the wide-bracket gap is NOT closed, and now it has an address: the STEP RULE, not the guarantee and not the reading places. fun1 is one function at growing widths — 7/8, 12/12, 19/15, 59/24, 63/44 — so we tie when narrow and lose as it widens, while our observed order is the HIGHER one (3.63 vs 2.02); 59 on a 2e4 bracket is what bisection needs, i.e. one halving per evaluation against their 2.3. With the safeguard removed entirely we still spend 46/57/61/68 against bisection 57/77/45/45 and Chandrupatla 24/44 — worse than bisection on two of them. |f|/|f'| is an absolute length and cannot march across decades; written into the paper as the stated limit. Also fixed a tracer bug that had best_of double-counting evaluations (2993 vs 1487)

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

results_who_caps_us.txt

@@ -0,0 +1,13 @@
+problem        width  bisect    CH     none     step  project     safe   credit
+fun1.1             1      42     8        7        7        7        7       19
+fun1.2             9      46    12       12       12       12       12       45
+fun1.3            99      49    15       30       19       30       19       50
+fun1.4         2e+04      57    24       46       59       46       59       58
+fun1.5         2e+10      77    44       57       63       57       63       76
+fun3.1             5      45    44       61       64       61       64       46
+fun4.3         2e+04      57    56       73       70       73       70       58
+fun5.1             5      45    44       68       57       68       57       46
+
+legend: ✗ = the run did not reach the root (an unguarded method may not)
+if guard='none' marches where 'safe'/'project' crawl, the GUARANTEE is the cap;
+if 'none' crawls too, the STEP RULE is the cap.