Revision 3: exact-zero stop in section 4; Table 12 with the post hoc Lagouanelle variant (branch m>=2: corpus 4 5568, six corpora 18372, multiple/fractional 6540, APS 2960; A' 178/34/28), the controls' missing exit in its caption; the reading of Table 12 restated in 7.1, 6.6 and the conclusion - the analogy order transfers to the classical frame and works better there than in A's split (2809 vs 4042 on multiple roots), and A's layer as a whole (detector with exit) earns its place (+1233 vs -3934). Server: verify 548 OK / 0 BAD, regression x2 1239 passed, PDF 32 pages, 0 errors, 0 overfull.

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

apply_article_revision3.py

@@ -0,0 +1,49 @@
+"""Revision 3 into article/sim_numerics.md:
+  4  the exact-zero stop stated in section 4 (it holds for every method on every corpus)
+  5  Table 12: the post hoc Lagouanelle variant on the branch m >= 2 (marked), the missing exit of
+     the controls in the caption, and the conclusion from Table 12 restated in 7.1, 6.6 and 8
+Exact anchors, each found exactly once, or nothing is written.
+
+    python -u apply_article_revision3.py
+"""
+from __future__ import annotations
+
+PATH = "article/sim_numerics.md"
+R = []
+
+
+def E(old, new):
+    R.append((old, new))
+
+
+E("$x$-tolerance $10^{-12}$; budget 200 evaluations.",
+  "$x$-tolerance $10^{-12}$; budget 200 evaluations. Every method, ours included, stops when its bracket is no wider than $\\varepsilon_x$ or when it evaluates an exact zero of the function it works on; none stops on a small $|f|$.")
+E("**Table 12.** Chandrupatla on the transformed function: the multiplicity estimated during the run, against A′, the oracle of Table 11 and Chandrupatla on $f$. Totals, failures charged; the 148 multiple and fractional roots of Table 11, and the simple-root canonical set.",
+  "**Table 12.** Chandrupatla on the transformed function: the multiplicity estimated during the run, against A′, the oracle of Table 11 and Chandrupatla on $f$. Totals, failures charged; the 148 multiple and fractional roots of Table 11, and the simple-root canonical set. The estimated forms have no exit: an order once taken is held to the end of the run. A′ leaves its regime by the exit of §6.2.")
+E("| Chandrupatla on $g$, $\\hat m$ by Lagouanelle | 7526 | 30991 | 6041 | 7215 |",
+  "| Chandrupatla on $g$, $\\hat m$ by Lagouanelle | 7526 | 30991 | 6041 | 7215 |\n| the same, branch $m\\ge2$ only (post hoc) | 5568 | 18372 | 6540 | 2960 |")
+E("(A variant restricted to the branch $m\\ge2$ was not among the controls recorded.)",
+  "Restricted after the fact to the branch $m\\ge2$ (post hoc, `POSTHOC_lag_branch_2026-09-22.md`), it no longer breaks, but in this frame it hardly sees a multiple root either: 6540 on the 148 multiple and fractional roots against 7011 for Chandrupatla on $f$, and 5568 on corpus 4, with A′ ahead 178/34/28.")
+E("So the decision layer of A′ earns its place against the classical method with an estimated order as well; and the split (7), not the order estimate, is where A′ leaves most to the transformation.",
+  "Two conclusions follow. First, the order read by analogy transfers to the classical frame and works better there than in A′'s own split: on the multiple and fractional roots Chandrupatla's interpolation with that order beats A′ itself (2809 against 4042). Second, A′'s decision layer as a whole — the detector together with its exit — earns its place: without an exit the transferred detector loses more on simple roots than it gains on multiple ones, and A′ stays ahead on corpus 4 and over the six corpora.")
+E("§7.1 puts this claim against the detectors a reader would try first, and against the transformation with the multiplicity known in advance or estimated during the run.",
+  "§7.1 tests this against the detectors a reader would try first and against the classical transformation with the multiplicity known or estimated, and the outcome is sharper than the claim: the order read by analogy transfers to the classical frame and works better there than in A′'s own split, while A′'s exit is what keeps simple roots cheap.")
+E("Its decision layer beats Lagouanelle's estimate, Chandrupatla's band and no detector put in its place, and Chandrupatla's method on the transformed function with the order estimated during the run;",
+  "Its detector, the order read by analogy, beats Lagouanelle's estimate, Chandrupatla's band and no detector put in its place, and it transfers: inside Chandrupatla's interpolation on the transformed function it does better on multiple roots than A′'s own split, while only A′'s exit keeps simple roots cheap;")
+
+
+def main():
+    src = open(PATH, encoding="utf8").read()
+    bad = [o[:80] for o, _ in R if src.count(o) != 1]
+    if bad:
+        for b in bad:
+            print("ANCHOR NOT FOUND EXACTLY ONCE:", repr(b))
+        raise SystemExit(f"{len(bad)} anchors failed; nothing written")
+    for o, n in R:
+        src = src.replace(o, n)
+    open(PATH, "w", encoding="utf8").write(src)
+    print(f"applied {len(R)}")
+
+
+if __name__ == "__main__":
+    main()