Deriving the Scalar Field and Conformal Dynamics in NUVO Theory - Part 1 of the NUVO Theory Series

Building on the framework established in the pre-print From Newton to Planck: A Flat-Space Conformal Theory Bridging General Relativity and Quantum Mechanics, this paper treats the NUVO scalar conformal factor lambda(t, r, v) as a fundamental dynamical field. We derive its governing Lagrangian, formulate the Euler--Lagrange equations, and compute the corresponding energy--momentum tensor. The scalar field is shown to influence inertial response, proper time, and local energy distribution through its velocity and position dependence. A minimal coupling scheme to matter is introduced, along with the inertial concepts of pinertia and sinertia, which distinguish the scalar’s effects on different motion regimes. We demonstrate that lambda behaves as a coherent geometric modulator of physical observables and propose that it acts as the generator of a self-consistent flat-space geometry. This work establishes the scalar field’s foundational role in NUVO theory and prepares the ground for its covariant extension and application to general relativistic phenomena in subsequent papers.