  We prove that if two non-renormalizable cubic Siegel polynomials with bounded
type rotation numbers are combinatorially equivalent, then they are also
conformally equivalent. As a consequence, we show that in the one-parameter
slice of cubic Siegel polynomials considered by Zakeri [Za2], the locus of
non-renormalizable maps is homeomorphic to a double-copy of a quadratic Siegel
filled Julia set (minus the Siegel disk) glued along the Siegel boundary. This
verifies the the conjecture of Blokh-Oversteegen-Ptacek-Timorin [BlOvPtTi] for
bounded type rotation numbers.
