The codebook

• 2026-09-06 [Proved] Under a minimum-description-length score with a catalog of A = 667 atoms and at most P = 59049 positions, the name charge log2 A + log2 P kills every atom below 31 cells outright, 131 of the 667, while every surviving atom still pays its share of log2 A; the arithmetic of the score, not a measurement. Witness: lab/py/codebook.
• 2026-09-06 [Verified] The rearranged SVD of a level-5 carpet render returns its level-1 code 495 exactly at four block splits (sigma_2/sigma_1 <= 3.3e-15) and peels the five-letter magic word carpet(3), void(3), net(3), htree(3), vtree(3) into 495, 341, 186, 455, 365; under bit flips at 51 rates and 40 seeds each the code survives 40/40 to p = 0.30, 12/40 at 0.31, 0/40 from 0.32, against a block-mean baseline whose closed-form failure f/(1 + 2f) = 0.277638, f = (8/9)^4, is derived from the fill law and not from the sweep. Witness: lab/py/codebook.
• 2026-09-06 [Verified] The three-class codebook (Kronecker tiles, magic designs, life frames) under the MDL score loses to raw deflate on the tree's own render by 17212 bits, on text by 31375 and on a halftone by 31217 at Kronecker level 2, edges it by 29 bits on random bytes where deflate itself expands the stream by 47, and crosses deflate on the render only at catalog level 3; the uniform-bit control takes zero placements and saves -18 bits at every catalog depth 2 to 5, and every corpus reconstructs bit for bit from placements plus residual. Witness: lab/py/codebook.