Schrödinger Correspondence within the ρₜ–k Continuum Framework

<p>This work derives the Schrodinger equation as the quantum-limit envelope of the Physical Time (rho_t–k) continuum. Starting from the rho_t–NSB field equations, the Lyapunov functional yields the Time-tension term T[rho_t]; in the irrotational, dissipation-free limit, the system maps exactly to the Schrodinger equation via the Madelung transform. This demonstrates that quantum evolution arises as the linear transport of the Time-density medium, unifying the rho_t–k continuum with the standard quantum formalism.</p>