The 120° Derivation: Fibonacci Mod 2, the Golden Light Cone, and Why Orthogonality Is an Illusion

We derive the angular relationship between the three spatial dimensions from the Fibonacci recurrence. The generating equation φ² = φ + 1, reduced mod 2, produces a cycle of period 3 — a rotation by 120°. The characteristic polynomial of the Fibonacci matrix mod 2 is x² + x + 1, whose roots are the primitive cube roots of unity. No reduction produces period 4; the 90° angle does not appear. The conventional assumption of orthogonal dimensions (δᵢⱼ, Descartes 1637) is an axiom adopted because the circular norm (from i² = −1) defines perpendicularity as 90°. Over the reals, the golden norm N(a + bφ) = a² + ab − b² has signature (1,1): Lorentzian, not Euclidean. The Fibonacci matrix eigenvectors are causally…