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)