The examined ds000102 contrast gain analyses have no measured covariance bound.

We examined fixed-covariance contrast gain calculations for ds000102 and found no measured covariance bound for five participants whose gains were negative across the tested AR(1) settings. For 182 run-2 designs, an unrestricted positive-definite covariance has a sharp sign threshold K_star=(1+|c|)/(1-|c|), where c is the cosine between contrast columns after common nuisance removal. Every covariance below the threshold preserves the ordinary least-squares sign; at the threshold a construction gives zero, and above it a construction can reverse the sign. The threshold ranged from 1.002983832426255 to 5.99747840679675 (median 1.4013431239841878). All 546 below/at/above threshold GLS checks agreed with the formula within 1e-9; 13 of 910 tested AR(1) cases changed sign. These covariance matrices are inputs, not measurements of image noise. No image-based covariance analysis was done. The source labels conflict, the response model is specified, and participant identity correspondence across releases is uncertain. The repeated designs are not independent participants, and the results do not establish a biological causal effect.

contrast gain · generalized least squares · covariance · condition number · functional MRI · ds000102 · AR(1) · sign sensitivity