The A4 numbers are the first pieces of information used for the mapping.

The “A4 numbers” are the locations of the 2nd, the 4th, and 8th partial of A4 when A4 is tuned to A440.

To measure A4’s 2nd Partial:
Tune A4 to A440.
Set the AccuTuner to A5, play A4, and stop the lights (with the cents buttons).
The cents setting is the location of A4’s 2nd P.

To measure A4’s 4th Partial:
Tune A4 to A440.
Set the AccuTuner to A6, play A4, and stop the lights(with the cents buttons).
The cents setting is the location of A4’s 4th P.

To measure A4’s 8th Partial:
Tune A4 to A440.
Set the AccuTuner to A7, play A4, and stop the lights(with the cents buttons).
The cents setting is the location of A4’s 8th P.

These A4 numbers tell us a lot about the piano. 
First of all, we now know the target setting for A4.   Since this system uses the 4th Partial of A4 to tune A4 (A440), we now know the setting for A4 that will be used in the tuning.
Second, the 8th partial number is the setting to use if the technician wants to use a triple octave for A7.
And third, the 2nd Partial setting would be the setting for A3 if a pure 4:2 octave is desired for the A3/A4 octave.  If an A3/A4 4:2, 1/2 bps wide is desired, simply subtract 1.0 c from the 2nd partial setting.  The resulting A3/A4 octave will be a 4:2, 1/2 bps wide.

All that information just from measuring 3 partial settings of A4 when A4 is tuned to A440.