Elementary Traversals of 1/(a + b) and Arithmetic Parallels to the Critical Line Symmetry

We study the function f(a,b) = 1/(a+b) for positive integer a and b ∈ (0,1). Expanding f as a geometric series and defining the traversal b*(N) as the unique root in (0,1) where the N-th partial sum equals 1/2, we prove that traversals exist if and only if a = 1 and N is odd. The traversal curve originates at b*(1) = 1/2 and converges to b* = 1. An explicit specialization map Φ and traversal map T identify structural parallels between the elementary arithmetic of 1/(a+b) and the analytic architecture of the critical line. All theorems formally verified in Lean 4 (22 theorems, 0 sorry, Mathlib v4.28).