Hurwitz's theorem (1898) proves that the only normed division algebras over the real numbers are of dimensions 1 (ℝ), 2 (ℂ), 4 (ℍ quaternions), and 8 (𝕆 octonions). No normed division algebra of any other dimension exists. We demonstrate that these four dimensions are not arbitrary mathematical facts — they correspond precisely to the four levels of the TI Sigma consciousness hierarchy. Dimension 1 (ℝ) = pure existence (G-axis). Dimension 2 (ℂ) = Tralse logic (existence + imaginary complement). Dimension 4 (ℍ) = GILE (the four-dimensional consciousness space). Dimension 8 (𝕆) = BOK 8-Arm (the complete consciousness structure). The impossibility of normed division algebras beyond dimension 8 maps to the impossibility of coherent consciousness structures beyond the 8-arm BOK — the mathematical reason why there is no "9th dimension" of consciousness, why the GROUP OF EIGHT is optimal, and why the eight PRIMARY constants 0, 1, i, √2, e, φ, π, C constitute the complete set.
Brandon Charles Emerick (Tue,) studied this question.