https://doi.org/10.5281/zenodo.19901212
Abstract
The Panvitalistic Theory (PVT) models every physical measurement as a timeless rational comparison of six-dimensional volumes, $V_a = x\,V_b$ with $x\in\mathbb{Q}$. This paper supplies the object that previous PVT papers assert but do not construct: the precise \emph{selection principle} that singles out the admissible configurations of the geometry. We show, in sequence, (i)~that the bare constraint $\delta V = 0$ is the exact identity $\dd(\ln V)=0$ and carries no field structure; (ii)~that no external-time kinetic term is admissible, so the fundamental object must be \emph{elliptic} (equilibrium), not hyperbolic (evolution); (iii)~that the action scale is fixed by the angular dimension of $2\pi$ ; and (iv)~that demanding a dimensioned action of scale $\hbar$ produces an irreducible measure ambiguity. We resolve the latter by following the PVT ontology to its conclusion: the selection functional is \emph{dimensionless}, defined intrinsically on the configuration space $\mathcal{M}$ of the three internal angles, with no external integration measure. The natural metric on $\mathcal{M}$ is derived---not posited---as the Fisher--Rao metric of the volume $G_{ij}=\operatorname{diag}\,\csc^2\theta_i$. The resulting coupled equations have the isotropic $90^\circ$ configuration as their unique non-degenerate critical point. A continuum treatment of the fluctuations fails (the Fisher--Rao metric is non-compact and yields only one bound state); taking the PVT ontology literally resolves this, as the comparison chain is \emph{discrete}, and the bounded discrete Laplacian gives a stable, real, discrete spectrum without any sign or signature assumption. The link weight of the discrete chain is fixed by the endpoint ontology of the comparison (Convention~C), and the selection principle is declared explicitly: realized configurations minimise the action. At the exact, untruncated level the isotropic $90^\circ$ configuration is proved to be the unique global minimum: there is no symmetry-broken ground state, and all structure resides in the excitations. By Niven's theorem the spectrum is entirely rational precisely for chain lengths $N\in\{1,2,3,4,6\}$; we adopt $N=6$ [posited], where the spectrum is the integer set $\{1,2,4,5\}$ and the dynamically preferred deformation sector is itself rational (dynamical self-consistency), while at $N=12$ the dynamics prefers the irrational sector $3\mp\sqrt3$. Cubic vertices vanish; the corrected sector couplings are $\lambda_3=\tfrac{1}{144}$, $\mu_3=\tfrac{1}{24}$ (ratio $6$), and under the declared selection principle the quartic interaction favours democratic deformation of all three angles; the axis-concentration statement of an earlier draft is withdrawn. Two exact results follow: the lowest deformation branch in closed form, $\Delta S_{\min}(R)=N\bigl(1-\cos^3(R/\sqrt{3N})\bigr)$, and a localized, chain-length-independent anharmonicity extremum (participation ratio $\approx 2.6$ sites, democratic equipartition). Each step is marked [derived], [posited], or [open]; the reformulated open problems---deriving the endpoint convention and the selection principle from the comparison axiom, the physical role of the localized object, downstream consistency of $N=6$, and the first measurable dimensionless ratio---are identified explicitly as the next milestones.