There are three ways to increase your torso height: increase the width of the presidium(since the vertebrae are irregular bones), cause your osteoblasts to deposit more bone underneath the presidium, and to increase your inter vertebral disc height.
We want tubercular bone micro fractures in the vertebrae to release the stem cells which differentiate into osteoblasts which then deposit new bone beneath the presidium. What's the best way to do that given that your spine is hard to access(you can only get the spinous process given the fact that the ribs block everything)? Jumping(or rather landing with straight legs).
Jumping is the exercise where you can generate the most force. Other exercises with potential include squats, dead lifts, power cleans, etc but jumping is the simplest exercise and those exercises mostly causing shearing forces(periosteal width) it may take a lot of weight to cause tubercular micro fractures. Whereas jumping is an easy exercise to perform.
Up regulation of osteogenic factors induced by high-impact jumping suppresses adipogenesis in marrow but not adipogenic transcription factors in rat tibiae.
"Jump training is a high-impact training regimen that increases bone volume in young bones[Volume includes height]. The aim of our study was to determine whether down regulation of adipogenesis that is associated with up regulation of osteogenesis is detected after jump training in growing rat tibiae. Four-week-old rats were jump trained for 1, 2, or 4 weeks for 5 days/week, and the height of jumping progressively increased to 35 cm.
We performed morphometry to directly quantitate changes in bone volume and marrow adipocyte distribution in tibiae after the jump training. We also examined changes in the expression of osteogenic and adipogenic transcription factor proteins and mRNAs after the jump training. Four weeks of jump training induced an increase in tubercular bone volume, which was associated with the recruitment of runt-related transcription factor 2 expressing cells, as well as a decrease in marrow fat volume.
However, paroxysm proliferator-activated receptor-gamma2 protein and mRNA expression levels did not change after high-impact jump training. The mRNA expression levels of the adipocyte differentiation genes CCAAT/enhancer-binding proteins (C/EBPs)alpha, C/EBPbeta, and C/EBPdelta also showed no change during the training period in jump-trained rats. We suggest that the levels of osteogenic factors that were up regulated by mechanical loading from high-impact jumping suppress adipogenesis in marrow rather than adipogenic transcription factors."
Remember stem cells can differentiate into adipocytes, chondrocytes, or osteoblasts. If stem cells aren't differentiating into adipocytes they are more likely to be differentiating into osteoblasts(which is what increases height). Further, more tubercular bone colume means more red bone marrow means more stem cells. This is the tibia but still an increase in tubercular bone in the epiphysis in that bone would be good for height and the rats may have gained the same benefit in the tubercular bone in their vertebrae.