One exact bipolar loop gives residual partial correlation magnitude one with positive definite original covariance

We tested an exact signal relation in bipolar stereoelectroencephalography (SEEG). We added one endpoint channel to each consecutive contact path. The new channel was the sum of the original path channels. A proof shows residual partial correlation magnitude one for every channel pair in this loop. The original channel covariance must be positive definite. Identity-shrunk partial correlation tends to the same value as shrinkage tends to zero. We tested 124 paths from eight public SEEG recordings in OpenNeuro ds004473 version 1.0.2. The test used 48 fixed sections and 2,000 distinct original channel pairs with no shared contact. At shrinkage 0.001, the mean patient median absolute partial correlation rose from 0.125 to 0.943. The original signals and their correlation block did not change. The package includes the proof, an exact montage audit tool, source data recipes, code, and all results. The test constructs the redundant channels. It does not establish their presence in the original recordings.

stereoelectroencephalography · SEEG · bipolar montage · partial correlation · identity shrinkage · signal representation · redundant channels