What Primes Are: A Recognition Science Perspective on the Atoms of Arithmetic and Why Zeros Lie on a Line

We present an expository account of prime numbers as they appear in Recognition Science (RS), a framework that derives physical structure from a single primitive: the Recognition Composition Law. Within RS, primes are not mysterious random objects but the irreducible events in a universal ledger—the fundamental "atoms" of multiplicative accounting. This perspective illuminates the Riemann Hypothesis: zeros of the zeta function must lie on the critical line because any other configuration would violate the conservation constraints imposed by the ledger's eight-tick structure. We give an intuitive proof outline that builds geometric understanding before introducing technical machinery, making the underlying mechanism transparent. The central insight is that prime-frequency observables are bandlimited by the ledger's Nyquist cutoff, which bounds prime sums uniformly and forces zeros onto the symmetry axis through an energy-budget argument.