Part 6A: Structural Derivation of the H4 Interface Baseline - From Icosahedral Local Channels to the Four-Dimensional Golden-Ratio Measure

Part 6 of the Origin Geometry (OG) program introduced the geometric interaction hierarchy baseline I_int = 20ϕ⁴ ≈ 137.082039, where ϕ = (1 + √5) / 2 is the golden ratio. In Part 6, this quantity was presented as a candidate structural baseline arising from effective local interaction connectivity and four-dimensional volumetric participation in discrete H₄ geometry. The present Part 6A strengthens that argument by isolating the precise geometric assumptions under which 20ϕ⁴ follows as a conditional structural theorem rather than a post-hoc numerical selection. We show that the coefficient 20 arises from the local icosahedral vertex figure of the 600-cell: the nearest-neighbour shell of each H₄ vertex has the combinatorial structure of an icosahedron, whose twenty triangular faces define the natural local interface-channel count when interaction is treated as boundary-mediated geometric flux. We then show that the fourth power (ϕ⁴) is the four-dimensional measure factor associated with locally isotropic golden-ratio scaling on the H₄ substrate. The exponent 4 is not selected for numerical proximity to any physical constant; it is selected by the minimal complete support dimension of the pre-dynamical H₄ interface process. The result is not a derivation of the fine-structure constant. Rather, it establishes I_int = 20ϕ⁴ as a structurally preferred H₄ interface baseline, numerically close to the low-energy inverse fine-structure constant. This Part therefore clarifies the mathematical status of the 20ϕ⁴ expression and distinguishes it from both arbitrary numerology and completed quantum-electrodynamical derivation.