One is that the component of the unknot in the space of smooth embeddings of the circle in 3-space has the homotopy-type of the round circles, equivalently, O(3).
Interestingly, this statement is not equivalent to the generalized Smale Conjecture, in higher dimensions.
Another equivalent statement is that the group of diffeomorphisms of the 3-ball which restrict to the identity on the boundary is contractible.
Yet another equivalent statement is that the space of constant-curvature Riemann metrics on the 3-sphere is contractible.
is sometimes meant when referring to the generalized Smale conjecture.
[3] In late 2018, Tadayuki Watanabe released a preprint that proves the failure of Smale's conjecture in the remaining 4-dimensional case[4] relying on work around the Kontsevich integral, a generalization of the Gauss linking integral.
As of 2021, the proof remains unpublished in a mathematical journal.