Free scan regressors preserved REML with matched covariance and full rank; grid ML differed across 431 AOMIC designs

We compared scan deletion with one free regressor per removed scan. The proof showed equal restricted maximum likelihood (REML) for matched positive definite covariance and full-rank retained designs. The comparison kept original scan times. Independent dense checks passed in 431 AOMIC working memory designs and 100 general covariance cases. Ordinary maximum likelihood (ML) differed. With true AR(1) correlation 0.6, paired ML fits selected different grid correlations in 39.59% of draws. The mean spike-to-deletion variance ratio was 0.93233. Signals were simulated Gaussian noise. Designs and masks came from OpenNeuro PIOP1 and PIOP2 version 2.0.0. The package includes a fit tool, a design bank, source data, proof, all draw outcomes, and reproduction commands. A fresh source retrieval and full replay passed. The REML principle is established. This work adds a checked tool and a quantitative ML audit with finite designs. It does not measure brain activity or test a complete imaging pipeline.

restricted maximum likelihood · maximum likelihood · scan deletion · spike regressors · AR(1) covariance · task fMRI · motion censoring · simulation