The second one feels related to spin, which I noticed when I realized that this formula works for like only half integers including negatives prob, which suggests some sort of recursive decomposition or wtv. So like, [math] \begin{array}{r c l} x^0 = (x^{1/2})^0 = \left[ \tfrac{1}{2} \right]^0 := & [0] = 1[0] & = (1, 0,0,...) \\ x^{1/2} := \left[ \tfrac{1}{2} \right]^1 := & \tfrac{1}{2} & = (0, 1, 0...) \\ x^{1/2} \otimes x^{1/2} := & \tfrac{1}{2} \otimes \tfrac{1}{2} = 0 \oplus 1 = 1[0] \oplus…