What the display retains
The arrow plus its two transverse frame axes show the SO(3) rotation associated with SU(2). The quaternion q and spinor readout retain the double cover: q and −q give the same frame but opposite spinors.
The cyan marker shows complex phase. The pink layer shows traversal through the open sequence Input, L, G, N. Reversal flips its traversal arrows and stage order without rotating the gold arrow or changing complex phase. Flipping twice restores the same order.
L, G, N name the retained construction stages. Reading them backwards does not implement inverses of their projectors. The moving cursor shows traversal position, not a phase or an additional group parameter; playback stops at the final stage.
SU(2) has three continuous parameters, SO(2) has one, and process reversal is binary. The spatial display retains the spinor lift in its separate readout. Playback is a display operation, not a physical-time assignment.