8. Holographic Emergence in the Simulation Hypothesis: From Planck-Scale Coding to Quantum-Level Reconstruction

If holographic area scaling is a fundamental constraint on quantum gravity, a Planck-scale model should either reproduce that scaling or explain why it does not apply. This supplement argues that the ``Mathematical Electron'' model naturally produces a holographic architecture in an algorithmic sense. The macroscopic universe is not claimed to be literally two-dimensional. Rather, the model contains a two-domain Planck-scale update state, a deterministic reconstruction coordinate generated by cosmic expansion, and an effective three-dimensional output. The argument is developed in four parts: (1) the two-domain update layer and reconstruction map; (2) quantum orbital thickness from wave-state expansion smear; (3) area-scaling information capacity from pair-address networks; and (4) structural comparison with standard holographic frameworks. The result is an \textit{algorithmic holography} paradigm in which holography is not an added postulate, but an emergent property of the model's update architecture.