Sticky prices are not a thing
Prices in an economy are like monomers in a plastic polymer polymers. Individually there is litte resistance to change, they are not "sticky" as neo-keynesians assume. Looking at all of them as a whole in an economy it becomes unlikely that a bunch of prices will go in the same direction. And indeed in the authors find that individual prices are not sticky, but reference prices are.
But again, entropic forces can be overcome with coordinated action.
This reminds me that there is no theory of inflation.