How does Nickel Purity work?  

My testing indicates that it works very well, and very logically.
It would appear to quite simply be a Temperature Coefficient of Resistance (TCR) scale.
The scale of Nickel Purity is 10 - 100. The default on the new Infinite mods is 70.

I have found that a value of 10 is roughly equivalent to a TCR value of 0.001 and a value of 100 is 0.01.
Ni200's coefficient of approx. 0.006 would suggest a value of 60.
Titanium's coefficient of 0.0035 would suggest 35.
And Stainless Steel, whose coefficient is around 0.00094, would use a value of 10.
I have tested all these wires and various values, and found that they mostly work as expected:

Titanium on a setting of 35 vapes well, and much better than it does on a normal TC mod (DNA 40/Yihi).
However I have found a slightly better vape from increasing the value, up to around 42.
Stainless Steel on a setting of 10 also vapes well, and becomes properly usable for TC for the first time
But a temperature offset is still required - around 40-50°F I am finding.
I still need to do more thorough testing, including with other attys
With Ni200, a value of 60 would seem appropriate from the scale, but in practice I am finding the default of 70 works a bit better (no doubt that's why it's the default).