A two-moment beta test gave 53 percent mean relative tail error at a 0.1 percent level in 700 pairs of 2-second SEEG beta windows under an independent phase null

We tested a correlation rule that matches variance and excess kurtosis in a measured spectrum. We used 700 fixed channel pairs from 35 public recordings in 21 people. The source was OpenNeuro ds006519 version 1.0.0. Each input was a 2-second prestim SEEG beta window. The null had independent uniform phases and fixed Fourier magnitudes. At the planned two-sided 0.1 percent level, mean absolute relative tail error was 53.47 percent. A variance-matched Pearson rule gave 46.23 percent. The paired difference was +7.24 percentage points, with a person bootstrap interval from -22.90 to +54.28. The primary test did not show a mean improvement. The two-moment rule gave lower errors in all 21 people at the secondary 1 and 5 percent levels. A measured peaked spectrum gave a 3.47 percent null call rate at a 0.1 percent threshold. We provide a full-spectrum numerical tail tool, a proof that equal variance can give different tails, and three figures. Fresh source reconstruction, continuous integration, and seeded replay checks passed. Two independent phase simulations supplied 14 million controls. The package preserves code, provenance, compact spectra, primary scores, extra counts, and reproduction instructions. The result is a conditional calibration benchmark. It does not establish better decoding or safer brain stimulation.

stereoelectroencephalography · SEEG · beta band · correlation · null calibration · phase randomization · tail probability · spectral analysis · brain-computer interface · numerical inversion