Does savings lead to investment in physical capital? In the introductory macroecon textbook I'm reading, it's made clear that savings=investment.  Mathematically, this makes sense to me.  However, I'm having trouble understanding the qualitative implications.  

After looking through other similar questions, it's clear that this is due to an accounting identity where inventory accumulation due to savings is counted as investment.  

But, I stumbled across this blog post, https://mainlymacro.blogspot.com/2012/01/savings-equals-investment.html, that claims savings eventually equals investment in capital (S=DK).  From what I understand, the author of the post is saying that savings will lead to inventory accumulation, DS, which will eventually lead to output (Y) decreasing.  The output must decrease for the firm to avoid losing money.  Decreasing output will lead to income decreasing, and therefore savings further decrease to the point where savings equal DK, or investment in capital goods. 

Why does the eventual decrease in savings cause savings to equal investment in capital goods (S=DK)?  Am I correctly interpreting what the author of the post is saying?
I think that part of the blog post is just saying that savings may not equal investment in capital immediately, because there can be a delay caused by firms accumulating inventory.  But firms can't continue to accumulate inventory indefinitely, so this is only a transient phenomenon.  Sooner or later, inventory will reach a new equilibrium and savings will equal capital investment again.

He then goes on to talk about the reasons that a higher savings rate is unlikely to be sustained (the paradox of thrift).