Yes there absolutely is nuance. The mathematics used to determine whether a quantum system has a gap or not is indeed undecidable, but that undecidability only

Yes there absolutely is nuance. The mathematics used to determine whether a quantum system has a gap or not is indeed undecidable, but that undecidability only kicks in as the size of your system approaches infinity. For any finitely sized system, basically any actual system in the universe, the solution is computable/decidable.