φ-Power Scaling in Rotationally Coherent Systems: Dimensional Correspondence and Relational Depth

This technical note examines the appearance of φ-power scaling in dimensionless geometric ratios extracted from rotationally coherent, vortex-dominated systems. Using standard Kerr black hole geometry and representative rotational flow ratios from the Solar System, we identify consistent correspondences in which powers of the golden ratio φ align with the physical dimensionality of the associated observable (length, force, volume, pressure). The analysis is restricted to dimensionless quantities and does not introduce new constants or modifications to General Relativity.

The results are interpreted within a framework in which logical geometry and system dynamics jointly govern physical behavior, while φ appears as a recurring geometric index that highlights regimes of efficient recursive coupling. In this sense, φ does not generate physical quantities but serves as a marker for coherent structural organization, with the exponent of φ indicating the number of coupled interaction layers, or relational depth. A clear separation is maintained between informational thresholds (√e), physical structural scaling (φ), and an operational coherence corridor centered near λ ≈ 1.7. No claim of universality is made; rather, the observed scaling regularities motivate further tests in other vortex-like systems, including planetary atmospheres and galactic flows.