  We prove that an $\omega$-categorical core structure primitively positively
interprets all finite structures with parameters if and only if some stabilizer
of its polymorphism clone has a homomorphism to the clone of projections, and
that this happens if and only if its polymorphism clone does not contain
operations $\alpha$, $\beta$, $s$ satisfying the identity $\alpha
s(x,y,x,z,y,z) \approx \beta s(y,x,z,x,z,y)$.
  This establishes an algebraic criterion equivalent to the conjectured
borderline between P and NP-complete CSPs over reducts of finitely bounded
homogenous structures, and accomplishes one of the steps of a proposed strategy
for reducing the infinite domain CSP dichotomy conjecture to the finite case.
  Our theorem is also of independent mathematical interest, characterizing a
topological property of any $\omega$-categorical core structure (the existence
of a continuous homomorphism of a stabilizer of its polymorphism clone to the
projections) in purely algebraic terms (the failure of an identity as above).
