  In relation to the 4-dimensional smooth Poincar\'e conjecture we construct a
tentative invariant of homotopy 4-spheres using embedded contact homology (ECH)
and Seiberg-Witten theory (SWF). But for good reason it is a constant value
independent of the sphere, so this null-result demonstrates that one should not
try to use the usual theories of ECH and SWF. On the other hand, a corollary is
that there always exist pseudoholomorphic curves satisfying certain constraints
in (punctured) 4-spheres.
