  Construction of a top-down holographic dual of thermal QCD-like theories
(equivalence class of theories which are UV-conformal, IR-confining and have
fundamental quarks) {\it at intermediate 't Hooft coupling} and the
$G$-structure (torsion classes) classification of the underlying geometries (in
the Infra Red (IR)/non-conformal sector in particular) of the {\it
non-supersymmetric} string/${\cal M}$-theory duals, have been missing in the
literature. We take the first important steps in this direction by studying the
${\cal M}$ theory dual of large-$N$ thermal QCD-like theories at intermediate
gauge and 't Hooft couplings and obtaining the ${\cal O}(l_p^6)$ corrections
arising from the ${\cal O}(R^4)$ terms to the "MQGP" background (${\cal
M}$-theory dual of large-$N$ thermal QCD-like theories at intermediate
gauge/string coupling, but large 't Hooft coupling) of \cite{MQGP}. The main
Physics lesson learnt is that there is a competition between non-conformal IR
enhancement and Planckian and large-$N$ suppression and going to orders beyond
the ${\cal O}(l_p^6)$ is necessitated if the IR enhancement wins out. The main
lesson learnt in Math is in the context of the differential geometry
($G$-structure classification) of the internal manifolds relevant to the
string/${\cal M}$-theory duals of large-$N$ thermal QCD-like theories, wherein
we obtain for the first time inclusive of the ${\cal O}(R^4)$ corrections in
the Infra-Red (IR), the $SU(3)$-structure torsion classes of the type IIA
mirror of \cite{metrics} (making contact en route with Siegel theta functions
related to appropriate hyperelliptic curves, as well as the Kiepert's algorithm
of solving quintics), and the $G_2/SU(4)/Spin(7)$-structure torsion classes of
the seven- and eight-folds associated with its ${\cal M}$ theory uplift.
