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

In Holosphere Theory, coherence is transported across a discrete, rotating angular lattice. This work shows that the percolation exponent β = 3/2—introduced in Paper 21 for galaxy rotation-curve modeling—is not a tunable fit knob, but a system-level geometric constant selected by the transport stack itself. We motivate β = 3/2 from first principles through three independent derivation tracks: (1) RMS scaling inherited from nested-shell sourcing with surface-area dilution, (2) SU(2) triadic interference requirements that enforce a finite constructive-alignment window across three channels, and (3) conservation of a tensor-valued coherence current J^μ constructed from the angular-strain field ε_strain. We then operationalize the claim with a program-generated KPI phase-boundary experiment. Using a local gate-plus-repair corridor policy, the model produces a sharp survival boundary in the (r_s, θ) plane, captured by knee KPIs r_50, r_10, and a directional knee field r_50(θ). A controlled sweep over β reveals three distinct regimes: (i) over-permissive transport, (ii) collapse-like gate failure, and (iii) a marginally stable phase where the boundary is sharp, bounded, and directionally structured. The KPI signature in this marginal phase pins β = 3/2 as the phase-locking exponent consistent with the declared triadic admissibility rule. Overall, the results elevate β = 3/2 to a universal transport signature for three-dimensional angular-coherence systems, with downstream implications across gravitational, cosmological, and quantum-analog domains.