Non-Relativistic Reduction of the Existence Equation and Observable Deviations from the Gross-Pitaevskii Limit

Evidence Paper VII of the Existence Equation series The Gross–Pitaevskii equation has governed the theory of macroscopically coherent matter fields for over sixty years. Its nonlinear term g|φ|²φ is introduced phenomenologically — as the mean-field limit of contact scattering in dilute gases, as the BCS condensate amplitude in superconductors, as a self-coupling postulated by the physics of each application domain. The Mexican-hat vacuum structure implicit in GP is not derived within GP itself. It is imported. This paper inverts the hierarchy. The Existence Equation [1] contains the condensate structure as a primitive: the Mexican-hat potential V(A) = −(λ/2)A² + (α/4)A&sup4; is inherent to the theory's action,…