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Unlike DDL, whose Householder operator is orthogonal only at $\\beta \\in \\{0,2\\}$, our Data-Dependent Cayley rotation $Q(x)=(I+(\\beta/2)A(x))^{-1}(I-(\\beta/2)A(x))$ preserves orthogonality for all $\\beta$ and all inputs. To handle negation, an eigenvalue $-1$ case that Cayley provably excludes, we introduce the E$\\Delta$-MHC-Geo Hybrid, which combines Cayley rotation with Householder reflection via a learned operator-selection gate $X'=\\gamma(X)Q(X)X+(1-\\gamma(X))H_2(X)X$. A midpoint-collapse regularizer, $4\\gamma(1-\\gamma)$, encourages boundary gate decisions, where each selected component is orthogonal. 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