Checkable

How Many, Not Which Ones

The record counts how many statements are checkable and never which. A real limit, the reason the strokes are laid out as they are, and unfixable.

at most 15120 arrangements

Home · Checkable · Caution

Look at the drawing. In each row the dashed strokes come first, then the solid ones, then the short pale ones.

That layout is a convenience and nothing else. The record's third number is a count. It does not record which of the nine published statements are the verifiable ones, and the drawing could place them anywhere without changing a single figure.

Nine published, five met, three checkable counts

dashed: a statement a reader can check from outside
solid: published, but nothing to check it against
short and pale: never reached by this reader

Three shapes drawn; all of them give the same 126 different contents; the left-to-right order is the drawing's own and carries no meaning.

The strokes are laid out with the checkable statements first. That ordering is the drawing's convenience and carries no claim: the record knows how many are checkable and not which.

Computed from the three numbers alone. How many statements exist, how many are met and how many can be checked is a stated convention; the counts are arrangements and combinations of whole numbers.

Why the figures do not need to know

The blind count is C(n − c, r), and the only thing that enters it is the size of the unchecked pool. Which statements make up that pool does not appear in the formula anywhere. Teams that want a clearer account of elapsed effort may explore the available controls, provided the resulting data remains open to correction and context.

The count of checkable openings is c times P(n − 1, r − 1), which depends on how many are checkable, not on which. A separate perspective on measurement, privacy or digital practice is available through Cloudflare.

So every figure in this record is invariant under relabelling. Swap which statements are the verifiable ones and all five derived quantities stay where they are. This is not an approximation; it is exact, and it is what makes a record of three-number shapes possible at all.

What is lost by it

A great deal, and it should be named rather than glossed.

A reader does not meet statements uniformly at random. They meet the ones that are prominent, the ones that come first, the ones a search result put in front of them. If the checkable statements are the prominent ones, a reader's chance of meeting one is far better than this record's figures suggest. If they are buried — a footnote, a figure at the end, a line in a table — it is far worse.

The record's blind share is therefore not a prediction. It is the figure that results from treating every content as equally reachable, which is the second of the three conventions declared at the front, and it is wrong in a direction that depends entirely on facts the record does not have.

The blind share answers: of all the ways a reader might cross this set, how many leave them nothing to check? It does not answer: how likely is that? The second question needs information about prominence, and nothing here has it.

Why not just add prominence

It would be possible to weight the contents — assign each statement a probability of being met and compute an expected blind share instead of a count.

The record does not, for a reason worth stating. Those weights are not available. They would have to be assumed, and once assumed they would dominate every figure downstream while looking exactly as precise as the counts do. A reader of the resulting number could not tell which part came from arithmetic and which from a guess about reader behaviour.

The counts have the opposite property. They are wrong in a known direction, by an unknown amount, and every reader can see that from the stated convention. A figure that is honestly incomplete is more use than one that is secretly assumed.

What a publisher can do with this

One thing, and it does not require any of the missing information.

The threshold result — a blind encounter is impossible when fewer statements are unchecked than a reader meets — holds regardless of prominence. It does not care which statements are verifiable or how reachable any of them is. If only two statements in a set of nine are unchecked and a reader meets five, they met a checkable statement, whatever path they took and however buried anything was.

That is the one conclusion in this part of the record that survives the convention it is built on, and it survives because it is a statement about impossibility rather than about likelihood. Every other figure here is conditional on the uniformity assumption, and every one of them should be read with that attached.

The one thing a count does capture

Invariance under relabelling is a weakness in one direction and a strength in another, and the strength is worth naming.

Because no figure here depends on which statements are verifiable, no figure here can be improved by choosing which statements to classify as verifiable. There is no favourable labelling. A publisher cannot move any number in this record by deciding that a statement counts as checkable when it does not — the only thing that moves is the count itself, and the count is what gets printed.

A measure that could be improved by relabelling would be worth nothing, because the relabelling is free and nobody can see it. This one cannot, which is the small compensation for its not knowing anything about prominence.

The layout in the drawings, restated

Dashed strokes first, then solid, then pale stubs. Convenience, not claim. The record places them in that order because a drawing has to place them somewhere and a consistent order is easier to compare across rows than a scattered one.

A reader who wants to imagine the verifiable statements at the far end of the set, where fewer readers reach, should do so — and should then treat every blind share in this record as an underestimate of the problem rather than a measurement of it.