Geometric Origin of the Fine-Structure Constant from a Unified Substrate Framework

Unlike QED, which takes both the integer 137 and the dressing structure from experiment, this work derives the fine‑structure constant from first principles using the two‑channel causal substrate defined in the CARD framework. The geometric structure of the rate‑tracking equations fixes the bare interaction factor at 2/137 through two independent derivations, identifying 137 as the substrate's discrete coordination bound. CARD‑III then supplies the finite angular update rate of the transverse channel, introducing a deterministic latency parameter whose quadratic contribution produces the observed dressing of the coupling. Injecting the hydrogenic ground‑state velocity into the CARD‑III update law yields the correct dressed value, reproducing the empirical inverse fine‑structure constant 137.035999084. The result separates the coupling into a geometric invariant and a single empirical dressing coefficient, showing that α is a geometric partition of the substrate's finite coordination bandwidth.