What is Treasury Currency Outstanding?

I think that Treasury Currency Outstanding (TCO) is very odd.

First of all, what is it?  The dictionary defines it as "currency (as coins, United States notes, or Federal Reserve notes) other than gold coin or gold certificates for which the U.S. Treasury is directly responsible".  So I guess it is mostly coins, but also includes a small amount of United States Notes in collectors hands, which still have value as currency.

Second of all, why is it an asset on the Federal Reserve Balance Sheet?  Federal Reserve Notes (e.g. dollar bills) are liabilities.  Here is an explanation:

Source: http://www.phil.frb.org/research-and-data/publications/business-review/1988/brjf88sm.pdf

Very complicated.  I will use symbols to try to understand this. 

N = Federal Reserve Notes Outstanding, which are a liability of the Federal Reserve.  To be specific, in this formula, it includes all FRNs, either in circulation or held by the government.

C = Treasury Currency Outstanding (mostly coins), which are a liability of the Treasury, either in circulation or held by the Fed.

TC = Federal Reserve Notes held by the Treasury, which are not in circulation.  Note that is not the Treasury's checking account with the Fed, this is actual cash that the government has in its safes.

CIC = Currency in circulation. If everybody in the world (excluding the Treasury) added up all the cash and coins in their pockets, wallets and safes, this would be the total.

Formulas:

CIC = N + C - TC

CIC + TC = N + C

N = CIC + TC - C

It is just an algebra problem.  So that is why coins in your pocket are treated as an asset on the Fed balance sheet, even though it has no control over them at all (it doesn't possess them, mint them, or issue them).

What about coins held by the U.S. government?  They have no value until placed in circulation.  What about coins held by the Fed?  The amount is probably small enough that it can be ignored.  But suppose it wasn't minuscule, suppose it had $100 billion worth of quarters (or platinum coins).  Now someone buys some of the coinage with FRNs.  The asset would be reduced, as would the liability (because a dollar bill in the hands of the Fed has no value).  But wait ... it is still an asset, even in private hands, so that doesn't balance.

Try #2, have a separate line item for Treasury Currency held by the Fed, as an asset. When someone buys coins, on the asset side it would change to Treasury Currency Outstanding.  On the liability side, there is no change in CIC, because N decreases and C increases by the same amount.