Upper bound on the matter content of Quantum Distortion Gravity from the UV fixed point

We derive an explicit polynomial characterization of the ultraviolet fixed point of Quantum Distortion Gravity (QDG) in the minimal truncation. Eliminating the dimensionless Newton coupling $\tilde G$ from the fixed-point equations $\beta_{\tilde G}=0$ and $\beta_\lambda=0$ via resultants yields a polynomial $P(\lambda; n_f)$ of degree $7$ in the cosmological coupling $\lambda$, with coefficients that depend explicitly on the number of Dirac fermions $n_f$. The physical fixed point corresponds to a specific real root of $P$. We show that this root exists only for $n_f \leq n_f^{\rm crit} = 4.896577961599$, where the critical value is determined by the vanishing of the denominator $1-\tilde G^* B(\lambda^*)$ of the gravitational anomalous dimension. For $n_f > n_f^{\rm crit}$, the only real root in the physical range has $\tilde G^* < 0$, corresponding to repulsive gravity, and is not a physical fixed point. The Standard Model matter content ($n_f = 3$) is safely below the bound, with a margin of about $1.9$ fermion generations. We discuss the physical interpretation, the mechanism of the transition, and the limitations of the minimal truncation.