C₁ translation; K₄ I,R₂,Mₓ,Mᵧ; C₄ quarter turns; D₄ rotations + mirrors.
μ is the reduced fundamental-domain area detected from translation symmetries. Hₐ and Hₒ are adjacency and orientation entropies.
Periodic Spectrum searches primitive periods 1…m; v9 strengthens 1/2/3/4/6/8, mines lower-period substructures, and treats whole residual components as Companion shapes.
𝒟 is offline-first: 81,265 free connected holeless polyominoes (n=1…12), 1,611 Heesch non-tilers (n=7…10), plus exact periodic seeds. IDs Pn-#### are local canonical IDs.
A adaptive portfolio; D density optimizer; H human-like constructive search. Exact cover, MRV and local repair are internal tools, selected automatically.