Three questions, one calculation

RSI reads three numbers rather than deriving them: the proton's mass in electron masses (about 1836), Brannen's phase δ (about 2/9), and the strength of the strong force. They look like three puzzles. They are one.

The phase is the electron's mass. RSI proposes that carrying the electron's spin-½ winding around the three perpendicular axes of space gives it a phase fixed by geometry, π/12. At exactly that phase the electron would weigh nothing. The real phase sits a little below it, and that small gap is the electron's whole mass: √mₑ/A = sin ε + 1 − cos ε, with ε = π/12 − δ. The proton fixes the scale A². So, given the electron's mass, the phase and the proton-to-electron ratio are the same number. Taken from the electron and muon, the phase gives 1836.19 for the ratio, against the measured 1836.15.

The strong force is the same ratio. The medium's tension on a knot of size L is hc/L². The proton is 1,836 times smaller than the electron, so its grip is (1836)² times stronger: a few million times, as the strong force requires (to within about 25%).

One calculation. RSI proposes that all three come from one quantity: how much energy the 720° loop and the trefoil carry, which sets their sizes. RSI proposes that the sizes are set by the thin core of each vortex tube, through a twist that grows with the logarithm of the knot's size over the Planck length. That makes the sizes exponential in the knots' shapes, the kind of mechanism that turns a pure number into a large ratio. The test is demanding: each exponent must be derived to about one part in 100,000. When it is, 1836, the phase and the strong force all follow together.