It is not the role of physics to determine the ultimate nature of the driving principle. Its proper role is to establish coherent relationships between physical quantities and to explore their formal and empirical consequences. However, the discovery of the mode of action of the driving principle is decisive, because it necessarily orients the conceptual approach from which these relationships are established. It conditions the way in which fundamental quantities are defined, articulated, and interpreted.

It is at this level, in my view, that the central issue lies: the clarification of the fundamental concepts of mass, space, inertia, momentum, and time. These five notions constitute a basic partition, from which the various possible “harmonics” of the physical world can be studied—that is, the derived laws, dynamics, and structures. Before any discussion of models, equations, or specific mechanisms, it is therefore this fundamental partition that must first be examined. If we do not share a coherent understanding of these initial concepts and of their grounding in the mode of action of the driving principle, then subsequent developments—however sophisticated—are likely to diverge irreducibly.

From this standpoint, I can briefly outline how these initial concepts are defined, on my side, starting from the immanent and relational mode of action of the driving principle.

Mass
Mass corresponds to the unity of a body, a unity made possible by the action of the driving principle, allowing the body, as a particular unity, to enter into relation with its environment. There exist different forms of mass, engaged in actual relations with one another. It is this effective relation between forms of mass that provides the physical foundation of the equivalence principle.

Space
Space is not a mere geometric background, but a real reference space, constituted by effective relations. The expansion of space (for example, cosmic inflation) does not correspond to inertial motion; it can therefore exceed the speed of light, since there is neither inertia nor obstacle to this expansion. As an initial phenomenon, it is necessary for the very constitution of an inertial frame and can be understood as being made possible by particles of extremely low mass, assimilable to a form of dark matter in mutual repulsion.

Inertia
If inertia is defined as resistance to a change of state, it always presupposes the prior existence of a real reference space. One may distinguish an inertia related to the stability of a body within this space, and an inertia related to the existence of momentum. In both cases, inertia is not primitive: it depends on the constitution of the reference space and on the continuous action of the driving principle.

Momentum
Momentum (understood here not as motion itself, but as an instantaneous relational dynamical state, taken into account by the action of the driving principle) manifests the dynamic relation between the different forms of mass engaged in an actual relation. It expresses this relation physically and thus constitutes the dynamic foundation of the equivalence principle, by linking mass, inertia, and motion within a single relational configuration.

Time
Time is inseparable from the relational aspect of spacetime. There exists a present instant common to the universe, which is the condition for the actuality of action and change, but also a multiplicity of proper times, since the relation between two motions may vary according to spatial conditions. The variation of rhythms does not abolish the existence of a real present; it is one of its relational modalities.

If I now try to reformulate your own framework in terms of a fundamental conceptual partition—and please tell me if I am mistaken—it seems to me that you assign a primary role to geometry and symmetry (in particular that of the Monster group), that mass appears as a constraint or stress of the vacuum dependent on scale, that inertia is largely derived, that momentum is understood as a statistical flux, and that time is identified with entropic dynamics itself, arising from free energy minimization.

In other words, your basic partition appears to me to be essentially geometrico-thermodynamic, whereas mine is relational and causal, grounded in the actuality of action.

My question is therefore simply this:
is this indeed how you understand your own foundational conceptual partition? And do you consider that inertia and the reality of the present retain a fundamental physical status within it, or are they entirely derived from symmetry and thermodynamics?

It seems to me that it is precisely at this level—that of the initial conceptual partition—that any potential point of divergence lies, prior to any discussion of models or equations.
In other words, our possible disagreement would not concern mathematical tools or derived laws, but rather what we take, upstream, to be physically primary.