Jotun Chi is not pure white, 0001 is the purest white you can find for Jotun
if you want the 'purest' white, or nippon perfect white, but nippon perfect white is more for painting ceiling and not suitable for wall paint

you need to paint the wall and door with the same white and paint it at around the same time, when paint go through UV damage, daily usage wear and tear, the color will fade, even different type of paint from the same manufacturer with the same color code, it will have slight difference in color tone although they are still white

and white is the worst when it come to covering the previous paint job, maybe your previous paint job is affecting your current white tone, i painted 4 layer of Jotun supreme finish on my light blue color door with acceptable level of whiteness