Some conjectures on \({\mathcal S}_n\)-derived nuclear permutational (or NMR) spin encodings (Q1381396)

-- On existence of limiting \({\mathcal S}_n\)-module decompositional sets for weak \((\lambda\vdash n)\)-branching at high \(n\); -- on Voronoi polyhedral dual as geometric analogues to Cayley's \(SU2\times{\mathcal S}_n\uparrow{\mathcal G}\) embedding theorem; -- and on \(SU(m\geq 3)\times{\mathcal S}_n\) dual group with retention of self-associacy over subduced irrep set, as being the sufficient further condition to ensure the determinacy of \(SU(m\geq 3)\times S_n \downarrow {\mathcal G}\) embeddings.