Gauge Couplings in the Absolute Frame Theory: Derived Ratios, Geometric Left–Right Breaking, and the Induced-Coupling Boundary

Version of July 9th, 2026, based on technical development within the Absolute Frame Theory programme. The Absolute Frame Theory (AFT) derives the Standard-Model gauge group as topological data of an embedding X: M → A of the observable four-dimensional manifold into a flat fourteen-dimensional Euclidean substratum (N=14=4+10), the ten normal directions carrying an internal SO (10). We analyze the gauge-coupling sector of that construction and sort it, with marked epistemic status, into what is derived and what is not. Three results follow. First, AFT derives the coupling ratios and the weak mixing angle sin²θW = 3/8: because the full Standard-Model group descends from the single simple normal SO (10), the three couplings unify to one, and the surviving freedom is a single dimensionless number. Second, the scalar content is fixed by the embedding itself—the normal fluctuation field is the 10 of the normal SO (10), a Standard-Model Higgs bidoublet plus a color sextet—leaving AFT with no fundamental 126-type left–right order parameter; SU (2) R is a proper internal Pati–Salam factor of SO (10), broken at an intermediate scale, and the left-handedness of the weak interaction is correlated with the spacetime chirality through the Spin (14) frame-spinor. Third, we treat the unified-coupling value as an induced (composite) coupling. Below the substratum scale it runs with the full asymptotically-free beta function, but its boundary value is the finite induced coupling, which is logarithmically—not power—divergent, because the substratum is flat and the charged interface modes are a finite confined set rather than a Kaluza–Klein tower. The value gGUT is therefore renormalization-scheme dependent and not derivable from observations confined to M; it is identified by measurement, like the substratum constants of the gravitational and cosmological sectors. The gauge structure is derived; the gauge-coupling value is boundary data. This sharpens the programme's derivability boundary: the quantities AFT cannot derive include not only symmetry-orbit labels but ultraviolet-sensitive renormalizable couplings, the openness of the latter tracing to the flatness of the substratum.