In the first three parts of this paper we developed a unified, deterministic model of fields and particles based on the postulated existence of soliton-type (metron) solutions of the higher-dimensional vacuum gravitational equations. Following the demonstration in Part I that such solutions exist for a simplified, scalar prototype of the gravitational Lagrangian, the metron model was investigated in more detail for the Maxwell-Dirac-Einstein system in Part 2 and then applied in Part 3 to explain basic quantum phenomena such as the EPR paradox, interference effects in scattering experiments, and atomic spectra. In the final part of this paper we generalize the interaction analysis of the Maxwell-Dirac-Einstein system to include weak and strong interactions. It is shown that the principal properties of the Standard Model can be recovered by a four-dimensional, or (with closer agreement) five-dimensional non-Euclidean or Euclidean harmonic space background metric, assuming a suitable geometric structure of the trapped-mode metron solution. The solution is assumed to be composed of the basic fermion fields, representing leptons and quarks of different color and flavor, and the associated boson fields, which are generated by quadratic difference interactions between the fermions. The fermions are described by harmonic space metron components which are periodic with respect to extra (harmonic) space, the wave number components k(5) and k(6) defining the coupling constants for the electromagnetic and weak interactions, respectively, while the components k(7) and (in the case of a five-dimensional harmonic space) k(8) determine the strong-interaction coupling. The last harmonic dimension is needed, in combination with the other harmonic dimensions, to define an appropriate polarization tensor relating the metric-tenser components to the Dirac-field components such that the standard Dirac Lagrangian is recovered from the gravitational Lagrangian. A higher-order interaction corresponding to the Higgs mechanism is invoked to explain the electroweak boson masses. A quartic interaction in which the neutrino field appears quadratically exhibits the desired properties. Fermion masses are attributed to the SU(2)-breaking mode-trapping mechanism. The analysis is restricted to a single family; it is suggested that the second and third families can be described by higher-order trapped modes. The Standard Model gauge symmetries are explained as a special case of the general gauge invariance of the gravitational equations with respect to diffeomorphisms, applied to a particular class of coordinate transformations reflecting the geometrical symmetries of the metron solutions. The purpose of the inverse modeling approach pursued in this paper is twofold: it is demonstrated generally that soliton-type solutions of the higher-dimensional vacuum gravitational equations exhibit a sufficiently rich structure to reproduce the principal results or quantum field theory, as summarized in the Standard Model, while at the same time specific geometrical features of the anticipated metron solutions are identified, which one can then seek to confirm with exact numerical computations. Such computations should yield not only the symmetries of the Standard Model, but also all universal physical constants and particle parameters.
