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

Can a finite quantum source generate conserved momentum and symmetric stress before a smooth spacetime metric is assumed? Version: 5.1 Concept DOI: 10.5281/zenodo.21303020 Author: Ali Attar Gravity reference: quantumtraction.org/gravity Main Book: Quantum Traction Theory, v10.01 The finite source evolves on an A7-closed, capacity-bounded real-\(J\) domain: \[ \boxed{ \dot\rho_\Gamma =-\frac1\hbar[J_\Gamma H_\Gamma,\rho_\Gamma] +\sum_B\mathscr D[B](\rho_\Gamma) +\sum_D\mathscr D[D](\rho_\Gamma) +\sum_R\mathscr D[R](\rho_\Gamma), \qquad P_{A7,\Gamma}\rho_\Gamma P_{A7,\Gamma}=\rho_\Gamma. } \] Once the transport Hamiltonian is populated, its active support and relative phase-curvature rate are fixed: \[ \boxed{ W_H(e)=\frac{2|t_e|}{\hbar}\,\Pi_e^{A2}. } \] Independent series/parallel composition selects one regular geometric conductance form: \[ \boxed{ W_{\rm geom}(e)=\kappa_{A2}\frac{A_e}{\ell_e}, \qquad \kappa_e^H=W_H(e)\frac{\ell_e}{A_e}=\kappa_{A2}. } \] The second equality is an internal isotropy cross-lock. It can fail edge by edge; observed \(G\) does not enter either side. Boundary-preserving refinement is tested by the exact Schur response: \[ \boxed{ L_{\rm eff}=L_{bb}-L_{bi}L_{ii}^{+}L_{ib}. } \] The framework then constructs finite four-momentum and symmetric metric-response stress: \[ \boxed{ P_0=\frac{H_\Gamma}{c}, \qquad P_a=-\hbar J_\Gamma D_a, \qquad T_H^{\mu\nu}=T_H^{\nu\mu}. } \] The residual deformation problem is not compressed into one fitted error term. It is resolved into five independently auditable components: \[ \boxed{ \mathfrak A_h =\mathfrak A_{\rm nonlocal} +\mathfrak A_{\rm anisotropy} +\mathfrak A_{\rm channel} +\mathfrak A_{\rm projection} +\mathfrak A_{\rm boundary}. } \] A periodic \(4\times4\times4\) cubic source supplies a sharp naturality test: its first positive Laplacian eigenspace has multiplicity six. The full eigenspace projector is invariant, while an arbitrary ordered choice of three modes is not. The next source theorem must therefore derive a physical three-frame rather than select one by basis order. The same endpoint carries the six gravity faces: \[ \boxed{ G_A^{({\rm end})} =G_A^{(\nu)} =G_A^{({\rm EM})} =G_A^{(H\to{\rm lab})} =G_A^{(t)} =G_A^{(\gamma H)}. } \] The strongest present non-gravitational anchored landing is \[ \boxed{ G_A^{(H\to{\rm lab})} =6.674301412456\times10^{-11}\ {\rm m^3\,kg^{-1}\,s^{-2}}, \qquad \delta_G=+0.211626\ {\rm ppm}, \qquad z=+0.009416. } \] The source remains frozen during every gravity comparison: \[ \boxed{ \frac{\partial\{H_{\rm phys},W_H,L_H,D_X,T_B,\mathfrak A_h\}} {\partial\{G_{\rm obs},G_{\rm lab},\text{gravity residuals}\}}=0. } \] Reproducibility packet: 127-page PDF and complete LaTeX reconstruction source; 180 relative-Hamiltonian selector trials and 64 explicit nonuniqueness witnesses; 240 Schur-refinement trials and a complete 36-branch exponent enumeration; 160 Hamiltonian--geometry cross-lock trials; exact spectral-frame receipt, 200 Belinfante trials, and 240 anomaly decompositions; 10/10 detected mutations, full inherited verification chain, render audit, and SHA-256 manifest.