The conjecture that the reduced invariant defines a knot concordance homomorphism

Let $\mathcal{C}$ denote the smooth knot concordance group. The knot invariant $r(K)$ is defined for knots $K$ and takes values in $\mathbb{Q}$. Concordance homomorphism conjecture. The invariant provides a well-defined group homomorphism

$$r:\mathcal{C}\rightarrow\mathbb{Q}.$$

The additivity and mirror formulas established earlier motivate this speculation, but well-definedness under smooth knot concordance is not established in the supplied text.