The pieces

The paper everything starts from

One step in the map is needed by eleven others, takes a single day, and never expires. It is a photocopy.

Finding

The most load-bearing step in this map is a copy of the passport page. Eleven of the other thirty-five wait on it. It takes one day and never goes out of date.

Nothing else in the map combines those three properties, and the combination is worth a page because it is the clearest example of a quantity the map measures and nobody notices: how much of the structure rests on an act that costs nothing. To compare the map with real work patterns, reviewers can see the official documentation and define the decision, access rules and review date in advance.

Who waits on it

the step that waits	family	hard or soft
a record of having no convictions	papers brought	hard
a record of the partnership	papers brought	soft
a photograph cut to a set size	papers brought	soft
a statement written by the person	papers made	soft
a room for the first weeks	a place	hard
a lease in one's own name	a place	hard
a registered address	a place	hard
an account at a local bank	money	hard
a number for the tax register	money	hard
a sitting for fingerprints	body and time	hard
the file lodged	the file	hard

Eight hard, three soft, across five of the six families. The only family that does not wait on it is the file's own interior — the receipt, the decision, the card — and those wait on the file, which waits on it. A wider policy and evidence perspective is available from World Resources Institute.

One day, eleven consequences

The arithmetic is blunt. Begin the copy on day one and nothing in the map is ever held up by it. Begin it on the day it is first demanded and eleven separate chains have a day added to them, several of which are inside rings, where a day added does not simply add a day.

The map's worst delays are not caused by its slowest steps. They are caused by its fastest steps being left until last.

The slowest step in the map takes ninety days and holds up exactly one thing. The fastest step in the map takes one day and holds up eleven. A plan built around what takes longest will get this exactly the wrong way round.

Why it is not in any ring

For all its weight, the copy of the passport page stands in none of the forty-six rings.

That follows from its position: it waits on nothing. A step with no predecessors cannot be part of a closed chain, because a closed chain has to come back to it, and nothing can come back to a step that nothing leads out of in the first place.

So the most-required step in the map is also one of the thirteen steps that stand entirely clear of the knot. It is required by things that are deep inside rings, but it is not itself tangled.

This is a useful distinction and an easy one to lose. Being needed by many things and being caught in a circle are different kinds of importance, and only the second one makes an order impossible.

What the map is not saying

It is not saying that a copy of a passport page is a requirement anywhere. The map names no country, office or kind of permission, and this step is a stand-in for a class of thing — proof of who you are, in a form that can be handed over and kept — rather than a document anybody has asked for.

Nor is the figure eleven a measurement. It is a property of this drawing. A different reasonable drawing of the same territory would put the number somewhere between eight and fourteen, and the point survives any of them: there is a cheap step near the bottom that an unreasonable amount of the structure rests on.

What happens if it is lost

A copy of a passport page is the easiest thing in this map to replace — one day, no predecessors — and the map's structure means losing it is still expensive.

Eleven steps wait on it, eight of them hard. Six of those eleven are themselves inside rings, so a day lost here is not a day lost once. It is a day added to several laps that may already be longer than something inside them lasts.

what waits on it	inside a ring
a lease in one's own name	yes
a registered address	yes
an account at a local bank	yes
a number for the tax register	yes
a room for the first weeks	yes
a sitting for fingerprints	yes
the file lodged	yes
a record of having no convictions	no
a record of the partnership	no
a photograph cut to a set size	no
a statement written by the person	no

Seven of the eleven are tangled. That is the highest concentration of ring-standing successors behind any step in the record, and it belongs to the cheapest errand in it.

The map's cheapest step is the one whose absence is felt in the largest number of places at once.

The general case

Look at the map by the ratio of what a step holds up to what it costs in days, and a short list falls out:

step	days	things waiting on it
a copy of the passport page	1	11
the fee paid	1	5
a certification of that translation	7	3
a showing of regular income	6	4
a card that works locally	9	3

Five steps, none of them taking more than nine days, between them holding up twenty-six of the ninety-four dependencies in the map.

A quarter of all the waiting in this map is caused by five errands that take, altogether, a little over three weeks.

None of those five is anybody's idea of a milestone. Four of them are paperwork and one is a payment. They are exactly the steps a person puts off, because none of them feels like progress, and they are exactly the steps that decide how long everything else takes.