The absolute summability conjecture for exact interpolation spaces

Let $E$ be an exact interpolation space between $l^1$ and $l^2$ given by

$$E=(l^1,l^2)_S^K,$$

and let

$$X_E=(L^{\infty},G)_S^K.$$

Absolute summability conjecture for exact interpolation spaces. The embedding

$$X_E\subset (L^1,L^2)_S^K$$

is $(E,1)$-absolutely summing.

This is presented as an extension of the paper's preceding conjecture, motivated by interpolation heuristics and an example in the paper. No resolution is given in the supplied text.