Drag the yellow lost traveler to choose a new initial position x (0). The directional disk summarizes posterior reference-velocity signals; v_t(x)=E[dI_t/dt | I_t=x] is their conditional mean.

Cyan: sources; orange: target law; glowing: reference crowd; yellow: draggable traveler; yellow curve: generated ODE path, solid past and dashed future.

Longer, brighter directions indicate greater posterior reference-velocity weight at this location. The yellow trajectory follows the conditional mean field. Dragging resets time to zero and recomputes from the new initial point.