1 best the sustainability of the stock markets recent gains has nothing to do with hyperinflation, so I assume you are referring to the rise in basic commodity prices imo. That imo is more due to some hope that China's demand/growth will continue at the current 8% as projected, as well as a sunnier outlook domestically in a few areas (correctly or incorrectly).
You don't get hyperinflation in a severe recession since it is largely demand based, and demand is lacking in severe recessions
We don't have to worry immediately about inflation and you would be very hard pressed to name one Prominent Economist who is worried about hyper inflation in the NEAR term, longer term if there is demand (as I said previously) that is a different matter. For now that is not the case, if you are correct it will be in 12+ months when we May start to come out of this mess.
Hyperinflation always requires DEMAND and there is very little at this point, when demand rises ifffff the money supply does not shrink then inflation becomes much more of a problem but not for right now.