The four pairs that require each other

Four pairs in this map are mutually dependent. Each member waits on the other and on nothing else in that particular circle.

The eighteen-day pair

An account at a local bank waits on a showing of regular income. A showing of regular income waits on an account at a local bank. Teams dealing with repeated queues and handoffs can compare this approach in practice, then evaluate whether the resulting evidence actually reduces delay or ambiguity.

The dependency running from the account to the income is soft: an account can be opened on some other footing and the income shown afterwards. That one soft link is why this pair is passable, and it is also why nearly everybody who has done this has a story about the form they filled in that did not quite describe their situation. Additional public research relevant to complex systems and work can be found at IEEE.

The pair is short in days — eighteen — which makes it the cheapest ring in the map to walk once you are in it.

The twenty-eight-day pair

The account waits on a number for the tax register. The tax number waits on the account.

Here the soft link runs the other way: the tax number can be obtained provisionally without the account, and corrected once the account exists.

Two of the four two-step rings therefore run through the account at a local bank, which is the first sign of a pattern that dominates this record: thirty-four of the forty-six rings in the map pass through that single step.

The thirty-six-day pair

Cover against illness waits on the card in hand. The card in hand waits on cover against illness.

This is the only two-step ring in the upper half of the map, and the soft link is the first of the two: provisional cover is obtainable, and it is replaced once the card exists.

That single marking opens eight of the eleven rings in the map that avoid the place and money families altogether; the other three are shut. If it were hard instead, the whole upper half of the map would be as stuck as the lower half, and this record's claim that most rings have give in them would look very different.

The thirty-five-day pair

The file lodged and the sitting for fingerprints wait on each other, both hard.

It has its own page in this part, because it is the only shut pair and because it is the clearest statement of what a ring is.

What the four have in common

In every one of them, two institutions each want to see the output of the other.

A bank wants to know what you earn; the thing that establishes what you earn, in a form a bank will take, is produced through a bank. A tax register wants an account; the account wants a tax number. Cover wants proof of status; status wants cover.

Nothing in that is malice or carelessness. It is what happens when two systems are each designed to be careful and neither is designed to go first.

A two-step ring is the sound of two careful institutions declining to move until the other has.

How a two-step ring is usually described

Not as a ring. As two separate pieces of bad news, delivered a week apart by different people.

Somebody is told they need a tax number before an account can be opened. They go away and try to get a tax number, and are told an account is needed first. At no point does anybody say these two requirements are mutually exclusive, because no single person is aware of both.

The shape of that experience is identical across all four pairs here, and it is the reason this record exists in the form it does. The information needed to recognise a two-step ring is held by two parties who do not speak to each other, and the only person who meets both is the one with no standing to say so.

A two-step ring is the smallest object in this map and the hardest to be told about, because telling requires somebody who has seen both halves.

Why three of four give

The three giving pairs all have a provisional form available: a limited account, a temporary number, basic cover. The shut pair has none, because an appointment cannot be provisional. Either somebody's fingerprints have been taken or they have not.

That is the general rule the four pairs demonstrate. Documents can be provisional. Events cannot.

Of the six steps in the body-and-time family, five are events. Four of the map's rings pass through a place in the queue and all four are outrun by their own clock. The events are where this map stops being negotiable, which is worth knowing before spending effort on the documents.