Generalized Derivations and Canonical Envelopes of Complex α²-Weighted Ω-Hom-Lie Superalgebras

We study generalized derivations of complex multiplicative ${\alpha }^2$-weighted $\Omega$-Hom-Lie superalgebras. The chosen structural identity is shown to be stable under Yau twisting, and every regular algebra in this class untwists canonically to an $\Omega$-Lie superalgebra. To retain the auxiliary operators that occur in generalized derivation identities, we work with generalized derivation triples and quasiderivation pairs. In this framework, these derivation-type maps are treated as mathematical operators encoding infinitesimal symmetries of the underlying graded algebraic structure. The triple space is a Lie superalgebra, and quasiderivation pairs fit into a short exact sequence of Lie superalgebras whose kernel measures precisely the ambiguity of the auxiliary map. We prove ${GDer}_{\alpha }\left(L\right)={QDer}_{\alpha }\left(L\right)+{QCent}_{\alpha }\left(L\right),$ and establish the corresponding $\Omega$-compatible decomposition for balanced generalized derivations. We then construct a three-layer envelope for generalized derivation triples and a two-layer envelope for quasiderivation pairs, obtaining injective Lie-superalgebra embeddings into $\alpha$-commuting derivation algebras. A structural obstruction shows that, when ${\alpha }^2\ne 0$, the original nonzero $\Omega$ cannot simply be copied to the active layers of these two-step envelopes as their structural form. For centerless algebras, the full derivation superalgebra of the two-layer envelope is determined as an explicit semidirect product. Finally, a structure-constant criterion reduces the pair and triple spaces to homogeneous linear systems. For the regular family $H_{\tau }$, $\tau \in {\mathbb{C}}^{\times }\setminus \left\{1\right\}$, we obtain $\dim {Der}_{{\alpha }_{\tau }}=1$ and $\dim {QDer}_{{\alpha }_{\tau }}=\dim {GDer}_{{\alpha }_{\tau }}=4$, while the $\Omega$-compatible first-component space has dimension 3.