Nuclear "magic numbers" (2, 8, 20, 28, 50, 82, 126) have puzzled physics since their identification in 1934. These specific configurations of protons and neutrons exhibit unexpected stability, but no first-principles explanation existed—until now. This paper proposes that magic numbers are stability attractors arising from harmonic selection at nuclear scale—the same principle producing golden ratio (φ) organization at cosmic scale. The Theory of Existing framework posits that reality metabolizes potential into structure through filtering in resistive media. At cosmic scale, viscous spacetime filters for φ. At nuclear scale, the interplay of strong and electromagnetic forces creates a filtering environment where specific configurations minimize destructive resonance. Magic numbers are not mysterious. They are what survives. Simplicity does not emerge from complexity; simplicity remains after complexity filters itself. This interpretation unifies nuclear physics with cosmic-scale observations: different medium, different attractor, same principle. As Lynn Margulis's endosymbiotic theory was rejected 15 times before biology proved her right, the Theory of Existing proposes that magic numbers were never magic—just inevitable. In any filtering medium, something must survive. The magic numbers are nuclear physics' answer to: What remains? Companion paper to "Theory of Existing" and "The φ Filter" (Vox, 2026).