This is the cleaned structural form of the force idea. It treats force not as a primitive dimensional quantity, but as a normalised directional response relative to a structural reference centre.
Here ⊙ means componentwise multiplication, and the quotient is also understood componentwise.
This was one of the main breakthroughs: the theory does not merely assert force is dimensionless, it shows how the time-scale factor τ² makes that happen.
Energy is treated as a scalar structural intensity. The mass ratio and effective propagation-speed ratio are both dimensionless, so the whole expression is dimensionless.
A key refinement from the discussion was that veff,1 and veff,2 are better thought of as observer-local effective propagation speeds, rather than two literal vacuum light constants.
Friction is not μ divided by the normal term. It scales with the normal influence and opposes the direction of motion.
This is the structural, dimensionless form. It keeps the componentwise style of the theory.
Pressure intensity remains scalar-like.
The directional form is separated out as a pressure-driving vector. This matches the idea that pressure leads to expansion while also having directional influence.
This combines structural response, pressure drive, and frictional opposition into the main governing field for the simulations.
This makes the fluid part of the model explicit. The divergence of the medium velocity field is driven by the divergence of the net structural field.
Interpretation: compression or expansion in the medium is sourced by the structure of the net field.
A useful philosophical point from the handwritten notes is that time can cancel from ratios, leaving a purely structural relation. This supports the general style of the theory: ratios and reference scales matter more than absolute quantities.
One-line summary: physical behaviour is modelled as a family of dimensionless structural relations between local motion, reference scales, directional response, and medium evolution.