Maybe lost to history, the dots are references for the Fibonacci series, which when harmonics are considered, give a pure major chord with octave and perfect fifth redundancies. The dot at the 9th fret marks 2/5ths the string length. The harmonic there is of the 5th partial (the major third) -- this is the one that throws you off.
This is my observation, and it is so easy once seen, that I have little doubt that many people have stumbled across it. Nonetheless, Gibson and Martin guitars had nothing to say about it, and so far as I could see, nothing to see in google searches. THE DOTS MARK THE HARMONICS COMPRISING A PURE MAJOR CHORD.
Are the dots an atavism from pre-equal tempered tuning? In historical paintings of fretted instruments, or in museums, when are the earliest dots seen in their modern location??
open = 1 = do
12 = 2nd partial = do (octave over root)
7 = 3rd partial = sol (perfect 5th + octave over root)
5 = 4th partial = do (double octave over root)
9 = 5th partial = mi (double octave + major third over root)
3 = 6th partial = sol (double octave + perfect 5th over root)