Sample rank forced unit imaginary coherency in unregularized 20 second beta SEEG fits with real weights from 19 selected patients

We tested whether sample rank can force perfect imaginary coherency with real spatial weights. For K complex observations, we proved that a real rank sum greater than 2K forces at least one unit value. The proof applies to separate weights at one frequency and an objective with no penalty. We used preserved public OpenNeuro ds003876 version 1.0.2 inputs from a cited AutoSci study. The selected sample had 19 patients, 1,003 contact name group pairs, and 34 beta frequency bins. In 20 second fits, rank forced 8,228 of 34,102 scores to one, or 24.1 percent. Ten contact phase controls each retained all forced cells. The equal-patient fitted squared mean was 0.87615; the separate next-minute test mean was 0.02122. Longer fits or fewer signals removed forced saturation in this sample. This did not establish unbiased estimates. All 4,222,800 preserved Fourier coefficients rebuilt exactly from fresh pinned public source ranges. A full analysis repeat matched all 99 checked outputs. The package preserves a proof, rank tool, source code, inputs, weights, results, source recipes, hashes, and reproduction instructions. The empirical rates apply to the tested sample and objective.

imaginary coherency · SEEG · rank deficiency · canonical correlation · finite sample bias · signal processing · electrophysiology