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Relevant to top-down ${\cal M}$-theory dual of large-$N$ thermal QCD-liketheories at ${\it int}$ermediate coupling, induced by the $G_2$ structuresupported by the closed $M_7$ - a warped product of the ${\cal M}$-theorycircle and a non-K\"{a}hler six-fold which is the warped product of the thermalcircle with a non-Einsteinian deformation of $T^{1,1}$ - we obtain explicitly(Almost) Contact (3) (Metric)Structure(s) and a three-tuple of $SU(3)$structures along the "transverse" six-fold induced by the AC(3)MS on $M_7$.(Assuming the arguments to also hold for non-closed manifolds, similarstructures can be obtained on the non-closed $\tilde{M}_7$ - a warped productof the ${\cal M}$-theory circle and a non-K\"{a}hler conifold.) Theaforementioned ACS do(es) not yield a Contact Structure. We separately obtainan explicit Contact Structure on the seven-fold $M_7$, and then obtain anexplicit transverse $SU(3)$ structure from the same. These results are expectedto be very useful in the context of classification of non-supersymmetricgeometries relevant to top-down holographic thermal QCD at intermediatecoupling.

(Almost) Contact (3) (Metric) Structure(s) and Transverse $SU(3)$  Structures Associated with ${\cal M}$-Theory Dual of Thermal QCD at  Intermediate Coupling