Odd-base slice grammar

• 2026-08-28 [Verified] The odd-base generalisation rests on a choice of solid: Cook's predicate "at most one coordinate in the middle third" and the bang dim 3, code 23 rule "at most one odd coordinate" agree at base = 3 (20 of 27) and nowhere else, at base = 5 filling 4^3 + 3 * 4^2 = 112 of 125 against 3^3 + 3 * 2 * 3^2 = 81 = 4k^3 - 3k^2 at k = 3, and there is no canonical base-5 Menger sponge. Witness: lab/py/odd-base-slice-grammar.
• 2026-08-28 [Verified] In the comparison of the slice dimension against the dimension minus one, the dimension is the solid's own log(fill)/log(base) and never the ambient 3: at the ambient 3 the value 3 - 1 = 2 exceeds all four slice dimensions 1.8184, 1.6869, 1.8026, 1.7204 and the mod-4 split collapses. Witness: lab/py/odd-base-slice-grammar.
• 2026-08-28 [Verified] The four printed dimensions are consistent with the four printed rules and this is not evidence for either: the dominant roots (9 + sqrt(33))/2 = 7.37228, (11 + sqrt(369))/2 = 15.1047, (42 + sqrt(612))/2 = 33.3693, (28 + sqrt(3556))/2 = 43.8161 give log(root)/log(base) of 1.8183, 1.6870, 1.8026, 1.7204 at base = 3, 5, 7, 9, while 4k^3 - 3k^2 at k = 2..5 gives 20, 81, 208, 425 and dimension minus one 1.7268, 1.7304, 1.7430, 1.7544; a rule and its own dimension cannot cross-check each other. Witness: lab/py/odd-base-slice-grammar.
• 2026-08-28 [Proved] The middle diagonal layer sits at coordinate sum 3(base-1)/2, odd exactly when base = 3 mod 4 (3, 6, 9, 12 at base = 3, 5, 7, 9). Witness: lab/py/odd-base-slice-grammar.
• 2026-08-28 [Conjecture] No definition of a "blow-up of 4" for the slice exists in this tree, so the phrase carries no claim.
• 2026-08-28 [Conjecture] The two-tile grammar closes at ten odd bases with a 2 x 2 substitution matrix rational in base within each class of base mod 4.
• 2026-08-28 [Conjecture] That parity forces structurally different cells into the middle layer in each residue class, which is the mechanism of the mod-4 split.