A Static Carrier Construction for the Low-Energy Fine-Structure Constant in Recursive Interval Geometry
Abstract
A static carrier construction for the low-energy, zero-momentum fine-structure constant is formulated within Recursive Interval Geometry (RIG). The carrier hierarchy is fixed before numerical evaluation by four requirements: discrete minimal closure, space-filling compatibility, boundary recursion, and nonzero boundary-state recursion. Each free boundary variable has two states, active or silent. The link has two freely variable endpoints, the triangle has three freely variable edges, and the octahedron has eight triangular faces with one whole-shell closing relation, leaving seven freely variable faces. Thus \( b_1=2 \), \( b_2=3 \), and \( b_3=7 \), and exclusion of the all-silent state gives \( D_1=3 \), \( D_2=7 \), and \( D_3=127 \). Adding the three level counts gives the skeleton \( N_{\mathrm{sk}}=137 \), while choosing one state from every level gives the joint boundary-state resolution \( \Omega=D_1D_2D_3=2667 \). The localized base ring organizes this recursive arithmetic skeleton; the exact physical state is its continuous geometric readout in the real metric completion of the depth-one principal/structural space. The structural sector is built from three dimension-filtered terms in this continuous readout. Pairing-sphere geometry gives an exact null locus for the oriented link readout; the centre-preserving antipodal branch supplies the phase holonomy \( \pi \) and a two-endpoint support loss \( -2 \). The octet-truss completion locks the pairing circle to four…
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