TUF Layer 3 — The Spectral Coupling Coefficient: Derivation of c = −2/nμ from the Degeneracy of DΞ in A4

The Floriano Unified Theory (TUF) predicts fermionic masses via the spectral Dirac operator DΞ = D_Z9 ⊗ I23 + I9 ⊗ D_Z23 over the atemporal hyperspace Ξ. In Layer 2 the muon error was reduced from 0.112% to 0.0016%. A residual coefficient c ≈ −0.009888 multiplying the coupling operator S⊗S persisted. In this Layer 3 we derive this coefficient from the algebraic structure of A4: the degeneracy of DA4,9 at λ₀ = −√3/2 with multiplicity 2 generates two sectors under S⊗S, with exact Clebsch–Gordan coefficients CG3A = −1/3 (antisymmetric) and CG3S = +5/9 (symmetric). The muon belongs to the 3A sector. The topological quantisation condition yields c = −2/207. With this single derived coefficient and zero free parameters, the muon error falls to 0.0000348% and the tau error to 0.0000377% — a combined improvement of more than 3000× over Layer 1. A Python verification code is included in Appendix B. This paper is part of the TUF series:- Paper 0 (Ontological Foundation): https://doi.org/10.5281/zenodo.19024705- Paper 1 (Fermion masses): https://doi.org/10.5281/zenodo.18988060- Paper 2 (Three generations): https://doi.org/10.5281/zenodo.18991190- Paper 3 (Dark matter): https://doi.org/10.5281/zenodo.18991306- Paper 5 (Cosmological constant): https://doi.org/10.5281/zenodo.19024913- Paper 6 (Spectral fixed point): https://doi.org/10.5281/zenodo.19025379- Paper 7 (Atomic spectra): https://doi.org/10.5281/zenodo.19025651