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
parent 46c713cdd3
commit f5d036c9d8
13 changed files with 693 additions and 28 deletions
@@ -0,0 +1,22 @@
+guard=project:  family  no-gate  band   delta
+             fun1        99    263   +164
+             fun2       141    252   +111
+             fun3       338    310    -28
+             fun4       573    296   -277
+             fun5       456    239   -217
+             fun6       456    235   -221
+             fun7      1000   1000     +0
+             fun8        52    222   +170
+             fun9       105    249   +144
+
+guard=credit:  family  no-gate  band   delta
+             fun1       258    239    -19
+             fun2       292    271    -21
+             fun3       274    237    -37
+             fun4       294    234    -60
+             fun5       238    238     +0
+             fun6       238    235     -3
+             fun7      1000   1000     +0
+             fun8       220    218     -2
+             fun9       206    227    +21
+