The definition of $\lambda$ is fixed by the OPE coefficient (27).

Here $s\in \mathbb{N}$ corresponds to the $s+1$ dimensional representation of $\mathfrak{s}\mathfrak{u}(2)$ while $[a,b]$ are $\mathfrak{s}\mathfrak{p}(4)$ Dynkin labels, so that $[1,0]=\mathbf{4}$ and $[0,1]=\mathbf{5}$.

There is a unique super-conformal invariant structure of type $⟨{\mathcal{D}}_2{\mathcal{L}}_{0,[0,0]}^{{\mathrm{\Delta }}_{\mathtt{ext}}}{\mathcal{L}}_{0,[0,0]}^{\mathrm{\Delta }}⟩$. The relevant OPE coefficient can be extracted from the three-point correlator of the ${\mathcal{D}}_2$ and ${\mathcal{L}}_{0,[0,0]}^{{\mathrm{\Delta }}_{\mathtt{ext}}}$ superprimaries with the $Q^4{|}_{0,[0,2]}$ descendant of the exchanged operator of type ${\mathcal{L}}_{0,[0,0]}^{\mathrm{\Delta }}$.

This can be argued from the structure of the Witten diagrams or directly from the bootstrap, see Ref. [14].

According to Eq. (12), upon specifying the second and third operator in ${\mathsf{C}}^{(0)}$ we obtain a map ${\mathsf{C}}_{{\mathcal{D}}_2{\mathcal{O}}_{\mathtt{ext}}}^{(0)}:{\mathsf{d}}_4(\mathrm{\Delta })\to \mathbb{C}$. This map is composed with ${\mathrm{\Gamma }}_{\mathrm{\Delta },2\to 4}^{(2)}$, see (19), to produce a number.

This is an important difference compared to Refs. [11, 15, 16].

With the maximum values ${\mathrm{\Delta }}_{\mathtt{ext}}=14$ and ${\mathrm{\Delta }}_{\mathtt{ext}}=22$ for the length-four and length-two operators one can span all directions of ${\mathsf{d}}_4(\mathrm{\Delta })$ up to $\mathrm{\Delta }=26$.

While the perturbative expansion in ${\lambda }^{-1/2}$ is asymptotic, the expansion of CFT data, like ${\mu }_{{\mathcal{D}}_2}^2$, as a function of ${\mathrm{\Delta }}_{{\varphi }^2}-2$ appears to be convergent.