Dialog Part 1

Basics: stage 470×222px, all coordinates in px from the stage's top-left, everything clipped to the stage (its two top corners are rounded with radius 40px; the bottom corners are square). The animation is a 4s loop that plays by itself and is seamless; the video is 12s = three loops. T = seconds since the video start; u = (T + 0.25) mod 4 (loop time 0–4; the first frame is already 0.25s into the first opening). One tap every second: u = 0 taps "Delete file" (the dialog opens), u = 1 taps "Cancel" (it closes), u = 2 taps "Delete file" again (opens), u = 3 taps "Delete" (it closes and the file is replaced). Phase: h = 1 if u ≥ 2 else 0; v = u − 2h; if v < 1 the dialog is opening/open and A = v (seconds since the open tap); else it is closing/closed and B = v − 1 (seconds since the close tap); "del" = (h = 1) (the close was the Delete button). Loop index c = floor((T + 0.25)/4) mod 3 picks the file: FILES = [("Trip notes.pdf", "PDF", "2.4 MB · Edited today", violet→cyan), ("Budget plan.xlsx", "XLS", "860 KB · Edited Mon", mint→cyan), ("Beach photo.jpg", "JPG", "4.1 MB · Edited Sun", pink→gold)] (so 12s = all three files, then FILES[0] again). Because every value depends only on u and c, 12s equals 0s.

The dialog fades in while scaling up from 72% with a small overshoot, and closes by shrinking to 86% while fading. 
- Dim: dimK(i1 = 0.25).
- Open: k = seg(A, 0, 0.42); scale = lerp(0.72, 1, easeBack(k)); opacity = ease(seg(A, 0, 0.16)).
- Close (both buttons): k = seg(B, 0.06, 0.3); scale = lerp(1, 0.86, ease(k)); opacity = 1 − ease(k).
- Draw (if opacity > 0.001): translate (235, 111), scale uniformly, draw the dialog at that opacity.