'One to many.' Your magic software must be able to take one RGB value and map it sometimes to one CIELAB value, and sometimes to another. I haven't demonstrated this, but the reverse is also true. Your software must be able to map different sets of RGB values to the same CIELAB values.

Note to would be developer of RGB to CIELAB transforms: The pairs of colors above must map to the same CIELAB values, since they looked the same to me. I tried this same thing with the camera in my Samsung cellphone and my wife's iPhone. Maybe I just don't have a good enough camera? My camera is not 'top of the line', by the way but it's decent - it's a Canon G10. In some cases, the camera saw what I saw. On the other hand, the blacks match, and the blues, green, and reds are all good. Actually, the photo of the one on the paper looks closer to what my eye saw. The white on the paper is more of a peach color. While my eye said the two pinks were very close, the camera said that the one on the left is darker. I don't know what you see on your own computer monitor, but I see some colors that are just blatantly different.