 7.1 was cheaper in 29 of 60 far cells and 7 of 7 safeguards; with the fix 12 of 61 and 6 of 7, and on the wide-bracket set it now loses in every safeguard and drops 5 problems.

PREREG G1-G3 outcome on the fixed code: G2 (repeating step pattern, period from the data) PASSES Y1-Y4 and is ACCEPTED by the stop rule - proposed rule APS 2806 -> 2782 (below Chandrupatla's 2787), CHA 3220 -> 3169, both 6026 -> 5951, per problem vs Chandrupatla on APS 95/20/38 p = 8e-7. G1 fails Y1/Y2 (its Y3 miss was the sign bug), G3 fails Y2, A fails Y2. Regression 887 pass; the two red tests are the paper-number check (awaiting the paper update) and test_blend (fixed since, copy in stage16).

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

sweep_full.py

@@ -136,8 +136,9 @@ def label(spec):
     if len(spec) > 7 and spec[7] != "distance":
         tag = f"{tag}+dissim"
     if len(spec) > 9 and spec[9] != "none":
-        # the pair (off, on) must be distinguishable in a results file
-        tag = f"{tag}+ext"
+        # every extrapolation mode must be distinguishable in a results file
+        tag = f"{tag}+" + {"steps": "ext", "confirmed": "extC", "pattern": "extP",
+                           "steps+results": "extR"}[spec[9]]
     if len(spec) > 8 and spec[8] != "none":
         # the exponent must be visible in the label: (far, none) is false position and
         # (far, order) is the hypothesis, and a results file that cannot tell them apart
@@ -218,6 +219,18 @@ def _preflight_extrap_mode():
         raise SystemExit("extrapolate preflight FAILED: refusing to report zeros")
 
 
+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)."""
+    for mode in ("confirmed", "pattern", "steps+results"):
+        x, _n, ok = pure_root(lambda t: t - 1.0, 0.0, 3.0, 1e-10, 100, similarity="ratio",
+                              scale="derived3", guard="project", extrapolate=mode)
+        if not (ok and abs(x - 1.0) < 1e-8):
+            raise SystemExit(f"extrapolate={mode} preflight FAILED: refusing to report zeros")
+    modes = ("none", "steps", "confirmed", "pattern", "steps+results")
+    return [s[:9] + (m,) for s in build_grid_extrap(smoke) if s[9] == "none" for m in modes]
+
+
 def build_grid_extrap(smoke):
     """PREREG 2026-09-21: step extrapolation (A) inside the method, every cell as a pair
     (none, steps).  Tent with every reading and every guard; all nine functions without
@@ -374,10 +387,12 @@ def main():
     ordermode = "--order" in sys.argv      # slot 1: the similarity read BY PLACE
     decmode = "--decision" in sys.argv     # slot 2: the reading in the DECISION place
     extmode = "--extrap" in sys.argv       # A in the method: step extrapolation
+    ext2mode = "--extrap2" in sys.argv     # gates G1-G3 on the lengthening
     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_extrap(smoke) if extmode else
+    specs = (build_grid_extrap2(smoke) if ext2mode else
+             build_grid_extrap(smoke) if extmode else
              build_grid_decision(smoke) if decmode else
              build_grid_order(smoke) if ordermode else
              build_grid_cap(smoke) if capmode else
@@ -402,8 +417,9 @@ 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 extmode or decmode or ordermode or capmode or combomode or pointsmode or dirmode:
-        base = ("sweep_extrap" if extmode else
+    if ext2mode or extmode or decmode or ordermode or capmode or combomode or pointsmode or dirmode:
+        base = ("sweep_extrap2" if ext2mode else
+                "sweep_extrap" if extmode else
                 "sweep_decision" if decmode else
                 "sweep_order" if ordermode else
                 "sweep_cap" if capmode else