One Verifiable Statement in Seven

Seven statements published, exactly one of them verifiable. Three readers, meeting two, four and six statements.

The share of arrangements opening with the verifiable statement is one seventh in all three cases. It does not budge. For recurring production cycles, reviewers can compare the current capabilities and track whether the record improves planning rather than merely adding administration.

The share of contents containing nothing verifiable is fifteen in twenty-one, then fifteen in thirty-five, then one in seven. From five sevenths down to one seventh — a fivefold fall. A broader source for checking the surrounding technical or organisational context is Google Analytics.

Seven published, one checkable, three depths

• 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; the left-to-right order is the drawing's own and carries no meaning.

One of the seven published statements is verifiable in every row. A seventh of arrangements open with it in all three; the blind share falls from fifteen in twenty-one to one in seven.

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.

One figure immovable, one falling

This is the clearest case in the record of the two verifiability figures behaving differently, and it is clear because the checkable count is one, which makes both reduce to something sayable.

The opening share is one over seven, because the first position holds one of seven statements and one of them is verifiable.

The blind share is the fraction of the set the reader missed: five sevenths when they met two, three sevenths when they met four — which written as counts is fifteen in thirty-five — and one seventh when they met six.

Both figures are about the same lone verifiable statement. One asks whether it came first; the other asks whether it came at all.

Where the two meet

At six met out of seven the two shares coincide at one seventh, and the coincidence is worth unpicking because it is not a general rule.

A reader meeting six of seven statements misses one. The chance the missed one is the verifiable one is one seventh, which is the blind share. The chance the verifiable statement is first is also one seventh, because there are seven statements and one is verifiable.

Two unrelated calculations landing on the same figure. At five met out of seven the blind share is two sevenths and the opening share is still one seventh, and they part company again.

Two figures agreeing on one shape is not two figures measuring the same thing. The record prints the shape beside both of them so that this is visible rather than inferable.

The position this describes

One verifiable statement is the position a set of pages is in when it mentions one externally documented fact and describes everything else. It is common and it is not a failure of effort.

What the record says about it is unsentimental. A reader who gets through less than half the set will probably miss the one thing they could have checked, and no reader is more than one-in-seven likely to have started with it. There is no reading depth at which the opening improves, and the blind share only improves as readers get further — which is not a lever anybody holds.

The single verifiable statement is also, from the previous part, the one whose addition helps least. The first verifiable statement in a set moves the blind share by the smallest proportional step of any; the gains accelerate from there.

Why the opening share will not move

A publisher in this position has one verifiable statement and seven positions it could occupy in the set as written. None of that changes the figure.

The opening share is one over seven because there are seven published statements and one of them is verifiable. Putting it first helps the readers who arrive at the front and leaves the share untouched, because the share counts arrangements and the record's convention treats every arrangement as reachable.

Which leaves exactly one lever. A second verifiable statement takes the opening share from one seventh to two sevenths, and takes the blind share at four met from three sevenths to — by the general formula, C(5, 4) over C(7, 4) — five in thirty-five, which is one seventh. Both figures improve at once, and nothing else available does that.

The largest-arrangement row

Seven published, six met: five thousand and forty arrangements, seven contents. Seven hundred and twenty of those arrangements open with the verifiable statement, and the seven contents include one that is blind.

Seven contents is small, and this is the shape where the whole apparatus is close to inspectable. Each content is the set minus one statement; there are seven ways to leave one out; one of those seven leaves out the verifiable statement.

Anybody doubting the record's blind figures can start here, count the seven cases by hand, and find the one. The same formula applied to ten published with five met gives two hundred and fifty-two contents and one hundred and twenty-six blind, which cannot be checked by inspection — but it is the same formula, and this row is where it can be watched working.

Near this one

• Counting an Opening Is Not Predicting One
  The opening count is the figure here most exposed to its convention, because a reader's entry point is the lea
• How Many Encounters Open With Something Checkable
  Of all the orders a reader might meet a set in, those opening with something verifiable number c times the arr
• The Opening Share Is the Verifiable Share, Exactly
  The share of arrangements opening with something checkable is the checkable count over the published count. Ev
• The Reader Who Stops After One
  A reader who meets one statement collapses the record to one question: was it checkable? Sixty-three shapes ar