  A recent proposal for a superdeterministic account of quantum mechanics,
named Invariant-set theory, appears to bring ideas from several diverse fields
like chaos theory, number theory and dynamical systems to quantum foundations.
However, a clear cut hidden-variable model has not been developed, which makes
it difficult to assess the proposal from a quantum foundational perspective. In
this article, we first build a hidden-variable model based on the proposal, and
then critically analyse several aspects of the proposal using the model. We
show that several arguments related to counter-factual measurements,
nonlocality, non-commutativity of quantum observables, measurement independence
etcetera that appear to work in the proposal fail when considered in our model.
We further show that our model is not only superdeterministic but also
nonlocal, with an ontic quantum state. We argue that the bit string defined in
the model is a hidden variable and that it contains redundant information.
Lastly, we apply the analysis developed in a previous work (Proc. R. Soc. A,
476(2243):20200214, 2020) to illustrate the issue of superdeterministic
conspiracy in the model. Our results lend further support to the view that
superdeterminism is unlikely to solve the puzzle posed by the Bell
correlations.
