The Causal Ordering of the Integers

We introduce a novel ordering of the natural numbers $\mathbb{N}$ based on "causal generation" rather than magnitude. By defining the existence of a number as the moment its necessary prime factors are introduced, we reveal a hidden temporal structure to the number line. This structure separates integers into "low-entropy" (ancient/constructed) and "high-entropy" (young/random) classes. We demonstrate that this metric, "Causal Depth," serves as a potent feature for distinguishing semantic signals from stochastic noise.