The Conformal Universe

This paper introduces Harmonic Relativity, a conformal framework in which physical systems across nuclear, planetary, galactic, and cosmological scales are organized by a single φ‑rung ladder. By replacing the geometric factor π in action integrals with the algebraic invariant φ² at self‑similar critical scales, the theory predicts discrete preferred radii, energies, orbital distances, rotation‑curve boundaries, and cavity modes. We map Ca/Sn/Pb isotopic chains, Solar‑System semi‑major axes, ultra‑diffuse galactic rotation curves, and 21 cm cavity spectra onto the same rung hierarchy, recovering magic‑number kinks, asteroid‑belt and Kuiper dead zones, the 29 kpc galactic conformal boundary, and the Einstein‑desert angular window. The result is a single, cross‑scale architecture with ten falsifiable predictions spanning femtometers to megaparsecs.