Internal parametrization conjecture for L-packets over local fields of arbitrary characteristic

Let $G$ be a connected reductive group over a non-archimedean local field $F$ of arbitrary characteristic, and fix a Whittaker datum for its quasi-split inner form $G^{\ast}$. Let $S_\varphi^{+}$ and $\operatorname{Irr}_{\zeta_G}(S_\varphi^{+})$ have the meanings specified in the source, and let $Q$ be the quotient defined there, with $\widehat Q=\operatorname{Hom}(Q,\mathbb C^{\times})$.

Internal parametrization conjecture. There exists a canonical surjection

$$\operatorname{pr}:\operatorname{Irr}_{\zeta_G}\!\bigl(S_\varphi^{+}\bigr)\ \twoheadrightarrow\ \Pi_{\varphi}(G),$$

whose fibers form a torsor under $\widehat Q$.

This conjecture proposes an internal parametrization of an $L$-packet in arbitrary characteristic, including positive characteristic where the source notes that a theory of rigid inner forms is absent. Its resolution is not specified in the supplied text.