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

Can a finite quantum ledger produce a conserved gravity current without first assuming a smooth stress tensor? Version: 4.2 Concept DOI: 10.5281/zenodo.21303020 Author: Ali Attar Website: quantumtraction.org/gravity Main Book: Quantum Traction Theory, v10.01 The source is a finite, capacity-bounded real-\(J\) ledger. Its reversible transport, A3 birth, A2 endurance receipt, and completed-record channels obey \[ { ρ_Γ =-1[J_Γ H_Γ,ρ_Γ] +∑_B D[B](ρ_Γ) +∑_D D[D](ρ_Γ) +∑_R D[R](ρ_Γ), PA7,Γρ_Γ PA7,Γ=ρ_Γ. } \] The same Hamiltonian fixes the oriented microscopic current: \[ { j\,Hu→ v ={tᵤᵥ}{}J_Γ (a_u^ a_v-a_v^ a_u). } \] With head-positive incidence matrix \(B_Γ\), the active ledger sees A2 consumption while the full ledger sees the receiving receipt: \[ { d/dT n_v+c_vC_v -(B_Γ j^H)_v=b_v-d_v, d/dT n_v+c_vC_v+E_v -(B_Γ j^H)_v=b_v. } \] The finite source history is a relative cycle once the initial/final slices and declared A3 boundary are held external: \[ { ∂ Jᶠᵘˡˡ = L(T_1)- L(T_0)- BA3, ∂ᵣₑₗ Jᶠᵘˡˡ=0. } \] The laboratory camera preserves that finite boundary identity exactly: \[ { ∂ A_1(c)= A_0(∂ c), ∂ c=0∂ A_1(c)=0. } \] For a declared positive edge-weight packet, the endurance current is the unique minimum weighted-current-cost solution: \[ { L_D=B_IWB_IT, φ=L_D⁻¹s, jend=-WB_ITφ, B_Ijend=-s. } \] The finite-element camera is also controlled. Whitney access commutes with the boundary operator, while any noncommuting numerical projection carries an explicit access defect: \[ { dW_k=Wₖ₊₁δ, \|∇_μ T_hμν\|_{H⁻¹} ≤ Ch^p\| J^ν\|H^p. } \] The current is derived before a gravitational comparator is admitted: \[ { {∂ jendˢʳᶜ}{∂ Gobs}=0, {∂ Acurrent}{∂ Gobs}=0. } \] The same finite endpoint continues to carry all six gravity faces: \[ { G_A^{({ end})} =G_A(ν) =G_A^{({ EM})} =G_A^{(H→{ lab})} =G_A⁽ᵗ⁾ =G_A(γ H). } \] The strongest present non-gravitational anchored landing is \[ { G_A^{(H→{ lab})} =6.674301412456×10⁻¹¹\ { m^3\,kg⁻¹\,s⁻²}, δ_G=+0.211626\ { ppm}, z=+0.009416. } \] Version 4.2 closes the microscopic number current, local receipt accounting, finite relative boundary, exact distributional conservation camera, elementary subdivision naturality, and the Whitney conservation/error theorem at their printed scopes. The physical conductance packet, source four-momentum, symmetric stress theorem, and hypersurface-deformation algebra remain named source-law targets. Reproducibility packet: 108-page PDF and complete LaTeX source; 1,096 exhaustive graph/capacity cases; 32 typed local-channel cases; 140 chain/access trials and 160 grounded Hodge trials; 8/8 detected mutations; scientific and complete visual render audits; machine certificates and SHA-256 manifest.