Planck-Scale Mass Quantization of the Earth: The 108 Harmonic and Geodetic Corollaries

This paper investigates the relationship between the Earth's mass, when expressed in Planck units, and fundamental geometric constants. We demonstrate that the base-2 logarithm of the Earth's mass in Planck masses yields a value of 107.7579. This value converges on the 108 harmonic, a constant associated with pentagonal geometry and the Golden Ratio (\phi). We propose that the 0.2421 deviation from perfect integer 108 is a direct consequence of the Earth's rotational oblateness and gravitational binding energy. Furthermore, we establish a mathematical correlation between this 108 harmonic, the 72° geodetic spacing observed in global tectonic shear lines, and the 1080° temporal precessional cycle.