Descrição: Paraparticles beyond bosons and fermions can be exchanged via either the braid group (anyons, existing up to $D=2$ space dimensions) or the permutation group; in the latter case the space dimensions are not limited. Besides being predicted, anyons have been experimentally detected. The situation differs for paraparticles exchanged via the permutation group (``permutation-group parastatistics").\par The first test to detect their theoretical signature was published in 2021 (for \zzg parafermions; it was soon followed by a second paper proving the detectability of \zzg parabosons). Later on, two further papers proved theoretical signatures of permutation-group parastatistics. These works demonstrate that, in certain situations, a long-held belief on the ``conventionality of parastatistics" argument can be evaded: some measurements of permutation-group paraparticles cannot be recovered from ordinary bosons/fermions.\par The main question now is how to experimentally detect or engineer in the laboratory such paraparticles. For this aim a minimal setup for the theoretical test is here provided: a Gedankenexperiment (a simplified version of the two tests published in 2021) which, essentially, is a {\it flow chart} of logical operations. The key point is to present, to experimentalists, the necessary steps to be simulated/realized in the laboratory (possibly, by manipulating qudits).\par In this minimal setup, the detection/engineering of paraparticles is mapped into a {\it chirality test}. The mathematical setting is based on \zzg color Lie (super)algebras and derived mathematical structures.

Número: CBPF-NF-001/26