the lab frame index-by-index (r30s1d) and, for harmonic-flagged shells, projects 6d Cartesian components to 5d pure components in a second pass (genr22_reduce_pure). Both steps are linear maps acting on one shell index at a time, so they are fused here: each index is transformed once by T = C * R^T, where R is the per-shell rotated->lab rotation in the engine's component convention and C the Cartesian->pure projection. Pure 5d blocks are written directly; the 6d lab-frame Cartesian block is never materialized, and s-shell (identity) indices are skipped.
Component conventions (must match r30s1d_NN and the projection tables): d order xx,yy,zz,xy,xz,yz; rotated-frame cross components carry no sqrt(3) normalization while lab cross components do - the sqrt(3) is folded into the rotation, exactly as in r30s1d_07.