The science behind it.
We can calculate the expected 1RM using Wathen formula
https://en.wikipedia.org/wiki/One-repetition_maximum#Wathen
Once skill element is mastered, 1RM strength correlates highly with muscle mass, as per..
https://doi.org/10.1152/japplphysiol.00192.2021
http://dx.doi.org/10.1007/s11332-021-00740-z
Pull ups therefor serve as are proxy of how much skeletal muscle one has, assuming there are no severe imbalances between muscle groups. FFM other than skeletal muscle should scale cubicly with height. Hence by subtracting those (scaled correctly) from weight we arrive at body fat.
With current data of 40 samples, best fit scaling factor are 0.0189924 for height (before being cubed) and 0.244258 for 1RM. RMSE 6.5kg for bodyfat, Best fit exponent for 1RM and FFM other than skeletal muscle are very close to the expected values of 1 and 3. For comparison, smart scales vs dexa has RMSE of around 5kg and scales underestimate bodyfat by an average of 4kg. as per..
https://doi.org/10.2196%2F22487