The Heegner Kernel and the Pion as Boundary Probe: Yukawa Structure and Hadronic Scale from a Rank-5 Projection

A non-invertible rank-5 projection of a five-dimensional Majorana bulk field onto an observable four-dimensional boundary selects five admissible modes N_adm = {2,3,5,7,11}, four of which are Heegner numbers. The nine Heegner discriminants partition uniquely into three sectors: a boundary sector, a kernel sector H_ker = {19,43,67}, and the terminal discriminant 163. This tripartition identifies exactly three charged-lepton generations without free parameters. The kernel sector indices serve as generation labels. The relative charged-lepton mass hierarchy mμ/me and mτ/me is derived structurally from the Fibonacci transport amplitude and the beat theorem σ₊ − σ₋ = 1/2. Absolute masses follow conditionally on the Rydberg anchor R∞. The same projection yields the electroweak vacuum v_EW = 246.20 GeV and the Fermi constant G_F = 1.1666 × 10⁻⁵ GeV⁻², both conditional on R∞. As a precision consistency test, the pion decay constant F_π = 130.065 MeV is obtained at −0.10% from PDG without adjustable parameters. The derivation does not replace the QCD derivation of F_π. The axial-current matrix element and the CKM transporter remain open.