A Residual-Holonomy Candidate Derivation of the Inverse Fine-Structure Constant in the Fractal Consistency Law

This paper develops a candidate derivation of the inverse fine-structure constant within the Fractal Consistency Law (FCL/LCF). The proposal interprets electromagnetic coupling as an effective residual-holonomy stiffness of a fractal relational substrate. The central claim is not that the result is already a completed proof accepted by standard physics, but that the formula is theoretically constrained before numerical comparison. The derivation fixes the triadic factor from the minimal non-degenerate holonomic closure, fixes the correction exponent from the quadratic curvature structure of the holonomy functional, fixes the numerator by the Principle of Minimum Inconsistency, and fixes the holonomic channel count by a matter-photon closure rule. The resulting expression is α_LCF⁻¹ = 8√3π²(1 + 1/(50π²)) = 137.034378315548. Using the CODATA/NIST recommended value α⁻¹ = 137.035999177(21) only after the derivation, the relative error is 1.1828 × 10⁻⁵. A pre-registered audit with fixed k = 3, q = 2, c = 1, and s = +1 selects N = 50 as the best integer in 1 ≤ N ≤ 500. Additional adversarial and restricted tests are reported to assess numerological risk. The manuscript concludes that the result is a strong FCL-internal candidate derivation, not yet a final external theorem.