The ${\mathrm{\Phi }}_4^3$ and ${\mathrm{\Phi }}_6^3$ matricial QFT models have reflection positive two-point function

We extend our previous work (on $D=2$) to give an exact solution of the ${\mathrm{\Phi }}_D^3$ large-$\mathcal{N}$ matrix model (or renormalised Kontsevich model) in $D=4$ and $D=6$ dimensions. Induction proofs and the difficult combinatorics are unchanged compared with $D=2$, but the renormalisation - performed according to Zimmermann - is much more involved. As main result we prove that the Schwinger 2-point function resulting from the ${\mathrm{\Phi }}_D^3$-QFT model on Moyal space satisfies, for real coupling constant, reflection positivity in $D=4$ and $D=6$ dimensions. The K"all'en-Lehmann mass spectrum of the associated Wightman 2-point function describes a scattering part $\mathrm{\mid }p{\mathrm{\mid }}^2\ge 2{\mu }^2$ and an isolated fuzzy mass shell around $\mathrm{\mid }p{\mathrm{\mid }}^2={\mu }^2$.