Goolagong’s story persuaded Puppo to investigate Vilas’s case. Puppo insisted that Vilas had not initiated the research.

Over the past seven years, Puppo has led a small team that has produced nearly 1,100 pages of analysis, detailed tables and other statistics, also collecting newspaper and magazine articles and draw sheets from men’s tournaments in the years in question.

They concluded that Vilas should have been ranked No. 1 ahead of Connors for five weeks in 1975, beginning on Sept. 22, and for the first two weeks of 1976. The documents were delivered to the ATP at the end of last year.

“The ATP today has all the elements that it didn’t have in the ’70s but doesn’t want to recognize them,” Puppo said in an interview from Buenos Aires.

The ATP rankings, which are now released weekly, were not on a strict publishing schedule during the early years. They were released only 11 times in 1974 and 13 times in 1975.

Vilas was never atop the rankings when they were published. But Puppo maintained that the ATP should recognize what the order would have been in the periods of the season when no rankings were released. He also contended that the rankings were not published systematically, pointing to an unusually long 43-day gap between the rankings released on Sept. 16 and Oct. 29 in 1975. That is precisely the window in which Vilas, according to Puppo, would have initially been No. 1.

The ATP, with Puppo’s research help, has altered the record book before. Three clay-court titles were added to Vilas’s career total this year, bringing it to 49, after it was discovered that the tournaments’ surfaces had been incorrectly recorded.