  Scannell and Sinha considered a spectral sequence to calculate the rational
homotopy groups of spaces of long knots in n-dimensional Euclidean space, for n
greater than or equal to 4. At the end of their paper they conjecture that when
n is odd, the terms on the antidiagonal on the second page precisely give the
space of primitive Feynman diagrams related to the theory of Vassiliev
invariants. In this paper we prove that conjecture. This has the application
that the path components of the terms of the Taylor tower for the space of
classical long knots are in one-to-one correspondence with quotients of the
module of Feynman diagrams, even though the Taylor tower does not actually
converge. This provides strong evidence that the stages of the Taylor tower
give rise to universal Vassiliev knot invariants in each degree.
