One formula for all fermion masses: boundary wave theory from N_c = 3

We present a unified framework for the charged fermion masses and flavor mixing parameters, built from five postulates rooted in gauge topology and a single measured input: the number of quark colors N_c = 3. A universal mass formula on a one-dimensional boundary x in [0,1] with standing wave modes sin(N pi x) yields all nine charged fermion masses at 0.22% RMS with one measured anchor (m_tau). The coupling ladder g(q) = exp((q-1) T_F) follows from the SU(3) fundamental index T_F = 1/2. The CKM matrix is derived from quark mass ratios (Paper 2), all three PMNS mixing angles from charged lepton geometry (Paper 3), and the framework produces a complete scorecard of 22+ observables from 4 measured inputs.