Exposure

• 2026-08-30 [Proved] The exposed faces of a design's level power obey V(level + 1) = occ V(level) - 2 sum over the axes of P S^level, with occ the tile's filled cells, P its adjacent filled pairs along the axis and S the cross positions whose two end cells are both filled, because two adjacent blocks bury one face per spanning position and the spanning positions multiply by S a level; so V(level) is a sum of the powers occ^level and S^level in every dimension, the carpet perimeter closes as (4*8^level + 16*3^level)/5 (A381517) and the sponge surface as 2*20^level + 4*8^level (A332705), and all four counts fold from the residue corners without rendering the tile. Witness: mrlymath::formulas::surface prediction_matches_census_on_every_cube_code and the_corners_fold_what_the_tile_shows, sequences.