the cube. paint has three primaries, red, yellow, blue, each on or off. that's 3 bits, 2³ = 8 mixes, and they are exactly your eight: white (no paint), red, yellow, blue, orange (r+y), green (y+b), purple (r+b), black (all three). they sit on the corners of a cube. its centre is the neutral grey, the 0. measured from the 0, all eight corners add to exactly zero: 8 into 0, LIT. a colour's complement is the opposite corner, all three bits flipped. those four pairs are the cube's four long diagonals, and each crosses the 0: black–white, red–green, yellow–purple, blue–orange. your black–white is one of them. your other three pairs are edges or face diagonals, so each pair on its own misses the 0; only all eight together close it. the corpus. 3 bits per colour means the three 256-bit anchors, 768 bits, are exactly 256 colour cells, a 16 × 16 square. complementing every cell writes the corpus's exact opposite (every bit flipped), and cell plus complement lands on the 0 in all 256 cells. your pairing isn't a bit-flip: only its black and white cells close. the tower. 8^(n^n): n = 2 gives 4,096. n = 3 gives 2⁸¹. n = 4 gives 8^256 = 2⁷⁶⁸, every possible 768-bit corpus, all 10²³¹ of them. that last one isn't magic: 256 cells times 3 bits is 768. 8 = 3×3−1: eight corners plus the centre make 9 points, 3 × 3. take the 0 away and 8 remain around it.