This paper presents a zero-parameter consequence for the fine-structure constant (α) from the topological and information-geometric properties of a single Oloid manifold, under one explicitly stated physical postulate.Within the Information-Geometric Phase-Structure (IGPS) framework, we introduce the Distinguishability Coupling Principle: the postulate that the strength of the electromagnetic interaction is the operational distinguishability of the coupled charge sectors. Rather than positing the metric, we show that the Fisher—Rao form, the Bures metric, and the linear (length) accumulation are consequences of this principle — via the Chentsov—Petz classification (given a charge-preserving coarse-graining assumption), quantum measurement theory (Cramér—Rao bound), and the scale-freeness of the gapless seam CFT.Key Findings:The closed-form result: The geometric tree-level value and a self-consistent one-loop (Dyson) correction give:1/α = 8√3π² + (12 + 1/2π)πα ≈ 137.036The principal evidence is the tree term, which reproduces 1/α to 0.2% with no inputs; because it supplies 99.8% of the total, the geometry-fixed stiffness sits on a knife edge (correct to ~0.02%). The full relation matches CODATA to 3 × 10u207bu2076, though this figure is a low-sensitivity test of the correction coefficient rather than a high-precision one.No-Go Theorem for the quadratic count: In a scale-free 2D free-boson CFT (c=1), a dimensionless distinguishability count must be a Riemannian length (linear in the field), definitively excluding the energetic/quadratic (237) reading.Two-loop exactness: The O(α²) correction vanishes identically via the Schwinger-model exactness of the vacuum polarization, so no higher-order truncation is dropped.Structural by-products: The framework relates the Standard Model's colour and generation multiplicities (Nc = Ngen = 3) to one Z3 of the trefoil seam, via the Alexander polynomial — modulo one flagged Standard-Model-to-seam identification.Epistemic Status:We carefully separate what is rigorously derived from what remains a stated geometric primitive (the Fisher root √F = √3π and the discretization scale enter as primitives, not derivations). Every numerical ingredient — the phase area (8π), the contact-line modulus (√3), the WZW vertex (12), and the APS index term (1/2π) — is established independently in earlier IGPS papers without tuning against α. The tree-level weak mixing angle sin²(θ_W) = 1/4 lands 8% from experiment and is flagged as open. The framework's absolute mass scales remain open, requiring one external dimensionful anchor (akin to Λ_QCD and v in the Standard Model).