Fermion generations as standing wave nodes on a boundary Lagrangian

Third paper in the boundary wave framework series. Proposes that the three fermion generations arise as nodes of standing waves sin(Nπx) on an internal flavor coordinate, where N = 2P+1 and P counts gauge poles. A boundary Lagrangian with Dirichlet (left-handed) and Neumann (right-handed) conditions produces the standing wave as its equation of motion. Cross-sector span ratios (5/3 and 6/5) yield predictions for m_τ and m_u from three measured masses. Neutrino mixing angles emerge from charged lepton wave geometry corrected by generation-2 node shifts in the C₀ = 1/5 hierarchy. Produces 18 observables from 4 measured inputs and 5 structural postulates. ---Boundary Wave Framework Series (all submitted to Physical Review D):1. One formula for all fermion masses — https://zenodo.org/records/195787572. Decoherence spectrum of the Standard Model — https://zenodo.org/records/195787963. Fermion generations as standing wave nodes — https://zenodo.org/records/195788674. Electroweak masses and CP violation — https://zenodo.org/records/195789295. Strong sector, confinement, and hadron masses — https://zenodo.org/records/19579136