Fractal Scale Dynamics (FSD): A Unified Framework for Quantum, Planetary, and Galactic Systems without Dark Matter or Dark Energy"

We introduce Fractal Scale Dynamics (FSD), a scale-invariant geometric framework that describes rotational motion across more than 15 orders of magnitude — from atomic nuclei to galactic superclusters — without invoking mass, dark matter, or dark energy. The theory is built on a single, unifying equation: r_n = k · n^{D_F} · e^{γ(n-1)} where: - r_n is the characteristic radius of an orbit or rotation, - n is a continuous quantum number (the "Time Numerator"), - D_F is the local fractal dimension of spacetime, - γ is the rate of change of the fractal dimension, and - k is a scale constant. We show that: 1. The fractal gradient ∇D_F = -γ/r generates effective forces equivalent to gravity, inertia, and friction. 2. Mass is replaced by wave frequency via the De Broglie-Einstein relation (E = hν). 3. Planetary orbits are reproduced with 0.83% error for Earth. 4. Galaxy rotation curves are explained without dark matter (γ ≈ 0.40). 5. Axial fan flow profiles match PIV measurements at the phase-transition point r/R ≈ 0.325. 6. Heavy metal spectra (Uranium) show a predicted ~1 eV shift, measurable with current X-ray spectrometers. 7. Falsifiable weather predictions are provided for Athens and Cape Doro (2, 10, and 18 July 2026). The dimensionless constant γ ≈ 0.35 ± 0.05 appears invariant across all scales, suggesting that fractal geometry, not mass, is the fundamental source of all rotational dynamics. This work offers a new mathematical foundation for unifying quantum mechanics, astrophysics, and continuum mechanics under a single principle. All data and methods are fully documented. The predictions are time-stamped and falsifiable. This preprint is intended for open peer review and discussion.