A spectrum bound kept false beta network calls below 5 percent in independent phase controls from 35 SEEG recordings

We tested beta network links in 2-second windows from 35 public SEEG recordings and 21 patients. The test uses a standard exponential bound with the measured spectra. Its proof controls the chance of any false link in one fixed family under an independent phase model. Across 70,000 complete phase-control networks, the Bessel rule had a false-network rate of 0.561%, with equal weight per patient, at a 5% family target. Each recording stayed below 0.95%. The native-sample IID rule called false links in every control network. All tested families were too large for a Bonferroni call with 999 rank controls. In defined pair controls with phase differences in [-pi/2, pi/2], detection was 45.1% for the Bessel rule and 10.4% for the simple spectrum bound. The Bessel rule had more measured false calls; both bounds had the same proved upper limit. The full analysis repeated exactly. The package preserves code, a command-line tool, all input spectra, pair maps, control outcomes, three figures, a proof, source hashes, and a raw-data retrieval recipe. These results concern the phase model. They do not establish true brain connections or improved BCI performance.

beta network testing · SEEG · phase randomization · spectrum bound · Bessel function · multiple testing · brain-computer interfaces