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We present a limited static-sector construction for the low-energy fine-structure constant within Recursive Interval Geometry (RIG). The recursive substrate itself is not reaxiomatized here; the inherited input is only the canonical principal/structural splitting together with the Ω-weighted norm. The paper introduces four principles: minimal closure with nonempty-state counting, a link–triangle–octahedral carrier hierarchy in one to three dimensions, a display-level readout principle, and a dimension-filtered expansion of the raw structural term. From these assumptions one obtains \( D_1=3,\;D_2=7,\;D_3=127 \), interpreted as nonempty boundary-state counts on minimal one-, two-, and three-dimensional carriers, hence the additive skeleton \( N_{\mathrm{sk}}=137 \) and the multiplicative resolution Ω=2667, together with the display-level form \( \alpha^{-1}=\sqrt{N_{\textup{sk}}^2+\Omega^2\ell_{\textup{raw}}^2} \) . What is not yet absorbed into deeper internal structure is reduced to three residual bridge coefficients in \( \ell_{\textup{raw}}=a_1/\Omega+a_2/\Omega^2+a_3/\Omega^3 \), which are taken in the working model to be \( a_1=\pi \), \( a_2=-2 \), and \( a_3=137+127/2 \). Their strongest current geometric readings are, respectively, the metric normalization of the minimal closed loop, the endpoint subtraction produced when an open interval is closed into a loop, and the sum of the full static skeleton with a third-level shared skeletal load. This yields \( \alpha^{-1}_{\mathrm{RIG}}=137.035999176253147\cdots \), differing from the 2022 CODATA recommended value by \( 7.47\times10^{-10} \) in \( \alpha^{-1} \), or \( 5.45\times10^{-3} \) ppb. The claim is therefore not that quantum electrodynamics has been derived, but that a logically explicit substrate model can be tested as a falsifiable interface proposal.