Issued, listed, or made?
A cap and a list are the same office. A made object has no office.
A numbered token from a fixed mint and an account from a registrar both look scarce. A made object can look like both. It is not in that category. The first two were given. Nobody gave you the third.
The giver is not only a clerk. A passport, a ticket, the account you use to read your email: each was handed out by an office that is still there, maintaining a list, and able to take you off it. A consensus network can do the same job without a clerk. The rule is a protocol, and the protocol is a policy a group keeps. Spreading the office across many machines does not take the rule out of policy. Being let in, and a rule letting you in, are still the same idea. Scarcity by permission. It works. It also charges rent: the rule has to keep being kept.
Permission is not the only way a thing becomes hard to get. A tree ring is scarce. You cannot have a hundred in a year, and nobody issues them. Limited by what it took to produce them, not by anyone controlling supply. Nobody hands them out. Nobody can take them back.
Copies are free, so a digital thing of that kind has to carry the cost inside itself. How that cost is put there is How do you make a digital thing scarce?
Allocated. A cap exists. Someone wrote the number. The scarce step is the rule that said how many. Admitted. You approach a registrar, or a network that agrees who counts. After listing, the object itself is cheap. The scarce step is getting on the list. They feel like opposites. Both are given. The rule that created the thing, or whoever can change it, can refuse the next one, or take this one back.
A made object has no such office. There is no cap to run out of. There is no list to join. The next one starts at zero. A hard-capped token is the usual mix-up. It is scarce. It is still issued.
Bitcoin, used as money, is this kind of limit: a supply rule, kept for as long as participants keep it. Bitcoin, used here, does not issue the object. It is an open sequence. What that sequence is, is How do you prove when the work happened? A post box is not a mint.
These are not one census. A number of cost-backed identifiers can sit side by side, different contracts, different resource commitments. Whether to accept one is a gate the holder keeps, not a census a protocol takes. Why is the check always cheaper than the making? What has been shown is one prototype of one candidate. The common foundation is the Bitcoin-anchored constraint, because Bitcoin is an open system.
It does not prove a person. It does not cap a population. The claim is never that you cannot make many. It is that many costs many times what one costs. A gate tries to stop the wrong arrivals. Making prices the arrivals. A system only the wealthy can enter has reinvented the office. Why that still bites when someone wants many at once is What kind of cost refuses to divide?