The Spectral Anatomy of the Buffer: Deriving the Flavor Hierarchy from the Vacuum Persistence Amplitude

We reformulate the Axiomatic Physical Homeostasis (APH) framework within the lan-guage of Source Theory. We demonstrate that the “Geometric Buffer Potential” Vbuf f eracts as a non-perturbative modification to the fermion self-energy operator Σ(p). We derivethe modified inverse propagator and show that the logarithmic form of the buffer poten-tial induces a spectral splitting of the single-particle Green’s function. In the Weak BufferRegime (κ < 1/8), the propagator develops exactly three stable poles, corresponding to thethree generations of fermions. We calculate the residues Zi of these poles, interpreting themas the origin of the mixing matrices. Finally, we derive the “Geometric Zeno Effect” as akinematic suppression of the decay width Γ, resolving the neutron lifetime anomaly.