  In the moduli space of polynomials of degree 3 with marked critical points
c_1 and c_2, let C_{1,n} be the locus of maps for which c_1 has period n and
let C_{2,m} be the locus of maps for which c_2 has period m. A consequence of
Thurston's rigidity theorem is that the curves C_{1,n} and C_{2,m} intersect
transversally. We give a purely algebraic proof that the intersection points
are 3-adically integral and use this to prove transversality. We also prove an
analogous result when c_1 or c_2 or both are taken to be preperiodic with tail
length exactly 1.
