Removing circular shifts at distances of 1 to 10 rows gave 5.31% mean null rejection under independent phases with fixed spectra for 50 cortical pairs in 20 ds006192 movie fMRI runs

We tested a circular-shift correlation rule with fixed spectra from 20 public movie fMRI runs. The null model gave each region independent Fourier phases. The test target was 5%. Removing shifts at distances of one through ten rows gave 5.307% mean rejection. The full circular rank gave 4.969%. A second rank over all circular origins gave 4.800%. Each of two fixed pair matchings used 200,000 independent phase orbits. We counted all origins within each orbit. We prove a 5% upper bound for the second rank when the relative circular origin is uniform conditional on its orbit. This applies established finite-group theory. The package includes a reusable tool, source data, hashes, results, and a checked retrieval recipe. A complete repeat from fresh source bytes matched every saved number. The estimates describe a fixed phase model. They do not identify false neural connections in recorded data.

circular shifts · correlation tests · finite-rank tests · Fourier phase randomization · fMRI · Monte Carlo calibration · time series