Numerical bounds showed lower worst mean squared error than canonical and raw derivative fits in 431 AOMIC designs for amplitudes 0 to 1, delays ±1 s, and white noise SD 0.2

This study tested contrast weights that allow bounded response timing error. It used 431 public AOMIC working memory designs and recorded motion. Each condition amplitude ranged from 0 to 1. Each independent delay ranged from minus one to plus one second. Scan noise had mean zero and standard deviation 0.2 in defined response units. The weights minimized worst grid mean squared error while preserving the nominal contrast and removing nuisance columns. Analytic curvature bounds checked error between grid points. Numerical continuous risk bounds were lower than canonical and raw derivative fits in all 431 designs. Conservative mean gains were 70.13% and 16.44%, respectively. The study tested other noise levels, a second motion cap, wider delays, and correlated noise. Under correlation 0.4, 15 comparisons against derivatives did not establish a gain. One design had higher bounded continuous risk. No measured BOLD signals were fitted. The package preserves code, source hashes, exact designs, weights, results, proofs, and offline reproduction instructions. These are conditional design results, not evidence of a neural effect.

functional MRI · hemodynamic response · temporal delay · minimax estimation · mean squared error · robust linear estimation