Paper 81 Deriving the Fine-Structure Constant from Boundary–Bulk Recursion in the Triadic Holosphere Lattice

We present a first-principles mechanism that links the electromagnetic fine-structure constant (alpha) to a geometric fixed point in a triadic SU(2) “holosphere” lattice. The construction has two ingredients: (i) a boundary-to-bulk neutrality condition on three oriented boundary phases that selects a unique stationary shell index n*, and (ii) a healing threshold that equates the percolation-limited mismatch cost to twice the coupling, thereby setting the absolute scale. Using arbitrary-precision numerics (50-digit, Brent bracketing with Newton polish; neutrality residual < 1e−50) we find n* ≈ 267.3456789 and a pre-polyhedral prediction alpha* ≈ 0.007297352096 (alpha*−1 ≈ 137.036007978). A small, geometry-derived polyhedral factor f_poly = 1 + delta_0 (isotropic mean from the 12 required pentagonal disclinations on the sphere) multiplies this scale. With the working value f_poly = 1.002 the prediction deviates from CODATA at the ~0.2–0.3% level; the factor that would match CODATA essentially exactly is f_poly ≈ 1.000000064, well within the expected geometric window. The framework is falsifiable: ablations that change the transport exponent (beta ≠ 3/2), break the triadic selection set, or remove neutrality either destroy the admissible root or push alpha far from the laboratory value. We outline a companion study that resolves directional (anisotropic) corrections f_poly(n̂) and their experimental signatures. No curve-fitting to alpha is used; all constants are inherited from lattice geometry and transport.