How Fractal Uncertainty Theory Derives 0, 1, and i from Interference

The single-slit and double-slit experiments are among the most fundamental demonstrations of quantum behavior. Every interpretation of quantum mechanics must account for them, yet none has derived the mathematical structures used todescribe them from the experiments themselves. In this paper we show that Fractal Uncertainty Theory (FUT) achieves precisely this. The which-way measurement problem is resolved without wave-function collapse or many worlds.We argue that the slit experiments, properly understood through FUT, constitute the physical origin of arithmetic itself.