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

On ${\cal M}$-Theory Dual of Large-$N$ Thermal QCD-Like Theories up to  ${\cal O}(R^4)$ and $G$-Structure Classification of Underlying  Non-Supersymmetric Geometries