There has been a fair amount of misinformation related to this program in recent months. About 50-60 cadets have graduated each of the past few years with a Scholars designation. Many of them did not graduate as a "Distinguished Graduate" (the top 100 or so by OPA ranking). Here is a link to the Class of 2022 Graduation Program.
https://www.usafa.edu/app/uploads/2022-Graduation-Full-Program-Final-OPT.pdf. You can see which cadets were in the Scholars program.
The recent incarnation (Martinson) appears to have rolled out with far fewer participants. According to a recent report to the Board of Visitors, only 23 cadets are involved in the program with intentions to expand participation with the Class of 2027.
https://www.usafa.org/News/BOV2022
In a class with roughly 1,000 cadets, 23 represent about 2.25% of the class. In any normally distributed population, the top 2.25% represents the second standard deviation from the mean, which suggests the cut-off would have been around 3.77 for GPA if GPA was the determining factor (it was not) and grade distribution has been in line with historical standards.
It is my impression that the Class of 2026 was not recruited into the Martinson Honors Program but was invited to apply and 23 were selected. I also believe that the 23 who were accepted, were accepted before Fall Semester grades were released, so I suppose high school GPA, SAT/ACT scores, and possibly mid-term grades were taken into account when determining which Doolies would be chosen (it could not have been GPA). My DD said she believes additional 26ers will be accepted into the program in the future (but that is a rumor at this point).