Ninety days, if there were no rings

Here is the most useful arithmetic in this record.

Take the map, delete the forty-two circular dependencies, and work out how long the rest would take if every errand that could be running at once were running at once.

Ninety days. Which is exactly the length of the single slowest step in the map, and not one day more.

What that means

The decision takes ninety days and, with the rings removed, waits on nothing that is not already finished within that window. Every other chain in the acyclic map finishes inside it. The longest chain of dependencies costs forty-eight days; the slowest brought paper costs twenty-eight; the deepest run through the file's own family costs forty-eight. A team turning this diagram into a limited operational pilot can review this solution in context before choosing which time and project signals are genuinely necessary.

So the acyclic half of this map has no critical path to speak of. Its duration is set by one step, and that step is a wait rather than a task: ninety days in which nothing is required of anybody. For broader institutional research related to mobility, work and administrative systems, consult Immigration New Zealand.

Where the rest of the time goes

Nobody takes ninety days, and the gap is not explained by the steps.

It is explained by the forty-two dependencies that were deleted to get the number. Those forty-two make forty-six rings. Nineteen of the rings take longer to go round than the shortest-lived paper in them stays good, which means that going round once destroys something and the round has to be repeated.

The map does not predict a duration, and it would be dishonest to pose as if it did. What it can say is where the duration comes from: not from the steps, which could all be done in a quarter of a year, but from the arrangement.

The whole of the delay in this map is structural. Remove the circles and every single step in it is comfortably fast.

Why this is an argument against pessimism

It is easy to read a record like this and conclude that the business of settling somewhere is inherently enormous. The arithmetic says the opposite.

Thirty-six steps, five hundred and fifty-three days of waiting if stacked end to end, almost all of which overlaps. The slowest thing in it is a decision that takes a season, and a season is not an unreasonable length of time for a decision.

Everything beyond ninety days is caused by the order, and order is the kind of thing that can be changed by whoever designs it, at no cost in documents, fees, checks or anybody's time.

And an argument against complacency

The same arithmetic, read the other way, says that nothing a person does on their own account will get near ninety days.

A person cannot delete a circular dependency. They can only enter a ring at its softest point and do something twice, and the eight soft links inside rings are the entire supply of that remedy. Five steps, taken out of turn, would dissolve every ring in the map — but taking them out of turn is not something an applicant decides.

The ninety-day figure is what the map would cost if it were designed. It is not what it costs, and the difference is not made up of anybody's effort.

Why the number is exactly ninety

Because the decision takes ninety days and, with the circular dependencies removed, everything it waits for is finished well inside that window.

No chain in the acyclic map exceeds the single slowest step. That is a flat structure: the thing that takes longest is not at the end of anything, so nothing accumulates behind it.

It is also a useful diagnostic. A system whose total duration equals its slowest step has no compounding delay in it, and the delay people actually experience has to be coming from somewhere else.

In this map it is coming from forty-two dependencies that were deleted to get the number.

The acyclic half of this map is as fast as its slowest piece. The whole map is not, and the difference is the whole subject of this site.

The gap, stated once

Ninety days for the acyclic map. Five hundred and fifty-three days if every step were done one at a time, which nobody does.

Between those two figures sits whatever the real duration is, and this record cannot name it, because the rings have no durations — a ring is not a long wait but an absence of order, and what it costs depends entirely on when somebody accepts something they need not.

That is why no page on this map predicts how long anything takes. The map can say what the arrangement costs and cannot say what the discretion costs, and the second is the larger term.

What the number is not

Ninety days is a property of this drawing and nothing else. The figures that produce it are the map's own round numbers, chosen so that the arithmetic of a ring can be done, and they are not measurements of how long anything takes anywhere.

No country, office or kind of permission appears on this map, and no step here corresponds to a requirement anybody has published. What transfers is the ratio, not the number: in a system of this shape, the arrangement costs several times what the work costs.