even2n_schatten_moment_bound

Even-order ($q=2n$) Schatten moment bound for the Rademacher-sampled matrix. For the Rademacher-sampled matrix $M_\varepsilon =$ rademacherSampledMatrix Ω ε p X and $n \ge 1$ with $2n \ge \log(n_1+n_2)$, the expected even Schatten moment is dominated by the sampled variance scale: $\mathbb{E}_\varepsilon\big[\|M_\varepsilon\|_{S_{2n}}^{2n}\big] \le \big(\sqrt{2n}\,e\,\rho\big)^{2n}$, where $\rho =$ rademacherSampledVarianceScale Ω p X $= p^{-1}\sqrt{\max(\text{rowEnergyMax},\text{colEnergyMax})}$. Proof (reduction): the Schatten even moment is routed through the Hermitian dilation trace ($\|M_\varepsilon\|_{S_{2n}}^{2n} \le \operatorname{tr}(\mathcal{H}_\varepsilon^{2n})$); the signed sum of per-coordinate rank-one dilations matches the symmetric Rademacher trace-moment engine, whose variance matrix $V = \sum_c H_c^2$ is block-diagonal $\operatorname{blockdiag}(\operatorname{diag}(p^{-2}\text{rowEnergy}), \operatorname{diag}(p^{-2}\text{colEnergy}))$ with $\lambda_{\max}(V) \le \rho^2$ (block-diagonal quadratic-form bound); the engine then yields $\tfrac{(2n)!}{2^n n!}\rho^{2n}(n_1+n_2)$, and the constant+window step ($\tfrac{(2n)!}{2^n n!} \le (2n)^n$, $(n_1+n_2)^{1/2n} \le e$) collapses it to $(\sqrt{2n}\,e\,\rho)^{2n}$.