Independent uniform contact and cell phases with fixed magnitudes give exact joint covariance and a five percent network error bound for fixed real SEEG montages

We asked whether fixed contact powers can support a fast test of imaginary SEEG network spectra. Independent uniform phases across contacts and spectral cells give an exact joint covariance for a fixed real montage. A standard concentration bound limits the chance of any edge rejection to five percent under the complete phase null. We tested a joint Gaussian approximation with two public resting SEEG records from OpenNeuro ds005670 version 1.0.0. Each network had 12 bipolar outputs and 66 edges. Primary null rejection was 5.45 and 5.05 percent at a five percent target, from 2000 networks per record. The exact contact rank test gave 5.05 and 5.65 percent. Gaussian calibration generation was much faster on the study host. The approximation has no finite-sample guarantee. The proved bound rejected no null or weak signal networks and was conservative here. The fixed signal gave little detection gain. The package contains the proof, code, compact spectra, all evaluation scores, source hashes, and retrieval instructions. Both source records rebuilt the spectra exactly. All six simulations reproduced their numerical arrays exactly, except run times. These results concern the stated phase model and fixed scaling. They do not establish neural connections or patient error rates.

SEEG · imaginary cross-spectra · joint covariance · phase randomization · network error control · Bernstein inequality · Gaussian approximation · intracranial EEG