The Boundary of λ = 2:

We establish that c = 2 is the unique positive integer satisfying two independent boundary conditions in the family of order-2 linear recurrences xn = xn−1 +c · xn−2: the algebraic condition r1 = c (dominant root equals coefficient) and the spectral condition |r2| = 1 (unit subdominant modulus). This mathematical result motivates an empirical investigation of whether the distinguished base λ = 2 appears in natural systems. We find statistically significant clustering (p < 0.01) of planetary orbital period ratios at values of the form 2 n/12, corresponding to musical consonances. We present this correlation without claiming causation, and propose falsifiable predictions including a specific orbital signature for a hypothetical Planet 9.