Reformulated Homogeneous Compression Theory: Kinematics, Effective Gravitation, and Multi-Scale Consequences

This work presents a reformulated version of the Homogeneous Compression Theory, a theoretical framework in which time, gravitation, and large-scale cosmic phenomena emerge from a universal microscopic compression process acting on matter. In the revised formulation, space itself is not compressed; instead, matter evolves along a hidden compression direction that is not directly observable in three-dimensional space. Observed time is interpreted as the macroscopic manifestation of this universal compression flow. As matter progresses along this hidden direction, it leaves a geometric trace whose projection into observable space generates the effective gravitational field. This trace is modeled as a damped logarithmic spiral structure whose geometry is naturally related to the golden ratio. From this structure the theory derives an effective gravitational potential consisting of a Newtonian term plus a logarithmic correction. This modification produces flat galactic rotation curves without introducing dark matter as a separate particle component. The same framework yields an equivalent density profile proportional to 1/r², consistent with observed large-scale gravitational effects. The model also predicts an enhancement of gravitational lensing that is directly tied to the same trace mechanism responsible for the rotation curve behavior. At cosmological scales, the universal compression rate produces an apparent redshift law that mimics the Hubble expansion, suggesting that part of the observed cosmological expansion may arise from the evolution of microscopic physical scales rather than the expansion of space itself. The work also outlines a minimal microscopic sector for the proton–electron interaction and identifies the precise location where a fundamental derivation of the atomic coupling constant should emerge within the theory. While some numerical structures involving the fine-structure constant appear suggestive, they are presented here as exploratory observations rather than final derivations. Overall, the reformulated theory provides a unified geometric interpretation linking microscopic compression dynamics with gravitational phenomena across atomic, galactic, and cosmological scales.