Why memory, and why a clock?

The obvious question is why memory is involved at all. The usual answer is that reading memory is slow, so forcing you to read a lot of it makes the work expensive. That is wrong. Fetching a piece of memory is quick. Most of the time goes to the processor doing arithmetic.

So why hold a region at all?

Because of what the arithmetic is arranged to need. Each step reads one small piece of a large region, mixes it into a running value, and the result decides which piece to read next. You cannot know the third piece until you have finished the second. There is no looking ahead. This is not a search for a rare hash. The work is the forced route through a region you have to keep holding.

A producer who stores nothing, or who stores on disk, pays more than one who holds the region in memory. The design did not impose the memory. It arranged the work so that memory is what anyone sensible would choose.

Which is why "is it limited by the processor or by the memory?" is the wrong question. They are coupled. What is being spent is occupancy: space held for a length of time. The processor is busy for some of that time and idle for the rest. The space is held either way.

That unit is familiar. Nobody rents a room. They rent a room-night. Two guests cannot occupy the same room on the same night. Ten nights costs ten nights whether one traveller takes them in a row or ten take them at once. Each leg holds its own region for its own duration.

The idle stretch is most of the arrangement. A leg runs its steps and then stops until the next public tick closes the stage. The region cannot be handed back during that wait because the stage is still open. Releasing it would abandon unfinished paced work. Most of an object's life is spent holding rather than running. That is not waste. It is time on a public clock nobody owns.

Then the difficulty: the two halves of the unit are not equally provable.

The space half leaves evidence. There is an object at the end, and checking it re-runs enough of the work to establish the leg results the object claims. The time half leaves nothing in the bytes alone. A producer can hand over a result and say it took a day. Nothing in the file distinguishes a day from a decade. Duration is the half the person claiming it cannot demonstrate.

What supplies that when is How do you prove when the work happened?