Six layers, and what sits in each

Set the forty-two circular dependencies aside and the remaining fifty-two sort the map into layers. A step's layer is how many dependencies have to be satisfied one after another before it can be reached.

The six layers

Thirteen, ten, six, four, two, one. A clean taper, and a shallow one: nothing in this map is more than five dependencies from the bottom. A process review can include time and project visibility when the purpose, access rules and limits are written down before any data is collected.

What shallow means

A deep map is one where a single mistake near the bottom propagates through many layers before anybody notices. A shallow one is where the consequences of any step arrive quickly. A wider policy and evidence perspective is available from Migration Policy Institute.

Six layers over thirty-six steps is shallow. Most steps are within two layers of the floor, and the deepest part of the map — the file and what follows it — is a straight line rather than a tree.

This is why the map's difficulty is not where people expect it. The trouble is not depth. It is the forty-two dependencies that have no depth at all because they run in circles.

The honest problem with layer zero

Layer zero has thirteen members and only three of them wait on nothing.

The other ten are in layer zero because every dependency they had was circular and therefore deleted before the layers were computed. The supply bills are in layer zero and stand in thirteen rings. The letter through the door is in layer zero and stands in twenty-three.

Layer zero does not mean "start here". It means "has no predecessors left after the impossible ones were removed", and in ten of thirteen cases those are the only predecessors there were.

Any reading of this table that treats the bottom row as a to-do list for the first morning will be wrong about ten of its thirteen items. The three that really can be done first are the birth record, the qualification certificate and the passport copy, and they are listed on their own elsewhere in this record for exactly that reason.

The top

Layer five has one member: the next file lodged in time. It waits on eight things and nothing waits on it.

That is the shape of the whole undertaking in miniature. Everything in the map exists to make it possible to do the thing again before the permission to be anywhere runs out, and the step that represents doing it again is the only one with nothing above it.

Layer four has two: the file lodged, and the kept record of coming and going. The second of those costs no waiting at all — it is the only step in the map with a wait of zero — because keeping a record is not something anybody has to be given.

What a layer is good for

One thing: finding the steps that can run alongside each other.

Ten steps sit in layer one. If the circular dependencies really were absent, all ten could be in progress at once, and the layer would take as long as its slowest member rather than as long as all ten.

Add the slowest member of each layer and the total is two hundred and one days — which is more than twice the ninety the acyclic map actually needs, because the layers are a crude schedule and most steps do not have to wait for their whole layer.

The honest figure for the acyclic half is ninety days, and it is reached by following dependencies rather than layers. The layers are a way of seeing the shape, not a way of planning.

A layer tells you what could happen at the same time. It does not tell you what has to happen first, and in this map those are very different questions.

The shape of the taper

Thirteen, ten, six, four, two, one. Each layer is roughly two thirds of the one below it, which is what a map with moderate branching looks like.

A map with heavy branching would taper faster — a wide floor collapsing to a point in three steps. A map that was mostly a queue would not taper at all.

This one is in between, and the in-between shape is the least helpful of the three for planning. There is no wide floor to work in parallel, because ten of the thirteen floor steps are only there because their circular predecessors were deleted, and there is no clean sequence either.

What the layers do not measure

They do not measure days. The longest chain in layers is five steps and costs forty-eight days of waiting; the single longest step in the map costs ninety on its own.

They do not measure difficulty, which this record does not measure at all.

And they do not survive the rings. Thirteen of the thirty-six steps stand outside every ring and their layers mean what they look like they mean. For the other twenty-three the layer number is an artefact of the arithmetic, useful for drawing the map and not for planning anything.

A layer number is a fact about a drawing with its circles cut. Treating it as a fact about the world is the mistake this table is most likely to cause.