The Universal Processing Law (UPL): A Computational Ontology for the Unification of General Relativity and Quantum Mechanics

The Universal Processing Law (UPL) is a unified computational ontology that derives the mathematical structures of both General Relativity (GR) and Quantum Mechanics (QM) from a single set of local hardware principles operating on a discrete Planck-scale processing graph. The Core Postulate The physical universe is not a continuous geometric manifold but a finite, three-dimensional relational graph of Planck-scale processing nodes, called pixels, each executing discrete state-updates called Clicks. The Click is the primitive, invariant unit of existence: one Click is always one Click at the hardware level, irrespective of gravitational load or velocity. Time, as experienced by embedded observers, is not a fundamental dimension but an emergent, observer-relative count of Clicks allocated to the rendering of physical processes. The Master Equation The single governing equation of the theory is: N₋₎₂₀₋ = C_ Lg Lᵥ where N₋₎₂₀₋ is the local processing budget (Clicks available at a pixel), C_ = 1 Click per hardware cycle is the absolute ceiling, Lg = 1 - 2GM/ (rc²) is the Gravitational Yield Factor, and Lᵥ = 1 - v²/c² is the Kinematic Yield Factor. This equation is shown to be mathematically identical to the ADM lapse function in the 3+1 decomposition of General Relativity. Gravity, Time, and Motion Spacetime curvature is re-identified as an emergent rendering artifact arising from localized processing lag and asymmetric data routing bias on a fixed, non-deforming hardware substrate. The Einstein Field Equations are derived via Jacobson's thermodynamic method, recast as a Processing Conservation Principle at local causal boundaries. Quantum Mechanics In the quantum sector, the Born Rule is derived as an equivariance theorem of hardware routing dynamics. Wavefunction collapse is reinterpreted as a Decisive Click (computational buffer overload forcing branch termination). Quantum entanglement is formalized as a direct edge in the hardware adjacency matrix, providing a local resolution to Bell nonlocality that maps precisely onto the ER=EPR conjecture of Maldacena and Susskind. Strong-Field Regime: Distributed Rotational Rendering (DRR) The paper introduces the Distributed Rotational Rendering (DRR) mechanism, resolving the strong-field Kerr black hole regime. When both Lg and Lᵥ approach zero simultaneously at the event horizon of a near-extremal rotating black hole, the Conservation of Clicks principle redistributes the unprocessed angular momentum load through the routing bias vector ⁱ to distant hardware nodes with available capacity. A graph-level capacity analysis proves that UPL exactly recovers the standard Kerr quasinormal mode (QNM) spectrum with zero reflectivity (R = 0), consistent with precision measurements from GW250114. Applications to Current Anomalies The Cascade Freeze mechanism (pixel-by-pixel horizon growth via N₋₎₂₀₋ 0 overflow) is applied to the JWST early supermassive black hole anomaly. The Hubble tension is addressed as a Click-budget artifact: different cosmic epochs have different average Lg values, producing different measured expansion rates. Both applications are classified as EXPLAINED (mechanism identified) pending quantitative derivation. Companion Results Five companion papers derive quantitative results from the same master equation: the cosmological constant to 97. 3% accuracy, the Bekenstein-Hawking entropy S = A/ (4lP²), the objective wavefunction collapse time = / (8 EG), the Planck blackbody spectrum shape, and the standard Kerr QNM spectrum recovery. All theoretical concepts, derivations, and original ideas are the sole intellectual work of Ahmed Lahmidi. Contact: ahmed. lahmidi. contact@gmail. com