Diagonal cuts of the parity solid

• 2026-08-28 [Proved] Every diagonal slice of bang dim 3, code 126 holds exactly 3^level points at every admissible height, by uniqueness of the binary expansion of the height offset; checked at level = 1..8 by two enumerations sharing no code and to level = 14 by a height recursion; the constancy separates it from the digit-scheduled slices of Nakajima and Watanabe, whose non-autonomous IFS uses A_c^(j) = {0} or {1,2,3} by the height digit, so their digit changes the number of maps and this one only the orientation. Witness: mrlymath::three::diagonal.
• 2026-08-28 [Verified] The two central cuts of bang dim 3, code 126 decompose into six congruent Sierpinski gaskets of 3^(level-1) points each tiling a hexagon with an order-12 symmetry group, checked at level = 2..8 by rebuilding the pieces from the previous level (union, pairwise disjointness, sizes); the combined totals are 6 * 3^(level-1) = 2 * 3^level: 18, 54, 162, 486, 1458, 4374, 13122; the ambient object is the octahedron flake of dimension log(6)/log(2). Witness: mrlymath::three::diagonal.