Cyclotomic Hecke Quotients and Ariki–Koike PBW — Examples

Compute r=1 finite type A, n=1 the cyclotomic polynomial quotient, r=2,n=2 the rank-eight basis, and separated versus colliding generic content spectra. Do not apply the formulas of additive generators at v²=1 without an invertible normalization conversion.

These are planned worked examples and counterexamples for cyclotomic-hecke-quotients-and-ariki-koike-pbw, with empty item lists pending normal authoring and proof review. Each example must calculate from the stated hypotheses, and each counterexample must verify both its premises and the failed conclusion. This companion is a dependency leaf and supplies no theorem to another page.