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Okay, here's one. I might post like one a week or so if they don't engender too much shitposting. Difficulty may vary. Sorry, I don't post hags.⏱ 1w↩ 1
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…⏱ 1w↩