Induced-metric optimizer with non-zero off-diagonal blocks in the ambient metric: h = [[γI, a], [bᵀ, 1]]. The pullback becomes G = γI + ξ(alᵀ + lbᵀ + llᵀ) where l, a, b can be gradient, momentum, parameters, or zero. Inverse via rank-2 Woodbury or Sherman-Morrison. Setting a=b=l recovers the original metric.