https://doi.org/10.5281/zenodo.19901212
Abstract
The Panvitalistic Theory (PVT) asserts that every physical measurement is a rational comparison of two real objects, $V_a=x\,V_b$ with $x\in Q$, and that no dimensioned or dimensionless constant of nature exists. The first version of this paper rewrote the four classical force laws --- Newtonian gravitation, inertia $F=ma$, Coulomb's law and the Amp\`ere/Lorentz law --- in exactly this form, with $G,\varepsilon_0,\mu_0$ eliminated, and showed that their numerical values are closed-form functions of the Earth's geometry and decimal unit conventions ($cG=2/100$, $\varepsilon_0\mu_0 c^2=1$, accurate to the $10^{-4}$ level of the 1795 dual-scale inconsistency). This version supplies the missing structural layer: it shows \emph{why} standard physics (SP) contains constants at all, by identifying the laws of SP as \emph{isotropic projections} of anisotropic PVT structures.
Three structural results organise the account. \textbf{(i)} In the PVT $(L,T)$ system every SP constant is a pure power of the single measure $\pi\equiv T/L$: $c_{\mathrm{std}}=\pi^{-1}$, $G=\pi$, $e=\pi^{2}$, $k_B=\pi^{3}$, $h=\pi^{4}$ --- the \emph{$\pi$-ladder}, in which the exponent counts the internal angular measures a quantity carries. The isotropic projection freezes the three internal angles to $90^\circ$ ($\pi\to1$) and lowers one length grade per areal velocity ($L^2/T\mapsto L/T$); the removed length is re-imported as the law's constant. Each of the three non-inertial force laws purchases exactly one such length, reproducing the four-plus-three architecture. Gravitation is a \emph{volume} projection, electromagnetism an \emph{area} projection, organised in a single projection grammar. We further argue that treating the areal invariant $L^2/T$ as the linear constant $c=L/T$ is a category error that injects an uncancelled transcendental residue into SP; that measurement is inherently the areal (triangular) form $L^2/T$, so quantisation is a property of the \emph{measurement}, not of the continuous substrate; and that gravitational singularities are the shadow of freezing the live reciprocal pair $(c,G)=(\pi^{-1},\pi)$ into two independent numbers. All dimensional and numerical identities are verified symbolically. Every substantive statement is marked \derived, \posited{} or \opn.