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idiom:  spill the beans
  H(p)        = 3.9702
  H_u         = 4.6754
  H_s         = 5.0341
  H_u / H(p)  = 1.1776
  H_s / H(p)  = 1.2680
  bound  9.7095 >= 9.3266 >= 3.9702  [ok]

idiom:  call the shots
  H(p)        = 4.1562
  H_u         = 4.8985
  H_s         = 5.1535
  H_u / H(p)  = 1.1786
  H_s / H(p)  = 1.2400
  bound  10.0521 >= 9.6987 >= 4.1562  [ok]

idiom:  clear the air
  H(p)        = 4.3966
  H_u         = 5.0845
  H_s         = inf
  H_u / H(p)  = 1.1565
  H_s / H(p)  = inf
  bound  inf >= 10.1794 >= 4.3966  [ok]

idiom:  have a ball
  H(p)        = 4.3275
  H_u         = 4.8967
  H_s         = inf
  H_u / H(p)  = 1.1315
  H_s / H(p)  = inf
  bound  inf >= 10.0414 >= 4.3275  [ok]

idiom:  get the sack
  H(p)        = 4.5725
  H_u         = 5.0336
  H_s         = inf
  H_u / H(p)  = 1.1008
  H_s / H(p)  = inf
  bound  inf >= 10.5314 >= 4.5725  [ok]

idiom:  bite the dust
  H(p)        = 4.8609
  H_u         = 5.8842
  H_s         = inf
  H_u / H(p)  = 1.2105
  H_s / H(p)  = inf
  bound  inf >= 11.1081 >= 4.8609  [ok]

idiom:  break the mold
  H(p)        = 4.0735
  H_u         = 4.8791
  H_s         = inf
  H_u / H(p)  = 1.1978
  H_s / H(p)  = inf
  bound  inf >= 9.5334 >= 4.0735  [ok]

idiom:  lose ground
  H(p)        = 5.3857
  H_u         = 5.9977
  H_s         = inf
  H_u / H(p)  = 1.1136
  H_s / H(p)  = inf
  bound  inf >= 12.1577 >= 5.3857  [ok]

idiom:  make waves
  H(p)        = 5.1823
  H_u         = 5.5507
  H_s         = inf
  H_u / H(p)  = 1.0711
  H_s / H(p)  = inf
  bound  inf >= 11.7509 >= 5.1823  [ok]

idiom:  cut corners
  H(p)        = 4.1966
  H_u         = 5.1093
  H_s         = inf
  H_u / H(p)  = 1.2175
  H_s / H(p)  = inf
  bound  inf >= 9.7795 >= 4.1966  [ok]

idiom:  raise hell
  H(p)        = 5.3455
  H_u         = 5.6380
  H_s         = inf
  H_u / H(p)  = 1.0547
  H_s / H(p)  = inf
  bound  inf >= 12.0774 >= 5.3455  [ok]

idiom:  pull strings
  H(p)        = 4.6040
  H_u         = 5.2261
  H_s         = inf
  H_u / H(p)  = 1.1351
  H_s / H(p)  = inf
  bound  inf >= 10.5943 >= 4.6040  [ok]

idiom:  mean business
  H(p)        = 5.2846
  H_u         = 5.8409
  H_s         = inf
  H_u / H(p)  = 1.1053
  H_s / H(p)  = inf
  bound  inf >= 11.9555 >= 5.2846  [ok]

idiom:  turn tail
  H(p)        = 5.4387
  H_u         = 6.0759
  H_s         = inf
  H_u / H(p)  = 1.1172
  H_s / H(p)  = inf
  bound  inf >= 12.2637 >= 5.4387  [ok]

idiom:  rock the boat
  H(p)        = 3.9817
  H_u         = 4.6827
  H_s         = 4.7373
  H_u / H(p)  = 1.1760
  H_s / H(p)  = 1.1898
  bound  9.4200 >= 9.3498 >= 3.9817  [ok]

idiom:  lead the field
  H(p)        = 5.0036
  H_u         = 5.5948
  H_s         = inf
  H_u / H(p)  = 1.1181
  H_s / H(p)  = inf
  bound  inf >= 11.3935 >= 5.0036  [ok]

idiom:  strike a chord
  H(p)        = 4.8685
  H_u         = 5.9643
  H_s         = 5.4309
  H_u / H(p)  = 1.2251
  H_s / H(p)  = 1.1155
  bound  11.3952 >= 11.1232 >= 4.8685  [ok]

idiom:  run the show
  H(p)        = 5.2614
  H_u         = 5.6262
  H_s         = inf
  H_u / H(p)  = 1.0693
  H_s / H(p)  = inf
  bound  inf >= 11.9090 >= 5.2614  [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__full__geo__idiom.json
