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idiom:  spill the beans
  H(p)        = 3.7601
  H_u         = 4.6896
  H_s         = inf
  H_u / H(p)  = 1.2472
  H_s / H(p)  = inf
  bound  inf >= 8.9064 >= 3.7601  [ok]

idiom:  call the shots
  H(p)        = 3.9079
  H_u         = 5.0157
  H_s         = 4.3971
  H_u / H(p)  = 1.2835
  H_s / H(p)  = 1.1252
  bound  9.4128 >= 9.2022 >= 3.9079  [ok]

idiom:  clear the air
  H(p)        = 4.4107
  H_u         = 5.2729
  H_s         = 5.0532
  H_u / H(p)  = 1.1955
  H_s / H(p)  = 1.1457
  bound  10.3260 >= 10.2077 >= 4.4107  [ok]

idiom:  have a ball
  H(p)        = 4.1533
  H_u         = 4.7545
  H_s         = 5.0551
  H_u / H(p)  = 1.1447
  H_s / H(p)  = 1.2171
  bound  9.8096 >= 9.6930 >= 4.1533  [ok]

idiom:  get the sack
  H(p)        = 4.7428
  H_u         = 5.5599
  H_s         = 6.0013
  H_u / H(p)  = 1.1723
  H_s / H(p)  = 1.2654
  bound  11.5613 >= 10.8719 >= 4.7428  [ok]

idiom:  bite the dust
  H(p)        = 4.2435
  H_u         = 5.5978
  H_s         = 4.6275
  H_u / H(p)  = 1.3191
  H_s / H(p)  = 1.0905
  bound  10.2253 >= 9.8733 >= 4.2435  [ok]

idiom:  break the mold
  H(p)        = 3.4261
  H_u         = 4.5419
  H_s         = 3.8394
  H_u / H(p)  = 1.3257
  H_s / H(p)  = 1.1206
  bound  8.3813 >= 8.2386 >= 3.4261  [ok]

idiom:  lose ground
  H(p)        = 4.9108
  H_u         = 5.7120
  H_s         = 5.5522
  H_u / H(p)  = 1.1632
  H_s / H(p)  = 1.1306
  bound  11.2642 >= 11.2079 >= 4.9108  [ok]

idiom:  make waves
  H(p)        = 4.5406
  H_u         = 5.1974
  H_s         = inf
  H_u / H(p)  = 1.1447
  H_s / H(p)  = inf
  bound  inf >= 10.4674 >= 4.5406  [ok]

idiom:  cut corners
  H(p)        = 4.0242
  H_u         = 5.3604
  H_s         = 4.3914
  H_u / H(p)  = 1.3320
  H_s / H(p)  = 1.0912
  bound  9.7518 >= 9.4347 >= 4.0242  [ok]

idiom:  raise hell
  H(p)        = 4.8918
  H_u         = 5.2465
  H_s         = inf
  H_u / H(p)  = 1.0725
  H_s / H(p)  = inf
  bound  inf >= 11.1700 >= 4.8918  [ok]

idiom:  pull strings
  H(p)        = 4.5240
  H_u         = 5.3699
  H_s         = 5.1131
  H_u / H(p)  = 1.1870
  H_s / H(p)  = 1.1302
  bound  10.4831 >= 10.4343 >= 4.5240  [ok]

idiom:  mean business
  H(p)        = 5.7807
  H_u         = 6.5154
  H_s         = 6.5009
  H_u / H(p)  = 1.1271
  H_s / H(p)  = 1.1246
  bound  13.0164 >= 12.9477 >= 5.7807  [ok]

idiom:  turn tail
  H(p)        = 5.5030
  H_u         = 6.2761
  H_s         = 6.3775
  H_u / H(p)  = 1.1405
  H_s / H(p)  = 1.1589
  bound  12.6535 >= 12.3922 >= 5.5030  [ok]

idiom:  rock the boat
  H(p)        = 3.7066
  H_u         = 4.3291
  H_s         = 4.5701
  H_u / H(p)  = 1.1680
  H_s / H(p)  = 1.2330
  bound  8.8993 >= 8.7995 >= 3.7066  [ok]

idiom:  lead the field
  H(p)        = 4.7446
  H_u         = 5.5350
  H_s         = 5.4675
  H_u / H(p)  = 1.1666
  H_s / H(p)  = 1.1524
  bound  11.0026 >= 10.8754 >= 4.7446  [ok]

idiom:  strike a chord
  H(p)        = 3.9945
  H_u         = 5.1564
  H_s         = 4.4016
  H_u / H(p)  = 1.2909
  H_s / H(p)  = 1.1019
  bound  9.5580 >= 9.3754 >= 3.9945  [ok]

idiom:  run the show
  H(p)        = 5.0538
  H_u         = 5.7948
  H_s         = 6.0858
  H_u / H(p)  = 1.1466
  H_s / H(p)  = 1.2042
  bound  11.8806 >= 11.4938 >= 5.0538  [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__medial__geo__idiom.json