The planar Spectre and Tsiokos’s three-dimensional Chair44 are aperiodic monotiles whose tilings are hierarchical; they are compared here by exact computation. The Spectre inflates by the unit λ2 = √15 + 4 of ℤ[√15]. Its supertile perimeter is 2F3k+5+4 at every order k, proved by a finite exact certificate, so it grows by the unit 2 + √5 of ℚ(√5), faster than the linear inflation. The boundary of the limiting supertile is a fractal of box dimension log(2 + √5)/ log λ, and the tail of the common-ancestor levels of neighbouring tiles decays exactly by ν/λ2 . The inflation acts on the vertex module ℤ4 with two expanding and two contracting directions, and the internal plane is given exactly; the window is the attractor of contracting similarities, with boundary dimension log(5+2√6)/log(4+√15). The Chair44 inflates by the integer 2 on ℤ3 , with no Euclidean internal space (its internal space is 2-adic) and no twist; its centre set, that of the classical three-dimensional chair, has an explicitly computed pure-point diffraction measure. The main result is that every lattice-registered tiling obeying the 44 contact rules lies in the substitution hull, and that its symmetry group is conjugate to one of 1, C2 (a half-turn about a face diagonal), C4 and D4. Both statements use Kamenetsky’s unique-hierarchy criterion, whose finite certificate is checked here independently, and they transfer to every tiling by the Chair44 solid through Tsiokos’s registrationtheorem, which has been audited but not refereed. Orientation sums and contact matrices separate the two tilings. Four finite-patch computations then test whether the Spectre’s substitution hierarchy can serve as a clock: positional clustering shows no arrow, the radius needed to recognize an ancestor grows about threefold per level without making one, the look-back law is shared with a quadtree, and the parity flip of the construction shows in the outlines of supertiles and not in the tiles.