This work continues the program of operational reconstruction of observable physics from a timeless Euclidean model with a single real field. Building on the already reconstructed special-relativistic, gravitational, and minimal quantum layers of description, we show that, within a physically relevant family of reconstruction classes, a minimal Standard-Model realization of the operationally visible sector is singled out. The visible sector is thereby interpreted not as the full physical content of the class, but as an immediately observable gauge--fermionic substructure selected by phenomenologically motivated class parameters compatible with a stable observer, causal consistency, and a local relativistic quantum-field-theoretic regime. It is further shown that the selective extraction of the visible sector entails the existence of an invisible complement to it. Hidden content is introduced as an additional part of this complement, while its physically relevant part is treated as a hidden sector remaining compatible with the same working regime. Its gravitationally relevant non-vacuum part, insofar as it is essential for the purposes of the present work, is interpreted as dark matter. Thus, dark matter arises not as an external phenomenological appendage, but as a natural consequence of the incompleteness of the visible sector. In addition, it is shown that generational multiplicity is naturally interpreted as a parameter of the reconstruction class, while the space of Yukawa couplings arises as part of a finer parametrization of the visible sector. Finally, a structural formulation of the inverse problem for the parameters of the reconstruction class is given: observable physics is treated not only as a consequence of the class structure, but also as a basis for its partial phenomenological identification. In this way, the paper connects the extraction of a minimal Standard-Model realization of the visible sector, hidden content, dark matter, and the inverse problem within a unified class-structural scheme.