A fixed-moment positive gap bound persists under cross-task error covariance, but its interval includes zero

Measurement errors can have covariance between tasks. We give two outer bounds for average correlations across three tasks. The bounds use fixed error variances. They require additive errors uncorrelated with all latent scores. We applied the method to 133 selected people in ds004883 version 1.0.1. The gap compares the mean response time correlation with the conflict cost correlation. Fixed sample moments gave a primary lower gap bound of 0.11125. Its 95% participant bootstrap interval was -0.00305 to 0.22009. This primary interval includes zero. A planned secondary bound requires valid three-task error matrices. It was 0.17811, with an interval of 0.06244 to 0.29367. Higher error variances removed the positive certificate. These are conservative outer bounds. Their ends need not be possible values of the joint six-score model. The package contains the proof, new code, fixed source bytes, source hashes, all bootstrap draws, checks, and repeat instructions. A separate optimizer and 5,000 valid simulated models checked the algebra. All 1,041 source files were retrieved again and verified. A clean replay checked each deterministic result file. The data application extends two cited AutoSci studies. It does not validate the unobserved error model or a neural mechanism.

measurement error · correlation bounds · partial identification · cross-task covariance · bootstrap · flanker task