A walk timed against the clock jumps to its end after a hidden tab: push its start forward by the gap

type Path = { t0: number; delay: number; duration: number };
let path: Path | null = null;
let carryT0 = 0; // when the carried speed began to fade (the lesson above)
let lastT = 0;
// before: no gap handling, so u = (t - t0 - delay) / duration was 1 on the first frame back
function frame(t: number) {
  const dtMs = lastT ? t - lastT : 16.7;
  lastT = t;
  if (dtMs > 120) {
    const paused = dtMs - 16.7; // keep one ordinary frame of progress
    if (path) path.t0 += paused;
    carryT0 += paused;
  }
  const u = path ? Math.min(1, Math.max(0, (t - path.t0 - path.delay) / path.duration)) : 1;
  // draw at u; springs step with dt = min(dtMs, 50) / 1000
}