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Ultradiscrete hypergeometric solutions to Painlevé cellular automata
We propose new solutions to the Painleve cellular automata that
do not and cannot be derived using the ultradiscretization
method. We consider a lift of these equations to a
non-archimedean valuation field in which we may relax the
subtraction free framework of previous explorations of the area.
Using such a method, we derive a set of hypergeometric solutions
to the Painleve equations which has long been thought impossible
Ultradiscrete, Painleve, Hypergeometric, Tropical.