The first paper in this series introduced Distributed Presence (DP) as a structural-ontological framework in which a physical system’s mode of existence is constituted by its distribution across mutually exclusive states, prior to and independent of any interaction. Probability, within that framework, was shown to emerge from the geometry of this distribution rather than from an independent postulate; the Born rule, in particular, was derived as a structural consequence of presence accounting. Because DP characterizes what a system is rather than how it evolves, the framework is fundamentally non-dynamical: it requires no equation of motion to reach its central results.What the foundational paper left implicit, however, was the formal language in which the structural content of DP can be articulated with full precision. The present work supplies that language. Three interconnected formal pillars are developed here:(i) Minterms — the elementary, mutually exclusive structural modes that constitute the fine-grained ontological fabric of a system’s state space;(ii) Quantum numbers — the macroscopic invariants that label symmetry classes and constrain which minterms are physically admissible, thereby connecting DP’s ontological layer to the conserved quantities of standard quantum theory;(iii) Complex-valued structural components — shown to be algebraically indispensable for encoding phase relations and interference within DP’s own formalism, without importing the apparatus of Hilbert space.Together, these three elements furnish a self-contained formal architecture for Distributed Presence. The resulting structure reproduces the representational capacity of quantum-mechanical state descriptions while remaining grounded in the ontological vocabulary of the framework. Crucially, the present paper constructs formalism, not dynamics: it establishes the structural grammar from which dynamical extensions may subsequently be developed, but which already suffices for the non-dynamical results established in Paper I.
Sadeq Nasiri Vatan (Sat,) studied this question.