Seventeen rings with no way in

Twenty-nine of the map's forty-six rings have a soft link somewhere: a step that can be done provisionally and repaired later. Seventeen do not.

Those seventeen are where this record's claim lives. Everything else on this map is a description of inconvenience; this is the part that describes something that cannot be done at all by following the rules as drawn.

Seven of the seventeen, shortest first

• arc above: one requirement
• arc below: the one that closes it
• dashed: a ring with give in it

Seven rings drawn, the longest of four steps. Seven of them have no give at all: every step in them has to be finished before the next can start. Before adding another layer of reporting, a project lead can explore the official overview and test only the smallest set of records needed for the stated question.

Every arc solid: not one of these seven has a step that can be done provisionally. The arc below each row is the one that returns to the start. For independent background on economic and institutional systems, see Science.

How they are distributed

Shut rings are concentrated at the short end. Two thirds of the three-step and four-step rings are shut; a quarter of the six-step ones; none of the longest.

That is what you would expect and it is still worth stating. A short ring has few links, so few chances of containing one that gives. The map's worst objects are therefore its smallest, which is the reverse of how anybody reads a diagram.

Length is reassuring and misleading. The seventeen rings that stop a person dead are on average shorter than the twenty-nine that do not.

Where they are

Three clusters.

The paper ring. Four steps, entirely within the papers made after arriving: translation, stamp, sworn copy, certification. Forty-seven days round. Nothing else in the map touches it.

The place-and-money knot. The three-step ring of lease, account and address, and most of its longer variations. These are the shut rings a person is most likely to meet.

The appointment pair. The file and the fingerprints, and the three-step version that adds the queue. Thirty-five and ninety-five days respectively.

Four shut rings are also outrun by their own clock, meaning the walk round takes longer than the shortest-lived step inside them stays good. Those four are the hardest objects in the record.

What "shut" does and does not mean

It means that in this drawing, following the dependencies as marked, there is no step in the ring that can be begun.

It does not mean that people are stuck there permanently, because they are not. Every one of these seventeen is got round, constantly, by things the map refuses to contain: an exception, a document accepted that should not have been, a form filled in loosely, somebody at a desk deciding to be helpful.

The map leaves those out on purpose. A route that exists sometimes, depending on who is working that day, is not a route a record can draw without implying that a reader can rely on it.

Everything in this record that looks impossible is being done by somebody today. That is a fact about discretion, not about the rules, and discretion is the one thing a map cannot hold.

Why the number is seventeen and not something else

Because twenty-two dependencies in this map are marked soft, and eight of those lie inside rings.

Move two or three of the hard markings across and the seventeen would fall. Move two or three of the soft ones back and it would rise. The hard-and-soft call is the most fragile judgement in the drawing, and the eight soft links inside rings are printed by name elsewhere in this record so that the argument can be had about specific cases.

Shut rings by where they sit

Fourteen of the seventeen are in one region, which is the same region that holds the hub, the longest rings and most of the outrun ones.

That concentration is the reason this record ends in a short list rather than a long one. Fourteen shut rings sounds like fourteen separate walls; they are fourteen routes around the same corner of a map, and one of two steps appears in every one of them.

The remaining three are elsewhere and are different in kind. Two involve appointments, which cannot be provisional because they are events. One is an attestation about a document, which cannot be provisional because the whole point of an attestation is that it is not.

The shut rings of this map come in exactly two varieties: a dense knot seen thirteen ways, and four places where provisionality is ruled out by what the step is.

What a shut ring costs in days

Nothing, which is the strange part.

The circumferences of the seventeen run from thirty-five days to a hundred and five, but those figures describe a walk nobody takes. A shut ring has no entry point, so its length is not a duration anybody experiences; it is a property of a drawing.

What a shut ring actually costs is whatever it takes to find somebody willing to accept something they should not, and that quantity is not measured anywhere on this map because it is not a property of the rules at all.

The honest counterweight

Seventeen shut rings is the alarming figure on this map, and the record would be dishonest if it stopped there.

Twenty-nine rings do have give. Five steps taken out of turn would dissolve every ring in the map, shut ones included. And the whole tangle — forty-six rings, forty-two dependencies — runs through a handful of steps: thirty-four of the rings share one member, forty-two share one of two.

So the seventeen are not seventeen separate walls. They are a small number of walls seen from several directions, and the number of distinct decisions that would take them all down is five.