Projection as Differentiation: A Descriptive-Geometric Construction of the Quantum Explosion Singularity and the Cyclic Horizon Limit

This paper develops the descriptive-geometric space-time apparatus of Architect Saeed, demonstrating that perspective projection operates as a geometric differential operator, while reverse reconstruction embodies geometric integration. The passage of an entity along a rectilinear trajectory from negative infinity to positive infinity maps topologically into a complete 2\pi revolution around the circular horizon limit. In projective space, negative infinity and positive infinity converge into a singular vanishing point. This study traces the complete phenomenological lifecycle of the projected entity: Genesis at the vanishing point from negative infinity. Progressive spatial expansion and acceleration across the front plane. The Quantum Explosion singularity at the exact point of tangency with the horizon circle (intersection with the observer's eye-plane). Post-singularity contraction, compression, and decelerated migration along the horizon line. Cyclic re-emergence at the vanishing point as the entity approaches positive infinity. All dynamics are established through rigorous geometric constructions replacing empirical algebraic formulations.