The Panvitalistic Theory (PVT) currently employs two formally incompatible descriptions of the twelve volume operators. In the quantum-theoretic formulation they arise as the \(6+6\) degrees of freedom of a comparison pair \(V_A = x V_B\) acting on the tensor-product space \(\lvert V_A\rangle \otimes \lvert V_B\rangle\). In the general-relativistic formulation the same operators are treated as a phase-space structure (six coordinates plus six conjugate momenta) of a single volume element.  

 

This paper resolves the inconsistency by constructing a unified canonical algebra directly from the discrete comparison chain of the intrinsic variation principle. We show that each link of the chain corresponds to a comparison pair, introduce the natural basis change to center-of-mass and difference coordinates, and derive the canonical momenta via a discrete Legendre transform. The volume constraint \(\delta V = 0\) is implemented as a Dirac constraint on link space. Gauge fixing of this constraint is identified with the measurement postulate of the quantum-theoretic picture.  

 

The resulting projected algebra reproduces the correct canonical commutators, eliminates an ad-hoc \(\sin\theta\) factor from the fundamental brackets, and replaces an inconsistent coordinate--coordinate commutator by the explicit discrete constraint identity. The construction preserves rationality of the comparison factors \(x_n\) and yields a structurally coherent foundation for both the quantum-theoretic and the general-relativistic sectors of the theory. On this basis the companion papers on the quantum-theoretic and the general-relativistic sector will be reissued as version~2; the present note documents the derivations so that every change remains traceable.