For a US citizen you should report any signature campaign taxes at the moment you sell your bitcoin. If you were paid in bitcoin for the signature campaign, the bitcoin you earned would change your cost basis. Now you earned an amazing 0.01 bitcoin for a signature campaign. Your cost basis for this 0.01 bitcoin is 0, since you didn't pay anything for it. To keep things simple, I would recommend keeping your bitcoin separate or keeping all the documentation you need to separate your dates on your tax forms. But lets imagine you didn't keep any documentation or the IRS thought your proof was insufficient. You will likely have to pay taxes on the full 0.01 bitcoins. If you sold the 0.01 bitcoins for say, $120 you would pay the capital gains tax of 15% on the full $120.
This isn't even the main problem. Im not sure if you should declare it as income tax or as you say, 0 cost basis investment, of course you will always pay some tax in any case, the main problem is if you did not keep track record to prove where your bitcoins come from, they could simply claim that the origin could be from drug dealing or some criminal activity, note the "could". You can't prove it, they can't prove it, there is a conflict there. This situation varies a lot depending jurisdiction. Is this grey area that scares me the most. Worst case scenario and you will lose your coins as they confiscate them due "Illegal assets" or something.
For instance, many exchanges are now dead and people have lost tons of track records, or even current exchanges have extremely poor policies in trackrecord keeping, for instance Livecoin is an absolute mess which keeps only the last 30 days of trades, so I have lost some trading records there... honestly it is a nightmare trying to keep track of everything. Now if you try to sell some of these coins involved in lost records you may have problems. Like I said, a total nightmare.