rank_rpow_inv_le_exp_one_of_log_le

Window-collapse bridge (b) for the noncommutative matrix-Khintchine general-$q$ pipeline. For a natural number $N \ge 1$ (the matrix rank) and a real exponent $q \ge 1$ with $\log N \le q$, one has $N^{1/q} \le e$. This is the elementary estimate behind CR2009 §6.1's operator-norm/Schatten sandwich $\lVert X\rVert \le \lVert X\rVert_{S_q} \le e\lVert X\rVert$ valid for $q \ge \log n$: combined with $\lVert X\rVert_{S_q} \le \operatorname{rank}(X)^{1/q}\,\lVert X\rVert$ (node F6), it collapses the rank prefactor to the absolute constant $e$. Proof: $N^{1/q} = \exp(q^{-1}\log N)$ and $q^{-1}\log N \le 1$ since $0 \le \log N \le q$.