First thing to ask is what in particular is an identity. It can't be a passport, because then the issuer of the passports can create multiple identities. It can't be a device, because then manufacturer of the device can create as many identities as they want. The only remaining thing that comes to my mind is human body. So the system will have to directly interact with the body somehow. It will also have to regularly inspect that the body is still alive, because otherwise it will be possible to collect identities from the dead bodies. Not only it violates the constraints, but it also creates an incentive to create more dead bodies, which is an undesired side effect.
Uniqueness of the body can be checked with a combination of a DNA test and a fingerprint scan. (DNA test alone is not enough, because identical twins have same DNA, and fingerprint scan alone isn't enough either, because there were occurrences when different people had same fingerprints). But this only allows to check uniqueness, not to prove it.
There might be a system in which the ability to check uniqueness is enough. For example, it is possible to make system like this: to get the monthly share of UBI, person P generates a key pair K_priv, K_pub, scans their fingerprints and DNA, and sends a tuple (DNA, fingerprint, K_pub) to the blockchain. The system on the blockchain assigns a random subset S of its users to be verifiers of P. Every person from S scans fingerprints of P, performs a DNA test of P, checks that P is alive, and sends this results to the blockchain, signed with their own private keys. After this, the system checks the results, and if the majority of the verifiers agree, then the system sends UBI to the K_pub.
This system is decentralized, but it has some serious problems: what if P has sent fake fingerprints and DNA to the blockchain, and gave a bribe to the assigned verifiers? Then verifiers can create the fake identity, and share UBI among the group. To decrease probably of this fraud, it is possible make set of verifiers bigger, and raise the threshold of agreement (for example, 90% of verifiers must agree, to send share of UBI). But this gets too expensive and inconvenient very quickly.
Another option is to invent a method that not only checks the uniqueness, but also proves one. For example, if a person carries a device that constantly sends data about their biological activities to the system, and the system can distinguish the signals of real bodies from the signals of fake bodies. The signals might include heart rate, breath rate, EEG, and video stream from the surroundings. Making such discriminator is technically challenging, because artificial neural networks have shown that they are capable of generating very realistic data, fooling any kinds of discriminators. Another challenge is to make a distributed system with a high enough performance, to be capable of processing these data streams.
