UPDATE May 26, 2015:
After months of negociations and presenting this to the ATP, I am sorry to report that the ATP has refused to accept this study.
The project's result is now public:
ATP Reiteration Project 1973-1978
The short form explanation for Vilas being number 1 is in the document VilasNo1Explanation.doc. But the project extended to the entire period 1973-1978. Many players have in fact a better ranking than their recorded one, others have a lower ranking. Many names are not even ranked in the ATP database, although they earned points. This was done entirely with the original ATP ranking system, no modification to historic facts of the time. The initial study concerning the category of tournaments is present along with the more acceptable study that does not alter any category originally used by the ATP, even though it is incorrect. In both accounts, Vilas is number 1 in 1975.
The study even presents a scenario in which no error is corrected, but rather focuses on some weeks in which no rankings were published. It is important to note that Vilas is number 1 even in this case, in which no actual error (although there were many) is corrected. The ATP missed this fact at the original time, and now refuse to accept it because technology did not permit them to detect this back in 1975. Even though, 2 years later, in 1977, they detected Borg becoming number 1 for a short period of time, and the periodicity of the rankings increased.
This is now for all of you to judge. The work done is impartial, if the tennis public considers this an injustice made to tennis, let them speak now and decide if the original rankings need to be correct or remain at their historical incorrect values. I am not the judge of history, tennis fans are, it is all your sport.
Here is the New York Times article: