Paper 24: The Holosphere Percolation Exponent β = 3/2

In Holosphere Theory, angular coherence spreads through a rotating, three-dimensional lattice of discrete units called Holospheres. This paper shows that the exponent β = 3/2, used previously to match galaxy rotation curves without dark matter, is not a fitted parameter but a universal geometric constant. We derive β = 3/2 from first principles using three independent methods: statistical coherence dilution across nested shells, interference constraints from triadic spin symmetry, and tensor-based conservation of angular strain. We demonstrate that this exponent governs a wide range of phenomena, including galaxy rotation, redshift brightness decay, filament density profiles, and cosmic void edges. A minimal simulation confirms that β = 3/2 defines the boundary between runaway coherence and collapse. These findings suggest that β = 3/2 is a universal law of three-dimensional angular coherence, applicable across gravitational, cosmological, and quantum analog systems.