The Panvitalistic Theory (PVT) replaces the external time parameter and the irrational number \(\pi\) of standard physics with internal angular curvature \(\pi \equiv T/L\) and a single rational length scale. Physical reality is described by continuous 6-dimensional volumes, while all measurements are strictly rational comparisons \(V_A = x V_B\) with \(x \in \mathbb{Q}\). Dynamics are governed solely by the volume-invariance constraint \(\delta V = 0\).

 

In this work we derive Einstein's field equations directly from these axioms using the complete set of twelve volume operators obtained from the discrete comparison chain of the intrinsic variation principle. Each link corresponds to a comparison pair; canonical momenta are derived via a discrete Legendre transform, and \(\delta V = 0\) is imposed as a Dirac constraint on link space. Gauge fixing of the constraint yields an effective 4-dimensional description in the limit of maximal orthogonality. We explicitly verify that both the Newtonian limit and the Schwarzschild geometry emerge consistently, with singularities resolved into finite angular boundaries. The derivation eliminates the problem of time and the quantum-gravity incompatibility at the axiomatic level while reproducing all classical predictions of general relativity.