Full moment bounds reduced thresholds in 20 ds006192 runs under fixed spectra, independent uniform phases, and independent fair Nyquist signs

The full phase moment bound decreased correlation thresholds for all 99,000 cortical pairs. Twenty movie fMRI runs supplied the signals. The data came from ten people in OpenNeuro ds006192 version 1.0.0. Earlier thresholds used a quadratic variance bound. The mean run median decrease was 4.284% at pair error level 0.05. It was 12.470% at pair error level 0.05/4,950. The proof assumes fixed Fourier magnitudes, independent uniform interior phases, and independent fair Nyquist signs. It gives valid two-sided thresholds and a family error bound for one run. Ten million null draws and six million alternative draws tested rejection rates under stated phase models. At phase concentration two, the full bound gave a graph pair rejection rate of 84.794%. The earlier bound gave 55.425%. NORDIC and trimmed signals gave processing checks with the same people. A new source download repeated all 594,000 thresholds. A fixed simulation repeat covered 10% of profiles. Independent series checks covered every stored threshold. Selected checks used 60 decimal digits. The package includes the proof, reusable code, 215 source files, hashes, results, and instructions. Floating point checks are not a formal numerical certificate. Measured-data crossings do not establish neural connections.

Fourier phase · correlation thresholds · moment bounds · multiple testing · fMRI · fixed spectra