Artian's Gravity Reference Framework: Finite Source Theorems, Einstein Shadow, and Empirical Cross-Locks

From a finite quantum source to transport, three spatial directions, and the Einstein infrared shadow Can a theory define local transport and a three-dimensional spatial frame before assuming a smooth metric? This reference framework begins with a capacity-bounded real-\(J\) source whose physical state remains inside the completed A7 domain: \[ \boxed{ \dot\rho_\Gamma =-\frac1\hbar[J_\Gamma H_\Gamma,\rho_\Gamma] +\sum_B\mathscr D[B](\rho_\Gamma) +\sum_D\mathscr D[D](\rho_\Gamma) +\sum_R\mathscr D[R](\rho_\Gamma), \qquad P_{A7,\Gamma}\rho_\Gamma P_{A7,\Gamma}=\rho_\Gamma. } \] The transport problem is reduced to a source-patch count, a serial address depth, and one explicit allocation coefficient: \[ \boxed{ W_C(e) =\frac{C}{\tilde t_A} \frac{A_e}{S_{\min}} \frac{\ell_A}{\ell_e} \Pi_e^{A2}, \qquad S_{\min}=\frac{\pi}{4}\ell_A^2, \qquad H_{\mathrm{tr}}=H_{\mathrm{nn}}(C)+H_{\mathrm{unresolved}}. } \] Parallel additivity and serial inverse-additivity force both geometric exponents to one. The remaining scalar \(C\) is the fraction of the declared A6 spectral budget assigned to the reversible nearest-neighbour block; it is not selected from measured gravity. The exact two-address source map makes the distinction operational: \[ \boxed{ p_{u\to v}^{\mathrm{coh}}(T)=\sin^2\!\left(\frac{WT}{2}\right), \qquad p_{u\to v}^{A2}(T)=1-e^{-\gamma T}. } \] The local three-dimensional module is derived without choosing the first three eigenvectors of a degenerate shell. If \(\mathcal R\) exchanges the three opposite face pairs of the A5-X orientation packet, then \[ \boxed{ P_{\mathrm{sp}}=\frac{I-\mathcal R}{2}, \qquad P_{\mathrm{sp}}^2=P_{\mathrm{sp}}, \qquad P_{\mathrm{sp}}^{\dagger}=P_{\mathrm{sp}}, \qquad \operatorname{rank}P_{\mathrm{sp}}=3. } \] The projector is physical; an ordered triad is a gauge representative. The local frame bundle is therefore \(O(3)\), with spatial orientation and the inter-cell connection/holonomy isolated as separate source theorems. The same finite source carries an exact microscopic current and a commuting conservation camera: \[ \boxed{ \widehat j^{\,H}_{u\to v} =\frac{t_{uv}}{\hbar}J_\Gamma \left(a_u^\dagger a_v-a_v^\dagger a_u\right), \qquad \partial\mathcal A_1(c)=\mathcal A_0(\partial c). } \] At the infrared readout level, the endpoint identity and the declared local, covariant, conserved, second-order metric domain give \[ \boxed{ G_A=\frac{\ell_A^2c^3}{\hbar}=\frac{\hbar c^5}{E_\ast^2}, \qquad G_{\mu\nu}+\Lambda_{A3}g_{\mu\nu} =\frac{8\pi G_A}{c^4}T_{\mu\nu}^{A2}. } \] Six sectoral faces read the same endpoint: \[ \boxed{ G_A^{(\mathrm{end})} =G_A^{(\nu)} =G_A^{(\mathrm{EM})} =G_A^{(H\to\mathrm{lab})} =G_A^{(t)} =G_A^{(\gamma H)}. } \] The strongest present non-gravitational anchored face uses the measured Fermi constant and lands at \[ \boxed{ G_A^{(H\to\mathrm{lab})} =6.674301412456\times10^{-11}\ \mathrm{m^3\,kg^{-1}\,s^{-2}}, \qquad \delta_G=+0.211626\ \mathrm{ppm}, \qquad z=+0.009416. } \] The surface count independently links the Einstein coupling and horizon address density: \[ \boxed{ \kappa_{\mathrm{QTT}}=\frac{Q_\Sigma}{\hbar c}=\frac{8\pi G_A}{c^4}, \qquad N_H=\frac{2\pi A}{Q_\Sigma}=\frac{A}{4\ell_A^2}. } \] The release includes the complete inherited verification chain plus exact transport-clock checks, finite exponent enumeration, all 24 proper and 24 improper signed octahedral face actions, 240 random \(O(3)\) frame tests, 240 weighted-projector tests, 240 Schur-refinement trials, hidden-channel witnesses, componentwise anomaly checks, and 12 detected mutations. Stable references: gravity framework concept DOI · QTT Main Book v10.01 · gravity authority page · QTT Lexicon · Two Universes