budget-CoT per-item: paired ties with latent arms confirmed (p>=0.69)

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

results-loop/stats_final.json

@@ -370,6 +370,30 @@
    "a_only": 15,
    "b_only": 7,
    "p": 0.13380050659179688
+  },
+  "budget-cot vs loop k=4, overall": {
+   "n": 500,
+   "a_only": 36,
+   "b_only": 37,
+   "p": 1.0
+  },
+  "budget-cot vs loop k=4, hard": {
+   "n": 55,
+   "a_only": 14,
+   "b_only": 11,
+   "p": 0.6900379657745361
+  },
+  "budget-cot vs distill k=1, overall": {
+   "n": 500,
+   "a_only": 29,
+   "b_only": 26,
+   "p": 0.7877061896700435
+  },
+  "budget-cot vs distill k=1, hard": {
+   "n": 55,
+   "a_only": 8,
+   "b_only": 6,
+   "p": 0.79052734375
   }
  },
  "best-of-3 ORACLE (any-pass)": {