"The theory's central puzzle remains unresolved: the way quantum systems are described mathematically differs from what scientists observe when measuring them."
Someone is saying something wrong. Calculations of quantum system agree very well with measurements of quantum systems, otherwise we wouldn't use the calculations - and we do. The agreement between theory and experiment is tested to absolutely ridiculous levels of accuracy - like to ten (or more) digits.
We may not be all in agreement of what the model MEANS about how the universe works, and we may feel that it is crazy that things behave both like particles and waves which seems like it should be a contradiction, but things really are measured as behaving just like the mathematical model predicts. That certainly isn't an "unsolved central puzzle."