Entanglement as Backend Memory Aliasing: Resolving the EPR Paradox via Algorithmic Graph Routing in the Singleton

The 90-year conflict between local realism and quantum entanglement — crystallized in the Einstein-Podolsky-Rosen (EPR) argument and Bell's theorem — is resolved within the Algorithmic Theory of Reality (ATR) framework. This paper demonstrates that entanglement is the universe's fundamental memory-optimization protocol. When two systems interact, the Bennett-Landauer processing cost of maintaining two independent copies exceeds the cost of maintaining a single shared entry in the timeless Singleton backend. The rendering engine consolidates the redundant data into one backend address, with two lightweight memory pointers projected into the 3D spatial sub-state. Key Findings & Mechanisms: The Zeno Threshold (Zα) Trigger: When an observer measures a particle, the local entanglement entropy rate spikes. Breaching the local Zeno Threshold forces a Born Rule truncation, overwriting the shared backend address. Backend Memory Aliasing: Because the data address is shared, the distant pointer is instantly updated. No signal travels superluminally through 3D space; the update occurs at topological distance zero in the backend graph, rigorously preserving the no-signaling theorem. Saturating Tsirelson's Bound: By reframing the CHSH inequality as a strict topological routing limit on the 3D spatial graph, we mathematically and computationally verify that the backend aliasing protocol safely saturates the Tsirelson bound |S| = 2√2. The Monogamy of Entanglement: The Coffman-Kundu-Wootters (CKW) monogamy inequality is recovered as a strict consequence of backend memory exclusivity and finite pointer bandwidth. The same Bennett-Landauer mechanism that governs wavefunction collapse and macroscopic gravity is shown to govern quantum non-locality, uniting information thermodynamics with quantum foundations. The full computational verification suite (Python) is available at: github.com/srdrymn/atr-zeno-epr-paradox-numerical-verification