Overview Part 6 of the Origin Geometry (OG) program introduced the geometric interaction hierarchy baseline Iint = 20φ⁴ ≈ 137.082039, where φ = (1+√5)/2 is the golden ratio 6. 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. Geometric Basis of the Baseline 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. Mathematical Status and Scope The result is not a derivation of the fine-structure constant. Rather, it establishes Iint = 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.
The Duy Tan Truong (Tue,) studied this question.