A Geometric Reformulation of Prime Sparsity and Robin's Bounds via Discrete Fiber Bundles

This note presents a pedagogical and geometric reformulation of the distribution of prime numbers. By mapping the prime counting function π(x) onto a discrete fiber bundle indexed by natural numbers x ≥ 3, we translate variations in prime density into a well-defined spatial coordinate Z(x) ∈ ℝ⁺. While this framework does not yield new number-theoretic results, it provides a novel topological visualization of known analytic properties. Specifically, it demonstrates how Schoenfeld's bounds and Robin's criterion for Colossally Abundant (CA) numbers establish strict geometric envelopes that confine the spatial trajectory of primes conditional on the Riemann Hypothesis.