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Ethan Stoner
6611330747
get_final_path_from_real_time normalises elapsed time onto the sigmoid's input range with a 4.5 multiplier, and logistic_sigmoid(4.5) is 0.978, so the bezier was never evaluated at its endpoint. move_mouse then looped on `while time.monotonic() < end_time`, so it never asked for a sample at movement_time either and the `t > movement_time` branch was unreachable from there. The pointer was left short of the point move_to_element chose, on every move. Clamping the loop's last sample to movement_time is the smaller half of this, but on its own it only recovers 0.05px of a 2.8px median offset, since the sigmoid is what the rest of the shortfall comes from. So the path now hands back the endpoint once t reaches movement_time rather than only once it passes it, and the clamp is what makes that branch reachable. Measured over 6000 simulated moves at 200px travel, against a 10x10 control: median offset 2.82px and 13.02% of clicks landing outside the element before, 0.00px and 0.00% after. Also comments the 4.5 where it is, since the two are only correct together.