general_rademacher_matrix_2p_trace_moment_general_index

General-index Rademacher matrix $2p$-trace-moment bound. For a finite family of Hermitian matrices $H_c$ over an arbitrary finite index type $\mu$, indexed by $c \in \iota$, with the variance matrix $V = \sum_c H_c^2$ satisfying a quadratic-form domination $v^\top V v \le \text{normV}\cdot v^\top v$ for all $v$ (so $\lambda_{\max}(V) \le \text{normV}$), the symmetric Rademacher trace moment is bounded: $\mathbb{E}_\varepsilon \operatorname{tr}\big((\sum_c \varepsilon_c H_c)^{2p}\big) \le \tfrac{(2p)!}{2^p p!}\,\text{normV}^p\,|\mu|$. This lifts the standard $\operatorname{Fin} d$ Tropp/Khintchine engine to an arbitrary finite index $\mu$ via a reindexing equivalence $\mu \simeq \operatorname{Fin}|\mu|$ (trace and powers are reindex-invariant), and supplies the engine's eigenvalue hypothesis from the quadratic-form bound. Proof (reduction): reindex $V$ and each $H_c$ to $\operatorname{Fin}|\mu|$, convert the quadratic-form bound to the eigenvalue bound via the Rayleigh bridge, apply the $\operatorname{Fin} d$ engine, and pull the trace moment back unchanged.