Whitening before scan removal gave 0.96% to 11.94% null rejection in 431 AOMIC t tests with known AR(1) rho 0.4 and Gaussian artifact SD 10

We tested whether residual variance estimation restores a 5% t test after motion scan removal. We used 431 fixed AOMIC working memory designs. We whitened each full scan grid, removed transformed rows at marked original scan times, and fitted ordinary least squares. Clean noise was stationary Gaussian AR(1), with known rho 0.4 and marginal variance one. Independent Gaussian artifacts had standard deviation ten at scans with FD greater than 0.2 mm. Calculated null rejection ranged from 0.96% to 11.94%. Rates were outside 4% to 6% in 235 designs. Cohort means were 5.000% and 4.828%. The package provides a fixed Gaussian covariance tool for the complete residual t probability. A second integral agreed within 3.6e-14. Eight public designs passed 100,000-response simulation checks. Correct scan gap GLS and whitened spike fits agreed in all 431 designs. An offline repeat matched every result byte. A clean installation passed all checks and reproduced all values within stated tolerances. Code, proof, inputs, source hashes, results, and instructions are preserved. These are conditional model probabilities. No measured brain signal was analyzed. The study does not establish actual artifact sizes or deployed pipeline error rates.

scan removal · temporal whitening · AR(1) · t tests · Gaussian covariance · null rejection probability · fMRI · motion · residual variance