• The internet gives us digital abundance. Cryptocurrency gives us digital scarcity. What’s in the middle?
• Some digital assets can be copied indefinitely. Some can’t be copied at all. What are some that can be copied a bit?
• What’s an asset that you’d go out of your way to get, but would also happily give away?

In his 1872 novel Erewhon, also credited as being one of the first novels to speculate about artificial intelligence, Samuel Butler described ‘musical banks’. Hubs of a parallel economy, these institutions dispensed and dispersed currency that was useless as a medium of exchange. Whilst Butler was satirising Victorian attitudes to religion - and not from a position of reverence - the question of how such currency might be instantiated is an intriguing one.

Many of the valued things that we give away for free have a revered place in society. This project is not about those, but is about financial instruments like vouchers. ‘10%-off-first-purchase’ vouchers, say. Other examples include things like referral codes, sign-up codes for forums, etc. These things are an asset-class, but are not currently supported by decentralised infrastructure.

Taking the example of the ‘10%-off-first-purchase’ voucher, and considering its properties, the problems associated with issuing a crypto-analogue of a voucher become clear.

• The issuer of the voucher is willing to discount their products in order to improve their sales. They are willing to issue the voucher in a set quantity. They are willing to let prospective customers pass the voucher to other prospective customers. Indeed, the value of the voucher to the issuer is enhanced if customers organically do this. More ‘buzz’ produces more sales.
• The voucher has narrow monetary value to prospective customers as it can be exchanged for ‘10%-off’ a range of products from a specific vendor. However, once a prospective customer redeems the voucher (becoming simply a customer) it no longer has monetary value to them, though it can still have value to others.
• An existing customer can pass the voucher to a prospective customer without losing anything. They can be benevolent without incurring any cost. A prospective customer can request the voucher from an existing one knowing this. The issuer can benefit from an interaction between private individuals that might otherwise not have happened.
• However, the voucher becomes a liability to the issuer if it becomes available on-demand from a centralised entity like an exchange.
• An exchange makes it possible for holders of the voucher to profit by selling it. Voucher-holders may choose to sell the voucher rather than making a purchase from the issuer or passing it to a friend. Prospective customers may then be required to buy it. The benefit in terms of ‘buzz’ is lost. Worse, a rent-seeking intermediary is profiting at the issuer's expense.

Issuing a transferrable digital voucher as a conventional token or NFT could lead to its rapid exploitation by third parties. To be effective - and useful to its issuer - a voucher should be efficiently propagated at the interface between social and financial networks, but it must also be resistant to commodification.

Conventional ‘scarce’ digital tokens and NFTs cannot be copied but can be sent between individuals. A transaction between individuals equates to a loss to the sender and a gain to the recipient. In contrast, a copyable ‘abundant’ digital asset can be sent to a recipient while also being retained by the sender. An intermediate situation would be a token or NFT that can be retained by its sender but only copied and sent a limited number of times to a limited number of recipients. This kind of asset could be viewed as ‘semi-scarce’ and/or ‘semi-abundant’. The design would favour propagation because a sender could send it without losing it. On the other hand, an individual sender would not be able to distribute it to an unlimited number of recipients.

One way to design a copy-spendable NFT voucher, a CS-NFT, would be as follows:

1. The CS-NFT is a badge. The ‘voucher’ functionality (ie. the ‘10%-off’) utilises the CS-NFT as a badge, so it is not necessary for an owner to send the CS-NFT in order to redeem it.
2. The CS-NFT is ‘soulbound’ unless copy-spent via a CS-component. This prevents an owner from sending it conventionally if it can’t be copied.
3. To copy-spend the CS-NFT, the sender sends the CS-NFT and a recipient address to the CS-component.
4. The CS-component determines whether each CS-NFT it is sent is ‘copy-competent’ or not. If it is ‘copy-competent’, the CS-component makes two copies and burns the original. One of the copies is returned to the sender and one is sent to the recipient. Alternatively, if it is not ‘copy-competent’, the CS-NFT is returned to the sender.

This scheme partially reduces the potential for commodification of the CS-NFT by a third-party exploiter in several ways. First, because the copy-spend function of the CS-component is uncertain – the spendability of a CS-NFT is not guaranteed – it might be difficult for an exploitative seller to construct a way to exchange CS-NFTs for payment automatically and trustlessly. Next, although an exploiter may try to ‘farm’ a CS-NFT by copy-spending it amongst multiple accounts that they control, this would not necessarily increase the number that they could try to sell. The exploiter risks exhausting the intrinsic copyability of the asset, and ending up with immovable, unsalable, ‘soulbound’ CS-NFTs. However, it remains possible that a determined exploiter might still find a way to profit. Formally, a CS-NFT intended to propagate organically could be ‘farmed’ inorganically by an exploiter who mimics the pattern of organic propagation they observe in the rest of the network. Also, while the scheme provides a means of maximising the breadth of distribution, it does not provide the issuer with a means of limiting the rate of issuance or the total number of CS-NFT recipients to within reasonable or affordable bounds.

Some NFTs have a ““”DNA””” “””genotype””” that “””evolves””” and is used to procedurally generate graphics of some sort. However, some crypto developers appear to have borrowed these terms without first reviewing the extensive relevant literature in computational biology and coding theory.

Manfred Eigen published this just over fifty years ago. It’s advanced technology. The third of Arthur C. Clarke’s three laws is “Any sufficiently advanced technology is indistinguishable from magic.”. Well, for me, since I don’t have enough maths, Eigen’s writing might as well be a book of spells written in runes. If you do have enough maths, then maybe you will be able to appreciate it. Although if you don’t have enough biochemistry, maybe it will seem like a book of spells to you too.

Eigen’s work coined the terms ‘quasispecies’, ‘sequence space’, ‘error-threshold’, ‘extinction-threshold’ and ‘hypercycle’. Subsequent works that built on it came up with ‘neutral networks’ and ‘survival of the flattest’. Most relevant to a parsimonious design for a decentralised ‘10%-off’ voucher are the relationship between the ‘error-rate’ in replication (copying) and the phenomenon of quasispecies. A less dense explainer is here.

The principle is that an initial hypothetical self-replicating molecule consists of a sequence of digits; probably a short series of digits. This is its ‘genotype’. When it replicates (when it is copied), the copying of each individual digit is subject to an ‘error-rate’, mu. Errors result in changes to the sequence of the genotype of the copy. As the sequence of copies become more different from the original, their capacity to replicate – their copyability – is reduced. What’s interesting is that for certain initial sequences, and certain ‘error-rates’, modelling shows that within the population, you get a ‘cloud’ of diverse genotypes surrounding a rare original genotype, even though the original genotype is able to replicate more efficiently. The collection of genotypes that make-up the population is called a ‘quaispecies’.

Apply this to the way the CS-component determines whether a CS-NFT sent to it as part of a copy-spend transaction is ‘copy-competent’ or not, and the way it then copies and returns the copies if it is:

1. Each CS-NFT contains a ‘genotype’ sequence.
2. The CS-component contains a single ‘reference-sequence’.
3. Upon receiving a CS-NFT as part of a prospective copy-spend transaction, the CS-component calculates the ‘Hamming distance’ between the NFT ‘genotype’ and the ‘reference-sequence’. Below a certain distance the CS-NFT is copy-competent and the copy-spend transaction proceeds. Above that distance, the CS-NFT is not copy-competent and is returned to the sender.
4. When a copy-spend transaction proceeds, two new copies of the CS-NFT are minted and the original is burned. The ‘genotype’ of the original serves as a template for the ‘genotypes’ of the copies, but the copying is subject to an ‘error-rate’. Thus, the CS-NFTs returned to the sender and the recipient may (or may not) have a different ‘genotype’ from the original. If they do have a different ‘genotype’, the copies may (or may not) be copy-competent themselves.

The above scheme is parameterised to promote the generation of quasispecies of CS-NFTs with diverse ‘genotypes’. Added to this, the issuer can use an admin badge that allows them to update the parameters corresponding to ‘reference-sequence’ and ‘error-rate’.

If information from customers or analysis of the network suggests that an exploiter is ‘farming’ the CS-NFT, and the ‘genotypes’ that constitute the CS-NFT quasispecies network-wide are sufficiently diverse, then a change in the ‘reference-sequence’ can be engineered that will differentially disadvantage the exploiter. By biasing the exploiter’s CS-NFTs towards an ‘error-catastrophe’ whilst producing a neutral effect across the organically-propagating CS-NFTs, the issuer can fuzzily ‘range-ban’ the exploiter without actually possessing the NFTs themselves. The cool thing here is that this works even where an exploiter has ‘farmed’ CS-NFTs by mirroring copy-spend trajectories of organically-propagating CS-NFTs. The experience of organic customers, even if nominally disadvantaged by a change to the ‘reference-sequence’, would not be noticeably altered.

Issuer-changes to ‘error-rate’ could be used to limit the rate of issuance or the total number of CS-NFT recipients in an unbiased manner.

The Radix Scrypto Challenges code is released under Radix Modified MIT License.

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