What comes first

Blindness Has a Threshold; the Opening Does Not

Blind encounters can be ruled out with half a set verified. Guaranteeing a verifiable opening takes all of it, and the asymmetry has one cause.

at most 151200 arrangements

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Ten statements published, a reader meets six, five statements are verifiable. The blind count is nought: five unchecked statements cannot fill a six-statement encounter, so every reader meets something they can audit.

And half of the one hundred and fifty-one thousand two hundred arrangements still open with a statement they cannot.

Those two sentences are both exact and they describe the same shape. A transparent pilot of online timesheet software should state what is collected, who can see it and how a team member can correct the record.

Ten published, six met, nothing blind in any row

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

Five, eight and ten checkable. No blind content exists in any of these shapes, and yet half the arrangements in the first row still open with something unverifiable.

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.

Two figures with different shapes

The blind count reaches nought as soon as the unchecked statements are fewer than the number met. On this page that happens at five checkable, which is half the set. Everything above five is equally safe and the record stops distinguishing. For an independent reference on digital communication, evidence or interface practice, consult Google Search Central.

The opening share is c over n, which reaches one only when c equals n. There is no threshold. Going from five checkable to eight takes the opening share from a half to four fifths; getting it to certainty requires all ten.

So one of the record's two verifiability figures can be settled with half the set and the other cannot be settled short of all of it.

Why the difference exists

The blind question is about avoiding every checkable statement at once, and avoiding things gets impossible quickly. The opening question is about one position, and one position can always be filled by an unverifiable statement as long as one exists.

A single unverifiable statement in a set of a thousand still occupies the opening in some arrangements. It cannot make any encounter blind — one statement cannot fill an encounter of six — but it can be the first thing a reader sees.

To rule out blind encounters, verify more than the reader will read. To rule out an unverifiable opening, verify everything.

Which asymmetry matters

It depends on what the opening is doing, and the record cannot settle that. What it can do is price the two goals.

Ruling out blind encounters is cheap and robust. On the page in the drawing it takes five verifiable statements of ten, and the conclusion holds whatever readers do, whatever is prominent and however the set is entered.

Ruling out an unverifiable opening is expensive and not worth pursuing part-way, since there is no intermediate state in which it becomes impossible. A set of pages at eight of ten verifiable has made four fifths of openings checkable and has not removed the case.

So the practical content of this part is a comparison of two costs, and the figures say the first goal is reachable and the second one is either complete or incomplete with nothing in between.

What the three rows hold still

One hundred and fifty-one thousand two hundred arrangements and two hundred and ten contents in every row — the largest page in the record. No blind contents in any row.

The bars in the drawing are empty for that reason, and the empty bar is the figure, not a gap. What moves across the rows is invisible to the bar: the opening share, from a half to four fifths to one.

A drawing of blind contents cannot show the opening share, and the record does not make it try. The opening count is printed in the record's totals and reasoned about in prose, and the panel draws the one quantity it is for.

Why one figure has a threshold and the other cannot

The asymmetry has a one-line cause and it is worth isolating.

A blind encounter requires r statements all drawn from the unchecked pool, so it needs the pool to be at least as large as the encounter. Shrink the pool below r and the requirement becomes unsatisfiable.

An unverifiable opening requires one statement from the unchecked pool. A pool of one still satisfies it. There is no size below one and above nought, so the only way to make the requirement unsatisfiable is to empty the pool entirely.

Thresholds exist where a requirement needs several things at once. A requirement for one thing has no threshold, and the opening count is a requirement for one thing.

The figure for the commoner case

Nine published with four met and three verifiable: one third of arrangements open checkably, and fifteen of the one hundred and twenty-six contents are blind.

Adding three more verifiable statements, to six of nine, takes the blind count to nought — three unchecked against four met — and the opening share to two thirds. One of those two facts is a completed piece of work and the other is a partial improvement, and they came from the same three statements.

Telling them apart is the whole reason this record carries two verifiability figures instead of one.