"it may vary from node to node" - so, what is node? Do you mean a technology node (45nm, 25nm, ...)?
" number of extraction corners are defined by Foundry" - how many extraction corners are usually used for 45nm libs?
"extraction corners" - are we talking about delays over nets? After P&R all the nets (their length, width, etc) are known, so all the delays over these nets are also known, so why more than one RC extraction is required? Are you talking about RC extractions for different PVT (MIN/MAX or BC/WC)? So, if there are only two PVT conditions, how RC-extractions might be more than two? Number of PVT std libs = Number of possible RC extractions?
As for TYP libs, does anybody use them? What for?
"If you consider modes, then formula will become" - what modes do you mean? I know the PVT and OCV modes (is PVT mode?), what do additional modes exist?