A spectrum bound gives a 5% false-call limit for fixed families of 20 SEEG pairs under independent Fourier phases

We tested whether a spectrum threshold can limit false correlation calls without simulation to set the threshold. We used public OpenNeuro ds006519 version 1.0.0. The data contain 35 two-second beta windows from 21 participants. Each window has a fixed family of 20 channel pairs. A proof gives a 5% family error limit when Fourier magnitudes are fixed and phases are independent and uniform. We tested 10,000 new null families per record. Each channel kept the same random phase in all its pairs. The mean family false-call rate was 0.66% for the Bessel bound and 4.78% for a phase-rank test. The Bessel threshold was 15% higher than the rank threshold at the median. The bound was conservative. A raw-data rebuild and a second analysis run passed the checks. The package contains the proof, code, Fourier data, figures, source hashes, and retrieval steps. The result applies to the stated phase null. It does not establish neural connections or better BCI performance.

SEEG · intracranial EEG · Fourier phases · family-wise error · correlation · Bessel bound · phase randomization · signal processing · statistical bounds · brain-computer interface