Full spectra lowered conservative 5% graph thresholds by a mean of 12.91% in 20 ds006192 movie runs with fixed spectra and independent phases

We tested whether full Fourier spectra lower conservative correlation thresholds. We used 20 movie fMRI runs from ten selected people in OpenNeuro ds006192 version 1.0.0. Each run had 100 cortical regions and 4,950 pairs. At a nominal 5% limit for any rejection in one graph, all 99,000 primary pair thresholds decreased. The mean relative decrease was 12.91%. The rule uses the exact moment function under fixed spectra and independent region phases. A finite search and a union bound give a conservative error limit in real arithmetic. The proof permits dependent edges. Independent calculations checked 891,000 thresholds across three data settings and three error levels. A fresh-source replay matched all 66 analysis files byte for byte. In 2,000 coherent graphs from one source run, the new rule rejected in 0.6% of graphs. The package contains the source values, hashes, proof, code, pair results, figures, and reproduction commands. Binary FFT arithmetic is not interval certified. The study does not show that the phase model fits real brain data or estimate actual false neural connections.

Fourier spectra · correlation thresholds · multiple testing · phase randomization · functional MRI · conservative bounds · graph inference