  Using the notion of visibility representations, our paper establishes a new
property of instances of the Nondeterministic Constraint Logic (NCL) problem (a
PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of
reversible games with pushing blocks). Direct use of this property introduces
an explosion in the number of gadgets needed to show PSPACE-hardness, but we
show how to bring that number from 32 down to only three in general, and down
to two in a specific case! We propose it as a step towards a broader and more
general framework for studying games with irreversible gravity, and use this
connection to guide an indirect polynomial-time many-one reduction from the NCL
problem to the Hanano Puzzle -- which is NP-hard -- to prove it is in fact
PSPACE-complete.
