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 ℝ(√5) without assuming ℂ. Complex conjugation is the chirality flip Γ_seed ↔ Γ_adj — a geometric operation derived from the algebra, not an algebraic assumption. Positivity of the Born rule is not an additional axiom and is not, as earlier drafts claimed, an immediate consequence of the chirality flip: it is restriction to the forward cone of the indefinite Galois norm N(a) = p² − 5q² on ℝ(√5), an object with signature (+,−) whose hyperbolic-plane structure the standard positive-definite Hilbert space cannot host. The normalization condition ⟨ψ_seed|ψ_adj⟩ = √5 is derived from the chiral coupling Γ_seed·Γ_adj = √5·σ₃ (machine-verified). The measurement problem dissolves: measurement is the round trip through the golden conjugation, reading a topological invariant without disturbing a topological state. No collapse is required. Standard QM is recovered as the special case in which the adjoint amplitude equals the complex conjugate of the seed amplitude. A new §11 resolves the (2,2)→(1,3) selection: the excluded timelike direction is the right-handed neutrino, and parity violation is the crystallisation closure choice at t=0. Whether the indefinite norm N connects causally to the indefinite form appearing in the Dedekind factorisation of ζ_{ℚ(√5)} is explicitly left open; an earlier attempt to identify Riemann zeros with the null locus of N failed numerical adversarial review and the correct coordinate map, if any, is deferred to future work.