Part 2: Emergent Dimensionless Ratios from Discrete Four-Dimensional Geometry

Overview We investigate whether discrete four-dimensional geometric structures can generate stable dimensionless baselines prior to the introduction of dynamics. Within the Origin Geometry (OG) framework, physical constants are not assumed to be primitive numerical inputs. Instead, they are interpreted as possible effective remnants of deeper geometric and topological relations that survive coarse-graining from a higher-dimensional substrate to an effective three-dimensional description. Scope and Objective The present paper is intentionally pre-dynamical. It does not introduce field equations, quantization rules, renormalization flows, elastic dynamics, or phenomenological fitting procedures. Its purpose is narrower: to determine whether discrete four-dimensional geometry can contain intrinsic combinatorial constraints capable of producing nontrivial dimensionless structure before any physical interaction is specified. Methodology We argue that boundary faces, rather than vertices or edges, provide the natural carriers of geometric flux and interaction capacity in a discrete cell, consistent with the boundary-mediated character of physical flux, surface integrals, and area-based constraints in established physics. We then identify highly isotropic regular four-dimensional polytopes, especially the 600-cell, as representative structures for studying dimensionless geometric baselines under coarse-graining. Central Result The central result is not the numerical derivation of any observed physical constant. Rather, it is the identification of a structural mechanism by which dimensionless ratios may arise from topology, dimensionality, boundary capacity, and coarse-graining alone. Any later comparison with measured constants requires additional dynamical corrections, screening effects, and physical interpretation. Part 2 therefore establishes a static geometric baseline upon which subsequent dynamical and phenomenological developments may be constructed.