Explicit rank four Nahm sums that are modular have non-modular duals, refuting Zagier's duality conjecture.
Andrews, Bressoud polynomials, Rogers–Ramanujan type id entities, and applications, Ramanujan J 41 (2016)
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Counterexamples to Zagier's Duality Conjecture on Nahm Sums
Explicit rank four Nahm sums that are modular have non-modular duals, refuting Zagier's duality conjecture.