Here is the theory behind my HTFS formula:
The average error in HTFS for different VII types is only 6%.
However, I didn't study the error in ASTM D341 and density extrapolation, as the paper had the dynamic-viscosity values directly but not the density values.
Here is the comparison of my formula to the test oils in the paper. The oil (type of the base oil, DI, and VII) is described in the first column. I couldn't compare most DI-containing oils except Oil #11 because they didn't have high-temperature data on them.
Note that the DI (detergent inhibitor) package shears as well, in some case substantially. As a result, in the second Newtonian phase (ultrahigh shear rates, full temporary shear), you're left with the base oil + unsheared part of the DI + VII solvent but the VII polymer has no effect.
PMA VII is unusual in that the viscosity-boost rate increases with the temperature, greatly enhancing the viscosity index (VI). Some ultrahigh-viscosity-index 0W-20 oils may be using a PMA VII. The downside is that it requires a lot more polymer than other VII types, which could increase the deposit formation. Nevertheless, the formula still works for the PMA VII, as far as HTFS is concerned. Note that the calculation of the VI, which is a secondary calculation, is not accurate, especially for VIIs with a strongly temperature-dependent viscosity-boost rate.https://docs.google.com/spreadsheets/d/1gnOrQxsbymULx1s6_uBQi8zNHfJXg7lwwQpwzLSIWQI/edit?usp=sharing