The Wrong Square Root: i as Consequence of Golden Chirality, and the Born Rule over ℝ(√5)

The imaginary unit i = √(−1) enters quantum mechanics as a foundational assumption: wavefunctions are complex, evolution is unitary over ℂ, and the Born rule uses the circular norm |ψ|². We show that i is not a foundation but a consequence — specifically, the eigenvalue direction of the adjoint golden gamma matrix Γ_adj relative to the seed Γ_seed, constructed in companion Paper 191. A single sign flip in a 2×2 matrix over ℤ[φ] rotates the eigenvalue spectrum from the real axis to the imaginary axis. Traversing the golden split φ ↔ ψ in one direction produces real eigenvalues ±5^(1/4); in the reverse direction, imaginary eigenvalues ±i·5^(1/4). From this identification, the Born rule is reconstructed over…