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 \ _ =-1[J_ H_, _ +B DB (_) +D DD (_) +R DR (_), P₀₇, _ ₏_₀₇, =_. \] The same Hamiltonian fixes the oriented microscopic current: \ j^\, Hₔ ₕ =tₔₕ{J_ (aᵤ^ aᵥ-aᵥ^ aᵤ). } \ With head-positive incidence matrix \ (B_\), the active ledger sees A2 consumption while the full ledger sees the receiving receipt: \ d{dT nᵥ+cᵥCᵥ - (B_ jH) ᵥ=bᵥ-dᵥ, ddT nᵥ+cᵥCᵥ+Eᵥ - (B_ jH) ᵥ=bᵥ. } \ The finite source history is a relative cycle once the initial/final slices and declared A3 boundary are held external: \ J^ full = L (T₁) - L (T₀) - B₀₃, ₑ₄₋ J^{ full=0. } \ The laboratory camera preserves that finite boundary identity exactly: \ A₁ (c) = A₀ (c), c=0 A₁ (c) =0. \ For a declared positive edge-weight packet, the endurance current is the unique minimum weighted-current-cost solution: \ LD=BIWBI^ T, =LD^{-1s, j ₄₍₃=-WBI^ T, BIj ₄₍₃=-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: \ dWₖ=W₊+₁, \|_ ₓ䂴^\|₇^{-₁ Chᵖ\| J^\|₇㵵. } \ The current is derived before a gravitational comparator is admitted: \ j ₄₍₃^{ ₒₑ₂ G ₎₁ₒ=0, A ₂ₔₑₑ₄₍ₓ G ₎₁ₒ=0. } \ The same finite endpoint continues to carry all six gravity faces: \ GA^ ({ end) =GA^ () =GA^ ({ EM) } =GA^ (H lab) =GA^ (t) =GA^ (H). } \ The strongest present non-gravitational anchored landing is \ GA^ (H{ lab) =6. 67430141245610^-11\ m³\, kg^{-1\, s^-2}, 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.