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idiom:  spill the beans
  H(p)        = 51.8955
  H_u         = 62.4203
  H_s         = inf
  H_u / H(p)  = 1.2028
  H_s / H(p)  = inf
  bound  inf >= 105.1773 >= 51.8955  [ok]

idiom:  call the shots
  H(p)        = 53.5802
  H_u         = 65.5193
  H_s         = 53.5921
  H_u / H(p)  = 1.2228
  H_s / H(p)  = 1.0002
  bound  119.1114 >= 108.5467 >= 53.5802  [ok]

idiom:  clear the air
  H(p)        = 62.5644
  H_u         = 72.1593
  H_s         = inf
  H_u / H(p)  = 1.1534
  H_s / H(p)  = inf
  bound  inf >= 126.5152 >= 62.5644  [ok]

idiom:  have a ball
  H(p)        = 56.3443
  H_u         = 62.2656
  H_s         = inf
  H_u / H(p)  = 1.1051
  H_s / H(p)  = inf
  bound  inf >= 114.0749 >= 56.3443  [ok]

idiom:  get the sack
  H(p)        = 52.6146
  H_u         = 58.2279
  H_s         = inf
  H_u / H(p)  = 1.1067
  H_s / H(p)  = inf
  bound  inf >= 106.6155 >= 52.6146  [ok]

idiom:  bite the dust
  H(p)        = 47.9287
  H_u         = 57.2660
  H_s         = 47.9325
  H_u / H(p)  = 1.1948
  H_s / H(p)  = 1.0001
  bound  105.1985 >= 97.2437 >= 47.9287  [ok]

idiom:  break the mold
  H(p)        = 53.9715
  H_u         = 69.4829
  H_s         = 53.9715
  H_u / H(p)  = 1.2874
  H_s / H(p)  = 1.0000
  bound  123.4544 >= 109.3293 >= 53.9715  [ok]

idiom:  lose ground
  H(p)        = 58.4404
  H_u         = 66.6070
  H_s         = 58.4471
  H_u / H(p)  = 1.1397
  H_s / H(p)  = 1.0001
  bound  125.0541 >= 118.2671 >= 58.4404  [ok]

idiom:  make waves
  H(p)        = 49.7432
  H_u         = 53.6185
  H_s         = inf
  H_u / H(p)  = 1.0779
  H_s / H(p)  = inf
  bound  inf >= 100.8728 >= 49.7432  [ok]

idiom:  cut corners
  H(p)        = 46.6895
  H_u         = 59.8262
  H_s         = 46.6953
  H_u / H(p)  = 1.2814
  H_s / H(p)  = 1.0001
  bound  106.5215 >= 94.7652 >= 46.6895  [ok]

idiom:  raise hell
  H(p)        = 59.0044
  H_u         = 63.1516
  H_s         = inf
  H_u / H(p)  = 1.0703
  H_s / H(p)  = inf
  bound  inf >= 119.3951 >= 59.0044  [ok]

idiom:  pull strings
  H(p)        = 58.2272
  H_u         = 64.8137
  H_s         = 58.2458
  H_u / H(p)  = 1.1131
  H_s / H(p)  = 1.0003
  bound  123.0595 >= 117.8406 >= 58.2272  [ok]

idiom:  mean business
  H(p)        = 52.8547
  H_u         = 57.3056
  H_s         = 53.0699
  H_u / H(p)  = 1.0842
  H_s / H(p)  = 1.0041
  bound  110.3755 >= 107.0957 >= 52.8547  [ok]

idiom:  turn tail
  H(p)        = 67.0872
  H_u         = 75.9778
  H_s         = inf
  H_u / H(p)  = 1.1325
  H_s / H(p)  = inf
  bound  inf >= 135.5607 >= 67.0872  [ok]

idiom:  rock the boat
  H(p)        = 41.6363
  H_u         = 46.3793
  H_s         = inf
  H_u / H(p)  = 1.1139
  H_s / H(p)  = inf
  bound  inf >= 84.6588 >= 41.6363  [ok]

idiom:  lead the field
  H(p)        = 56.1382
  H_u         = 60.7719
  H_s         = 56.6844
  H_u / H(p)  = 1.0825
  H_s / H(p)  = 1.0097
  bound  117.4562 >= 113.6627 >= 56.1382  [ok]

idiom:  strike a chord
  H(p)        = 43.8912
  H_u         = 56.7999
  H_s         = 43.8912
  H_u / H(p)  = 1.2941
  H_s / H(p)  = 1.0000
  bound  100.6911 >= 89.1687 >= 43.8912  [ok]

idiom:  run the show
  H(p)        = 58.3229
  H_u         = 63.3454
  H_s         = inf
  H_u / H(p)  = 1.0861
  H_s / H(p)  = inf
  bound  inf >= 118.0322 >= 58.3229  [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__joint__idiom.json
