problem   ours   CH states   bracket halvings per evaluation:    ours  IQI-rec  IQI-brk
fun1.3      19   15      7                                       5.59     8.26     8.43
fun1.4      59   24      8                                       0.62    10.37     4.49
fun1.5      63   44      7                                       3.26     1.30     3.96
fun2.2      26   23     21                                       4.36     5.71     9.16
fun2.3      30   29     26                                       6.99    10.05    13.77
fun2.4      43   42     33                                       7.32     7.98     7.55
fun3.1      64   44     45                                       0.41     0.17     0.17
fun3.2      56   46     29                                       0.59     0.13     0.19
fun3.3      66   60     31                                       0.57     0.10     0.14
fun3.4      73   69     33                                       0.63     0.13     0.16
fun3.5      85   82     28                                       0.56     0.06     0.14
fun4.1      54   44     27                                       0.45     0.10     0.10
fun4.2      56   46     28                                       0.47     0.10     0.10
fun4.3      70   56     38                                       0.49     0.06     0.08
fun4.4      73   67     34                                       0.61     0.13     0.15
fun4.5      86   80     35                                       0.60     0.16     0.17
fun5.1      57   44     31                                       0.44     0.03     0.03
fun5.2      54   44     28                                       0.58     0.10     0.11
fun5.3      55   45     27                                       0.63     0.01     0.02
fun5.4      57   47     30                                       0.64     0.04     0.05
fun5.5      59   48     32                                       0.63     0.04     0.06
fun6.1      52   44     36                                       0.63     0.04     0.04
fun6.2      54   44     39                                       0.55     0.01     0.01
fun6.3      50   45     35                                       0.80     0.03     0.03
fun6.4      52   47     35                                       0.81     0.03     0.03
fun6.5      55   48     38                                       0.79     0.03     0.03
fun8.1      13   10      7                                       7.59    10.28    10.41
fun8.4      16   14     12                                       5.68     7.72    11.15
fun8.5      18   15     13                                       4.98     7.24     9.41
fun9.2      12    9      7                                       5.02     0.66     0.66
fun9.3      14   11     10                                       0.94     3.08     3.05
fun9.4      15   13      7                                       7.54     9.23     3.31
fun9.5      19   14      5                                       7.39     3.79     5.02

problems where we lose to Chandrupatla: 33, states 822

Q1  triples bracketing zero with exactly ONE negative Lagrange weight: 428/433  -> IDENTITY FAILS
    model defined and landing strictly inside the proven bracket: ours 86%, iqiR 77%, iqiB 77%

Q2/Q3  mean halvings per ONE evaluation from the same state (bracket | error), valid states only
  approach (error >= 1/2 bracket)  ours  1.32 |  3.39 (n=40)   iqiR  0.57 |  2.28 (n=6)   iqiB  0.53 |  2.14 (n=6)
  endgame                          ours  1.24 |  0.90 (n=669)   iqiR  0.83 |  1.27 (n=628)   iqiB  0.88 |  1.31 (n=631)

PAIRED on states where both are valid: mean (IQI - ours) bracket halvings
  iqiR: -0.34 per evaluation  (n=628)
  iqiB: -0.23 per evaluation  (n=631)
