Why the wide-bracket gap remains, taken apart on the SAME evaluations: 'order of the model' explains only a third. Of the 262 evaluations lost on 33 problems, 178 sit on fun3-fun6 - pure powers of order 3, 5, 9, 19 - where no interpolating model works (our step 0.41-0.81 bracket halvings per evaluation, IQI from our own points 0.01-0.17) and Chandrupatla wins by BISECTING 93-100% of his steps; our step is slower than bisection there and our 2x-bisection guarantee licenses it. His band inside our step confirms it per family: fun4/5/6 573/456/456 -> 296/239/235 against his 293/228/228, while +164/+111/+170/+144 on fun1/2/8/9 where it refuses good steps - slot 2's total was two opposite effects summed. Only fun1 (58) is model order: IQI from our three points 10.37 halvings against our 0.62; a convex two-point step cannot carry IQI's negative weight (428/428 non-degenerate states; five underflowed to -0.0).

The flat regime is not detectable by the three-point order estimate: m >= 2 (the exact condition for a tangent step to lose to a halving) fires on 0.2% of APS states and on only 5.8% of states of pure powers of order 3-19. Paper corrected where it said the whole gap is model order (widelimit, decision, abstract, future work - the refuted log transform removed). WARNING recorded in FINDINGS_model_order.md: article/sim_numerics.tex has carried a STALE header since the first commit (current text = sim_numerics.md, unchanged since 08-24); every paper edit of 09-20/21 went into the .tex, the .md has none of them. Which file is canonical is Valeri's call. The new text numbers trace to results_diag_*.txt but are not yet machine-checked by verify_article.py. Trace hook in pure_root is behaviour-neutral and pinned; 762 pass on the server twice. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 07:38:16 +01:00
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+"""Two checks on diag_model_order.py before its result may be stated.
+
+  C1  WHAT Chandrupatla does on the problems where we lose, by family: the share of his
+      steps that are bisections, from the traced mirror whose evaluation count is asserted
+      equal to the original's.  If the flat families are won by bisecting, the gap there
+      is not a better model on his side.
+  C2  the 5 states where "exactly one negative Lagrange weight" failed: print them.  The
+      sign argument is exact in real arithmetic, so each exception must be a
+      floating-point degeneracy (a weight that underflowed to 0, or f values so close
+      that a difference cancelled) - or the argument is wrong and must be withdrawn.
+
+    python -u diag_model_order_checks.py
+"""
+from __future__ import annotations
+
+import math
+from collections import defaultdict
+
+from scipy.optimize._tstutils import _CHANDRUPATLA_TESTS_DICTS
+
+from diag_model_order import ACC, MAXFEV, OURS, XTOL, ch_cost, iqi
+from explain_chandrupatla import chandrupatla_traced
+from simroot.baselines import chandrupatla
+from simroot.pure import pure_root
+
+
+def main():
+    fam = defaultdict(lambda: [0, 0, 0, 0, 0])     # bisect, iqi, ours n, ch n, problems
+    exceptions = []
+    for d in _CHANDRUPATLA_TESTS_DICTS:
+        pid = str(d["ID"])
+        f = d["f"]
+        a, b = (float(v) for v in d["bracket"])
+        r = float(d["root"])
+        st = {"trace": []}
+        x, n, conv = pure_root(f, a, b, XTOL, MAXFEV, stats=st, **OURS)
+        if not (conv and abs(float(x) - r) <= ACC):
+            continue
+        ch = ch_cost(f, a, b, r)
+        if ch is None or n <= ch:
+            continue
+        _xc, nc, okc, tr = chandrupatla_traced(f, a, b, XTOL, MAXFEV)
+        _xo, no, _oko = chandrupatla(f, a, b, XTOL, MAXFEV)
+        assert nc == no, f"mirror drifted on {pid}: {nc} vs {no}"
+        k = pid.split(".")[0]
+        cell = fam[k]
+        cell[0] += tr["bisect"]
+        cell[1] += tr["iqi"]
+        cell[2] += n
+        cell[3] += ch
+        cell[4] += 1
+        for s in st["trace"]:
+            if s["xp2"] is None:
+                continue
+            pts = ((s["x"], s["fx"]), (s["xp"], s["fp"]), (s["xp2"], s["fp2"]))
+            fs = [p[1] for p in pts]
+            if not (min(fs) < 0.0 < max(fs)):
+                continue
+            _xq, w = iqi(*pts)
+            if w is not None and sum(v < 0.0 for v in w) != 1:
+                exceptions.append((pid, fs, w))
+
+    print("C1  Chandrupatla on the problems where we lose, by family")
+    print(f"  {'family':<6} {'probs':>5} {'ours':>6} {'CH':>6} {'gap':>5} "
+          f"{'CH bisect share':>16}")
+    tot_gap = 0
+    for k in sorted(fam):
+        bi, iq, on, cn, p = fam[k]
+        tot_gap += on - cn
+        share = 100.0 * bi / max(bi + iq, 1)
+        print(f"  {k:<6} {p:5d} {on:6d} {cn:6d} {on - cn:5d} {share:15.0f}%")
+    print(f"  total gap on the losing problems: {tot_gap}")
+
+    print(f"\nC2  the {len(exceptions)} states breaking 'exactly one negative weight'")
+    for pid, fs, w in exceptions:
+        tiny = min(abs(v) for v in fs)
+        print(f"  {pid:<8} f = [{', '.join(f'{v:.3e}' for v in fs)}]   "
+              f"w = [{', '.join(f'{v:.3e}' for v in w)}]   "
+              f"zero weights: {sum(v == 0.0 for v in w)}   min|f| {tiny:.1e}")
+
+
+if __name__ == "__main__":
+    main()