A Deductive Layer for Fundamental Physics from Minimal Isotropic Unitary Transport on a Nyquist Lattice

A finite-information state at Nyquist scale $a$ is taken to be a primitive normalised Dirac spinor field $\mathcal{D}$ on an ambient combinatorial 4D lattice with no background metric. The spinor bilinears determine the local Lorentzian comparator data: the timelike current $\mathfrak{J}_A[\mathcal{D}]$, the effective metric$g_{AB}[\mathcal{D}]$, the local rest direction $u[\mathcal{D}]$, and the rest-space projector used in the next comparison step. On each local rest patch, the primitive spinor induces a derived $U(1)$ phase representative $\psi[\mathcal{D}]$. We ask what scalar macroscopic law is forced when this comparison, update, and readout loop closes self-consistently. Ambient 4D locality and $B_4$ symmetry force the unique even comparator on the two-coordinate shell. Its exact rest-space projection is the 3D $L_{19}$ stencil withweights $(w_0,w_1,w_2)=(-4,\tfrac13,\tfrac16)$; the low-mode symbol forces the diffusive scaling $s=na^2$; and the unique macroscopic scalar envelope is the intrinsic Schr\"{o}dinger equation\[ i\,(u\cdot\nabla)\Psi = -\frac{\lambda_q}{2}\,\Delta_\perp^{(u)}\Psi + O\!\bigl(a^2+a|\nabla u|\bigr).\]On the canonical macroscopic representative of every admissible reconstructible primitive state, the Madelung decomposition yields exact structural identities together with the exact intrinsic force law and the exact unified gravity-expansion-shear equation, from which the quasi-static Poisson law and PN hierarchy follow as derived projections. The same architecture also yields an exact finite-$a$ gauge edge-cancellation identity, a forced $O_h$-resolved bosonic channel menu with the scalar $A_{1g}$ sector proved and the $T_{1u}$ and $T_{2g}$ linear sectors discharged, and a many-clock compatibility closure whose unique local second-order divergence-free form is Einstein. Under the one-cell UV closure, $\lambda_q=1$ and\[ G_{\rm eff}=a^2c^3/(2\hbar)=G_N=G.\]No further foundational derivation is required here: once these seed equations are obtained, their downstream interacting consequences are inherited from the corresponding established physics rather than rederived redundantly.