Distributed Presence II: From Ontology to Formalism Minterms, Quantum Numbers and Applications

This paper develops the second stage of the Distributed Presence (DP) programme by articulating a rigorous structural ontology in which a physical system is primitively distributed across mutually exclusive states prior to interaction. In this non-dynamical framework, quantum superposition is not viewed as an epistemic deficiency, a pre-collapse transient, or a compact representation of hidden variables. Rather, it expresses the ordinary mode of existence of a system whose presence is structurally spread over its admissible outcome space. The central methodological claim is a strict separation between determination and realisation. Determination fixes which outcomes are structurally admissible and assigns their associated presence fractions PFi, while realisation concerns which single outcome is selected when an interaction imposes a one-channel constraint. No fundamental dynamical law mediates between these two levels. Predictive content arises from structural constraints alone, not from underlying equations of motion. In this sense, the intrinsic randomness of DP is not epistemic but reflects the minimality of structural specification: the presence fractions determine statistical weights, but nothing in the ontology selects which outcome is realised in an individual event. To make this ontology mathematically explicit, the paper introduces minterms: mutually exclusive signed structural configurations constituting the finest-grained specification of a system’s state-space. Minterms are neither hidden variables nor dynamical trajectories; they encode structural orientation information whose sign-components are systematically lost when transitioning to observable, unsigned presence fractions. Within this perspective, the Hilbert-space formalism appears as a mathematically efficient coarse-graining or compression of a richer mintermial structure. Quantum numbers (n, l, m, s), Pauli exclusion, and spin acquire structural interpretations: exclusion follows from minterm exclusivity, and spin is reconstructed as a topological closure property of signed structural patterns rather than as primitive angular momentum. The framework is further extended to structural energetics. Because a single normalized unit of presence must be distributed over a modal extent, contraction of that extent enforces a compensating increase in structural intensity. The Planck–Einstein relation E=hf thus emerges as a geometric consequence of modal compression under fixed normalization, yielding a unified structural account of discrete energy transfer, including the photoelectric effect, without invoking particle-like collapse events. The reconstructive capacity of DP is illustrated through structural reformulations of Born weights, interference, Bell non-factorizability, the Tsirelson bound, entanglement monogamy, and selected spectral regularities. The aim is not to replace the predictive machinery of quantum mechanics, but to offer an ontologically explicit and mathematically disciplined foundation that clarifies why the formalism has the structure it does.