The only "authoritative document" issued by the IRS to date relating to Cryptocurrencies is Notice 2014-21. It has this to say as the first Q&A:
Q-1: How is virtual currency treated for federal tax purposes?
A-1: For federal tax purposes, virtual currency is treated as property. General tax principles applicable to property transactions apply to transactions using virtual currency.
That is to say, it should be treated as property like any other asset. Basis reporting the same as any other property would apply, as described in IRS documentation like Publication 550, Investment Income and Expenses and Publication 551, Basis of Assets. You should be able to use the same basis tracking method as you would use for any other capital asset like stocks or bonds. Per Publication 550 "How To Figure Gain or Loss",
You figure gain or loss on a sale or trade of property by comparing the amount you realize with the adjusted basis of the property.
If the amount you realize from a sale or trade is more than the adjusted basis of the property you transfer, the difference is a gain.
If the adjusted basis of the property you transfer is more than the amount you realize, the difference is a loss.
That is, the assumption with property is that you would be using specific identification. There are specific rules for mutual funds to allow for using average cost or defaulting to FIFO, but for general "property", including individual stocks and bonds, there is just Specific Identification or FIFO (and FIFO is just making an assumption about what you're choosing to sell first in the absence of any further information).
You don't need to track exactly "which Bitcoin" was sold in terms of exactly how the transactions are on the Bitcoin ledger, it's just that you bought x bitcoins on date d, and when you sell a lot of up to x bitcoins you specify in your own records that the sale was of those specific bitcoins that you bought on date d and report it on your tax forms accordingly and keep track of how much of that lot is remaining. It works just like with stocks, where once you buy a share of XYZ Corp on one date and two shares on another date, you don't need to track the movement of stock certificates and ensure that you sell that exact certificate, you just identify which purchase lot is being sold at the time of sale.