From Phase-Spatial Closure to Einstein–Cartan Dynamics Global Frame Non-Closure and the Conditional Selection of the Tetrad–Palatini Action

Abstract

This paper develops a gravitational extension of phase-spatial invariance in which relativistic geometry is not assumed as the primitive arena of physics. The construction begins with the generator structure and with a real, homogeneous, rotationally invariant closure scalar on the carrier. In the antecedent phase-spatial construction, the null class identifies the invariant conversion modulus , while the automorphisms of recover Lorentz symmetry and the coordinate-dual Minkowski structure. The present paper asks what follows when this local closure architecture is allowed to vary from point to point. Keywords: phase-spatial closure; Einstein–Cartan gravity; tetrad–Palatini action; Lorentz invariance; invariant light speed; tetrad; Lorentz connection; curvature; torsion; frame transport; gravitational foundations; action selection