How does a pre-quantum, pre-spacetime theory know about the low-energy fine structure constant and mass ratios?

Because such a theory is needed both in UV and in IR, and the octonionic theory is such a theory. UV is obvious, but IR could do with some explaining.

Even at low energies, there can be a situation where for a given system, all sub-systems have action of the order \hbar. Then there is no background classical spacetime anymore, and the pre-quantum, pre-spacetime theory is required. e.g. when a massive object is in a quantum superposition of two position states and we want to know what spacetime geometry it produces.

The pre-theory is in principle required also for a more exact description and understanding of the standard model, even at low energies. And the octonionic theory achieves just that, thereby being able to derive the low-energy SM parameters. This is BSM in IR, and has implications for how we plan BSM experiments: these have to be not only towards UV, but also in the IR.

The O-theory has only three fundamental constants, and these happen to be such that both the UV and IR limits can be easily investigated. These constants are Planck length, Planck time and Planck's constant \hbar. Note that, as compared to conventional approaches to quantum gravity, Planck's constant \hbar has been traded for Planck mass/energy. And this is very important:

The pre-theory is in principle required whenever one or more of the following three conditions are satisfied: times scales T of interest are order Planck time, Length scales L of interest are order Planck length, actions S of interest are order \hbar.

If T and L are respectively much larger than Planck time and Planck length, but S is of order \hbar, that requires the pre-theory in IR.

If T is order Planck time, then the energy scale \hbar / T is Planck energy scale. However, \hbar / T is in IR for T >> Planck time, and yet the pre-theory is required (for an exact in-principle description of SM) if all actions are order \hbar.

The BSM physics in IR is achieved by replacing 4D Minkowski spacetime by 8D octonionic non-commutative spacetime. This is the pre-theory analog of flat spacetime - and it has consequences - it predicts the low energy SM parameters, without switching on high-energy interactions in the UV.

Going to high energies is just like in GR. In GR we switch on the gravitational field around Minkowski spacetime and doing so takes us from IR to UV. Same way, in the O-theory we switch on SM interactions and would-be-gravity, *around* the `flat' octonionic spacetime [=10D Minkowski] and this takes us from IR to UV. But unlike in the GR case, we already learn a lot of BSM physics in the IR, because the spacetime is non-commutative. String Theory missed out on this important IR physics, because it continued to work with 10D Minkowski spacetime which is commutative, and from there went to UV. Should have looked at octonionic spacetime and Clifford algebras.