The economics behind this is staggeringly flawed.

Technological innovation increases wealth. This is a basic economic principle as evidenced by the industrial revolution (machines took over most of those old jobs, and now there's much less unemployment, poorhouses don't exist, and the average person is much richer in real terms.) To speak of some kind of saturation point where there is a machine for everything is pretty crazy.

Let's step into lala-land and assume there's one machine that can produce anything and perform any task. It requires no maintenance and no inputs. What's the problem? Everyone can have everything. No money required. Winning.

Stepping back to reality all these machines will require production, sales efforts, maintenance, electricity, network infrastructure, yadda yadda. Goods-producing machines will need a supply chain and QA, and people to figure out what to make with it next. And when exactly do we foresee machines taking over the service industry? A machine that provides business consultancy? Cuts your hair? Caters to your animalistic needs? This stuff is a long way off if it's even possible.

Even when machines can do all this we'd need to remove every source of friction in the economy before we could even begin to dream of approaching that saturation point - in short that means global governance and regulation, no taxes, free trade, no behaviour limiting contracts, no currency risk, no language barrier. All of these things create market distortions that create the potential for profit, and where the potential for profit exists, people will exploit it, and there will be jobs.

Long story short: we have many, many problems left to solve before we can all kick back and let the robot butler massage our feet.

Further, the idea that a basic income is best tackled with a crypto-currency is nonsense. Crypto-currencies, like other currencies, derive their value from the underlying assets. You can mine coins, but you can't mine value. In the UK we have a bottom-line tax rate of about 30% of GDP, and about 30% of that is social security. We're a generous country in this regard and have lots of people happily living their lives doing nothing. It's pretty close to this romantic notion of 'basic income'.

If you haven't done the maths on that yet, the UK's percentage of GDP spent on social security is 30% x 30% = 9%. Assuming SocialCoin is the only currency in the world and that global PPP is uniform (and in line with the UK today), we need to solve (as per the 10% of mining proceeds idea):

required_inflation * 0.1 = 0.09
required_inflation = (0.09/0.1) = 0.9 = 90%

A world with 90% inflation is a world in crisis. Assuming instead that we give all mining profits to the needy, we'd still need to maintain 9% inflation...which is also a world in crisis.

I haven't, and won't, even touch on the absurdity of the very notion of 'basic income' (but there's a reason it doesn't enter economists heads).

All in this is just a thin and problematic veil over the desire to redistribute wealth from those who have it to those who don't. Theoretically this is already solidly solved - you take lumps of money from the rich (in any currency you fancy), you walk over to the poor, and you hand it to them. You don't add conditions to it and you do everything to seriously minimise administration costs. This is the second fundamental theorem of welfare economics.