Omega Dynamics and the Riemann–Boltzmann Correspondence

New version provides structural clarification and refinement of the Omega Dynamics framework. This revision introduces explicit formulation of primordial structural necessity, clarifies the non-branching single-trajectory ontology, refines the treatment of black hole saturation and intelligence as local admissible selection, and presents a restructured conclusion emphasizing irreversible structural stabilization. This version replaces the earlier formulation of admissible trajectory contraction with a more precise account of irreversible structural reduction. -------------------------------------------------------------------------------------------------------------------------------- This paper proposes an interpretive framework, referred to as Ω-dynamics, in which physical evolution is described as a monotonic reduction of an accessible possibility space through irreversible event fixation. In this framework, an event is defined as an irreversible selection among available alternatives, and the cumulative history of a system is characterized by the progressive constraint of its remaining possibilities. Time is not treated as an independent physical dimension, but rather as an ordering parameter that indexes the sequence of irreversible reductions of the possibility space. Entropy is correspondingly interpreted as a logarithmic measure of the remaining accessible possibilities, establishing a direct conceptual correspondence with information-theoretic entropy and the minimal entropy cost of irreversible operations as formalized by Landauer’s principle. Spatial structure is interpreted as the geometric organization of residual possibilities after event fixation, rather than as an a priori background manifold. Within this view, large-scale gravitational structure is discussed qualitatively as arising from inhomogeneous distributions of accumulated events, while black holes are treated as limiting configurations in which dynamically accessible possibilities are effectively exhausted. These interpretations are intended to remain compatible with established entropy bounds and observational descriptions, without introducing new forces, particles, or dynamical equations. Ω-dynamics is not proposed as a unified field theory. Instead, it provides a higher-level structural lens through which time, entropy, irreversibility, and spatial organization can be jointly interpreted. (v1.1) Minor clarifications have been made to improve mathematical precision and structural articulation.The formal content remains unchanged.