A Scale-Explicit Geometric Framework for the Foundation of Mass, Density, and Effective Light Speed

This paper introduces a pure Euclidean geometric framework demonstrating that standard physicsimplicitly operates under the assumption of a globally constant scale baseline (w = 1) and afixed coupling strength (v = 1). By lifting these restrictions, we construct a scale-explicit baselineparameterized by two dimensionless ratio factors – the scale context (w) and the degree of coupling (v)– defined strictly over the observed system as a unified physical entity. Under these metrical definitions,mass, density, and the effective speed of light are not intrinsic constants, but emergent quantitieswhere the coupling ratio (v) determines effective density and the scale ratio (w) regulates volumetriccapacity, forcing the effective speed of light into scale-demonstrable behavior in extreme regimes.From this geometric baseline, we demonstrate that gravitational fields, scalar field acceleration,orbital equilibrium velocity, time dilation (positional and kinetic), and orbital mechanics emergedirectly as 3D geometric manifestations of scale variations (w). The model is empirically validatedacross both mesoscopic satellite telemetry (LEO, MEO, GEO) and macroscopic galactic velocityprofiles, where flat rotation curves and their associated centripetal acceleration profiles emergedirectly from localized scale variations (w), resolving the galactic mass discrepancy purely throughspatially varying radial field geometry.