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idiom:  spill the beans
  H(p)        = 3.3386
  H_u         = 4.2754
  H_s         = inf
  H_u / H(p)  = 1.2806
  H_s / H(p)  = inf
  bound  inf >= 8.0636 >= 3.3386  [ok]

idiom:  call the shots
  H(p)        = 3.5504
  H_u         = 4.6554
  H_s         = 3.9710
  H_u / H(p)  = 1.3112
  H_s / H(p)  = 1.1185
  bound  8.6263 >= 8.4870 >= 3.5504  [ok]

idiom:  clear the air
  H(p)        = 3.9902
  H_u         = 4.8346
  H_s         = 4.6016
  H_u / H(p)  = 1.2116
  H_s / H(p)  = 1.1532
  bound  9.4363 >= 9.3666 >= 3.9902  [ok]

idiom:  have a ball
  H(p)        = 3.6612
  H_u         = 4.2464
  H_s         = 4.6030
  H_u / H(p)  = 1.1598
  H_s / H(p)  = 1.2572
  bound  8.8494 >= 8.7088 >= 3.6612  [ok]

idiom:  get the sack
  H(p)        = 4.2843
  H_u         = 5.0381
  H_s         = inf
  H_u / H(p)  = 1.1759
  H_s / H(p)  = inf
  bound  inf >= 9.9550 >= 4.2843  [ok]

idiom:  bite the dust
  H(p)        = 3.9160
  H_u         = 5.3188
  H_s         = 4.2648
  H_u / H(p)  = 1.3582
  H_s / H(p)  = 1.0891
  bound  9.5836 >= 9.2183 >= 3.9160  [ok]

idiom:  break the mold
  H(p)        = 3.3102
  H_u         = 4.3241
  H_s         = 3.7805
  H_u / H(p)  = 1.3063
  H_s / H(p)  = 1.1421
  bound  8.1046 >= 8.0068 >= 3.3102  [ok]

idiom:  lose ground
  H(p)        = 4.8386
  H_u         = 5.5384
  H_s         = 5.7436
  H_u / H(p)  = 1.1446
  H_s / H(p)  = 1.1870
  bound  11.2819 >= 11.0634 >= 4.8386  [ok]

idiom:  make waves
  H(p)        = 4.1709
  H_u         = 4.7874
  H_s         = inf
  H_u / H(p)  = 1.1478
  H_s / H(p)  = inf
  bound  inf >= 9.7280 >= 4.1709  [ok]

idiom:  cut corners
  H(p)        = 3.6547
  H_u         = 4.9105
  H_s         = 4.0388
  H_u / H(p)  = 1.3436
  H_s / H(p)  = 1.1051
  bound  8.9493 >= 8.6957 >= 3.6547  [ok]

idiom:  raise hell
  H(p)        = 4.6037
  H_u         = 5.0272
  H_s         = 6.1520
  H_u / H(p)  = 1.0920
  H_s / H(p)  = 1.3363
  bound  11.1793 >= 10.5938 >= 4.6037  [ok]

idiom:  pull strings
  H(p)        = 4.3273
  H_u         = 5.0550
  H_s         = 5.1294
  H_u / H(p)  = 1.1682
  H_s / H(p)  = 1.1854
  bound  10.1844 >= 10.0408 >= 4.3273  [ok]

idiom:  mean business
  H(p)        = 5.5690
  H_u         = 6.1498
  H_s         = 6.9834
  H_u / H(p)  = 1.1043
  H_s / H(p)  = 1.2540
  bound  13.1332 >= 12.5243 >= 5.5690  [ok]

idiom:  turn tail
  H(p)        = 4.8765
  H_u         = 5.9166
  H_s         = 5.3547
  H_u / H(p)  = 1.2133
  H_s / H(p)  = 1.0981
  bound  11.2713 >= 11.1394 >= 4.8765  [ok]

idiom:  rock the boat
  H(p)        = 3.0850
  H_u         = 3.7983
  H_s         = 3.8140
  H_u / H(p)  = 1.2312
  H_s / H(p)  = 1.2363
  bound  7.6123 >= 7.5562 >= 3.0850  [ok]

idiom:  lead the field
  H(p)        = 4.0766
  H_u         = 4.8802
  H_s         = 4.7458
  H_u / H(p)  = 1.1971
  H_s / H(p)  = 1.1641
  bound  9.6260 >= 9.5395 >= 4.0766  [ok]

idiom:  strike a chord
  H(p)        = 3.6373
  H_u         = 4.7754
  H_s         = 4.0634
  H_u / H(p)  = 1.3129
  H_s / H(p)  = 1.1172
  bound  8.8388 >= 8.6609 >= 3.6373  [ok]

idiom:  run the show
  H(p)        = 4.6009
  H_u         = 5.3065
  H_s         = 5.5921
  H_u / H(p)  = 1.1534
  H_s / H(p)  = 1.2154
  bound  10.8987 >= 10.5881 >= 4.6009  [ok]

bound  H_u + H_s >= 2 H(p) + 2 log 2 >= H(p)  holds for 18/18 phrases

Wrote 18 idiom results to results/sweep/json/qwen3-8b-base__medial__geo__idiom.json