The five-dimensional configuration space

The second condition supplies the factor π⁵. The proton exists in ordinary three-dimensional space. Yet RSI holds that describing the flow of three intertwined, non-intersecting rings requires a higher-dimensional configuration space, or phase space. A phase space is a map of every possible state a system can occupy.

If the flows of the three inner loops crossed, the turbulence would make the proton violently unzip. Their fluid flux must therefore stay in distinct, phase-locked rotational states. The theory holds that the full angular phase space for this nesting has a volume proportional to π⁵. This is the geometric limit for packing three rotating toroids into one boundary without destructive interference.

Multiplying the six axes by π⁵ gives a predicted mass ratio of 1836.118. The measured value is 1836.153, so the two agree to about 19 parts per million. The same expression was noted by Friedrich Lenz in 1951, and explaining the small remaining difference is an open goal. The paper concludes that the proton works like a high-performance gearbox, displacing far more of the field while staying synchronized with the universal harmonic.