The holography of spread complexity. A story of observers

A bstract Building on the pioneering work of [1], we propose a holographic description of spread complexity and its rate in 2D CFTs. By exploiting SL (2, ℝ ) symmetry, we explicitly construct the Krylov basis, expressing spread complexity as a linear combination of generator expectation values. Within the AdS/CFT correspondence, we translate these boundary expectations directly into bulk kinematic variables. These findings suggest that spread complexity manifests as the energy measured by a bulk observer, with its rate corresponding to the radial momentum.