The physical principles of M theory also include the n-alities that arise from the Machian nature of inertia. Carl Brannen has made great progress undertanding inertia for the first rung. See this PF post about the particle masses. They are organised according to the primes 2 and 3. This number 3 is the 3 that we have been discussing in recent posts. In the world of 3, one would work with trialgebras, rather than bialgebras; trioperads rather than bioperads. Naturally that is a master idempotent-swapping trioperad.
Physically, we observe that the classical reality that emerges from considering all scales is nothing short of a Mathematical God. The unreasonable effectiveness of mathematics is no longer unreasonable.
Behold, I come quickly: hold that fast which thou hast, that no man take thy crown.