The Andrews–Gordon Family as a Test Case for the Local-to-Global Reconstruction Principle

This note presents the Andrews–Gordon qqq-series as a higher-rank test case for the local-to-global reconstruction principle developed in the companion paper From Ramanujan Summation to Modular Monodromy. The Rogers–Ramanujan pair corresponds to the first non-trivial vector-valued case of rank 222. The Andrews–Gordon hierarchy extends the same mechanism to arbitrary rank k≥2k \geq 2k≥2, producing a kkk-dimensional vector of qqq-series whose modular transformation law can be interpreted through l