Bellman--Shoreline Search in Arbitrary Dimension: Exponential Vector Oscillators, Active Memory, Precession, and Effective Computability

We study online search for an unknown affine hyperplane in $\mathbb{R}^D$, for arbitrary fixed finite dimension. Building on a companion self-similar cell reduction and support-function formulation, we ask how the mechanism changes as the normal space grows from $\mathbb{S}^0$ to $\mathbb{S}^{D-1}$.