The guitar tuning is the initial state on guitar by which all possible states are known.  The guitar tuning is a point in tuning space represented by a 6-digit number such as 0 7 5 3 4 5, commonly known as Open D Minor when intonated at D2 pitch level as D A D F A D.

In guitar tuning space every tuning is one step away from every other tuning because for any two tuning vectors there is a difference vector which changes one tuning into another using a single operator.

Given unknown tablature for the song “Happy Birthday” written in an unknown tuning there is one and only tuning which makes sense of the unknown tab, which otherwise seems to be nonsense for every other tuning.  Clearly if every possible tuning is used to interrogate the unknown tab, the authentic tuning will be found.  Also, if the tuning used to write the tab is D A D F A D, and the tab is interrogated using D A D F# A D, the song will be recognizable but every note falling on the F# string will be off-key and the error can be used to deduce the string should be tuned to F, not F#.

Most common tunings are within 3 strings of each other, but clearly there cannot be more than five steps to go from any tuning to any other.

In affine theory and music copyright law every possible guitar tuning is a simple mathematic derivative of music that any trained musician can make, but clearly there is one and only one authentic guitar tuning used to compose and record guitar.  Finding the tuning used to record guitar is possible by interrogating the music, but an additional step is required to determine both tuning and intonation, which surprisingly is only slightly more difficult than find the tuning for unknown tabs.

I see this question as similar to the 3-color map problem in topology because the guitar is finite so there must be a way to learn the tuning from a record.   If there is a way to learn the guitar tuning, then there must be a deductive system of logic and implication that can find the best-possible tuning.

Tablature makes more sense as the number of tunings considered increases but clearly considering every possible tuning is not required.  In practice, there is certainly a maximum number of tunings that are used in popular music, on a order of magnitude between 10 and 100.  The number of useful tunings is clearly highly determined, but how? Why isn't every tuning just as good as any tuning?

If it is possible to learn guitar by auditor surveillance of a record, then can anyone calculate the minimum number of guitar tunings that must be considered?  How many times does tablature need to be re-written until the sequence of tabs converges on the best-possible?  I realize that there is no way to prove the absolute best but in any specific collection the best is always clear.  Can tabs just get better and better in definitely?