  Two 3-fold flops are exhibited, both of which have precisely one flopping
curve. One of the two flops is new, and is distinct from all known algebraic
D4-flops. It is shown that the two flops are neither algebraically nor
analytically isomorphic, yet their curve-counting Gopakumar-Vafa invariants are
the same. We further show that the contraction algebras associated to both are
not isomorphic, so the flops are distinguished at this level. This shows that
the contraction algebra is a finer invariant than various curve-counting
theories, and it also provides more evidence for the proposed analytic
classification of 3-fold flops via contraction algebras.
