Full-Scale Empirical Proof of the Dynamic String Force Formula:Unified Log-Periodic Oscillations from Microscopic Quarks toCosmological Planetary Orbits

This paper reports an empirical discovery spanning nearly 30 orders of magnitude: the log-periodic oscillation predicted by the Dynamic String Force Formula is simultaneously detected in three completely independentphysical systems: (1) microscopic high-energy scattering data of the proton structure function from HERA ZEUS; (2) four sets of classical fluid mechanics wake experiments (flow around a cylinder, aircraft wingtip vortex, shipwake, turbulent free shear layer) ; (3) orbital radius distribution of the eight planets in the solar system . Independent fittings of the three datasets all show a stable characteristic frequency ω ≈ 0.75, goodness-of-fit χ 2/ndf allclose to 1.0, and statistical significance ranging from 7.4σ to 8.3σ, all far exceeding the 5σ discovery standardin particle physics.This cross-scale and cross-system consistency and symmetry in eigenfrequency indicate that the DynamicString Force Formula is not merely an empirical fitting tool, but a direct mathematical expression of the cosmicenergy string structure. This paper also briefly describes the theoretical construction logic of the formula: basedon the static string force framework, it integrates fractal quantization of the Fibonacci sequence, spiral phasemapping of Euler’s formula, and scaling self-similarity of the Mandelbrot set, with a phase-transition criterionbetween particle states and energy eigenstates at the Planck scale.