One of the dimensionless ratios first (several decades ago) calculated by the Combinatorial Hierarchy was the proton/electron mass ratio of about 1836.15, and one of the main reasons I bothered writing a python script to calculate the Combinatorial Hierarchy itself, rather than merely the cardinal numbers of its levels, was to find a linkage between the first 3 levels of the CH and the 4th (proton to Plank mass ratio) – which would imply a unification of EM with gravity.
Chasing down a formula for the proton radius in which the proton to electron mass ratio plays a part:
α^2/(𝜋(mp/me)R∞) = proton radius = 8.41235641(34 ±26)e-16 m
(which is better accuracy by far than that measured), the source blog refers to a recent paper “The Origin of Mass and Nature of Gravity” that apparently came up with a similar formula. This half-hour video talks about the paper.
I found the fact that the proton radius (known only to low accuracy) can be calculated from other constants that are known to high accuracy to be most intriguing.