Mapping of the Golden Angle Symmetric Envelope Interface Chain to the Fine-Structure Constant on Its Sub-Envelope Surface

Within the cross-layer mapping framework of the Symmetric Envelope Interface Chain, this paper studies how the Golden Angle Symmetric Envelope Interface Chain (parent layer) maps its structural properties to the sub-envelope surface (physical world), manifesting as the fine-structure constant α. The parent layer is the Golden Angle Symmetric Envelope Interface Chain, with its growth rate fixed to b_golden = ln(φ)/(2π), corresponding to the golden angle. The parent layer calls forth the child layer through the bridge variable Λ(t), and the child layer reads with its own ruler lp and frequency f_max. This paper proves that the golden angle structure of the parent layer is mapped to the fine-structure constant α in the child layer, with the expression: α = (E_e · λ_e) / (4π · ħ · c) = (x / (4π)) · (c / v) On Earth's projective layer, x = 2π, v = 1.093845 × 10⁶ m/s, hence α = 137.036. The child-layer observer cannot read the parent layer's b_golden, but only reads α as a "fundamental constant." Keywords: Golden Angle; Symmetric Envelope Interface Chain; fine-structure constant; cross-layer mapping; projective layer; bridge variable; sub-envelope surface