The Operator Formalism of Geometric Homeostasis: Derivation of the Vacuum Piezoelectric Effect and Solar Stiffness Modulation

We formulate the Axiomatic Physical Homeostasis (APH) framework within the lan-guage of Source Theory. We define the Associator Hazard A(x) not as a classical scalar,but as a quantum operator acting on the vacuum persistence amplitude. We derive theeffective interaction Lagrangian coupling this geometric source to the electromagnetic field,identifying a “Piezoelectric Vacuum” effect with coupling strength κAP H ∼ O(1). Finally,we derive the annual frequency modulation of the predicted 1.81 GHz signal due to thevariation in local vacuum stiffness induced by the Solar gravitational potential.