Checkable

Half Checkable Is Almost Entirely Safe

With half of a set checkable and half of it met, exactly one content is blind — on every page where that arrangement occurs, whatever its size.

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Half the published statements are checkable. The reader meets half the set. How many of the possible contents hold nothing verifiable?

One. Not a proportion, not an estimate: exactly one, on every page where that arrangement occurs.

Ten published with five met and five checkable: one blind content out of two hundred and fifty-two. Eight with four met and four checkable: one out of seventy. Six with three met and three checkable: one out of twenty. Readers applying this idea to real teams can look through the product tour and compare reports with outcomes instead of reading them in isolation.

Half published checkable, half the set met

the whole bar: every content a reader might come away with
the dashed part: contents holding nothing checkable

Three shapes drawn.

Ten with five met, eight with four, six with three — each with half the published statements checkable. In all three the blind count is one.

Computed from the three numbers. A blind content is one holding no checkable statement: that is a property of the page, not a prediction about any reader.

Why it is always one

A blind content must be drawn entirely from the unchecked statements. With half checkable there are exactly as many unchecked statements as the reader meets, so there is exactly one way to do it: meet all of the unchecked ones and none of the others. For additional background relevant to the interpretation of online work and information, see CISA.

C(n − c, r) with n − c equal to r is C(r, r), which is one. The arithmetic is that short, and it holds for any page size.

What this does to intuition

Half verifiable sounds like a halfway position. It is not. It is a position in which the blind share is one over the contents figure — one in twenty on the smallest page in the drawing, one in two hundred and fifty-two on the largest.

The reason is that a reader has to avoid every checkable statement simultaneously, and avoiding five specific statements while drawing five from ten leaves precisely one option. The requirement is not halfway hard. It is nearly impossible, and it gets harder as the page grows.

Halving the checkable count does not halve the blind share. The blind share is a count of ways to avoid, and ways to avoid collapse long before the halfway point.

The asymmetry with the other direction

Going the other way is not symmetric, and the contrast is worth holding.

One checkable statement in eight, with four met, leaves thirty-five of seventy contents blind — half. Four checkable in eight leaves one of seventy. So the first three checkable statements take the blind share from one half to one in fourteen, and the fourth takes it from one in fourteen to one in seventy.

Each statement added has a larger proportional effect than the one before, which is the opposite of how most additions behave. The first one barely moves the share; the last one before the threshold moves it by a factor of five.

Where the drawing's three rows agree and differ

All three rows have a blind count of one, and that is the point of drawing them together.

They differ in what one means. One in twenty is a share of five percent. One in two hundred and fifty-two is four tenths of one percent. The same count, over contents figures that differ by a factor of more than twelve, which is why the record reports the count and the contents figure rather than the count alone.

The bars show the share rather than the count, which is why the dashed portion is nearly invisible on the ten-published row and merely small on the six-published one. A drawing that showed the count would have drawn three identical bars and said nothing.

The same case one size smaller

Four published, two met, two checkable: one blind content out of six, and the structure is identical — two unchecked statements, two met, exactly one way to meet both.

Six contents is small enough to write out, which makes this the row where the claim can be checked rather than believed. Label the statements A and B verifiable, C and D not. The pairs are AB, AC, AD, BC, BD, CD. Only CD holds nothing verifiable.

One in six here, one in twenty at six published, one in two hundred and fifty-two at ten. The same arrangement of the three numbers, and the share collapsing as the page grows, because the single blind combination is being measured against a contents figure that grows and grows.

Why the share keeps falling as the page grows

One blind content, measured against twenty, seventy and two hundred and fifty-two. The count is pinned at one by the arrangement of the numbers; the denominator is not pinned at anything.

So the half-verifiable position gets better as the set gets longer, and it gets better quickly. A reader of a six-statement set in that position has a one-in-twenty chance of the blind reading under the record's convention; a reader of a ten-statement set has one-in-two-hundred-and-fifty-two.

Length helps here, and it rarely does anywhere else in this record. The reason is worth holding: the lone blind combination becomes a smaller and smaller part of a space growing combinatorially around it.

What this does not establish

It does not say that half checkable is sufficient, or that a set of pages reaching this position has solved anything.

The blind share being one in two hundred and fifty-two means a reader is very likely to meet something they can verify. It says nothing about whether what they can verify is worth verifying, whether the five unchecked statements carry the load of what the pages are claiming, or whether a reader who met four checkable statements and one unchecked one came away believing the unchecked one.

The record counts reachability and stops. Everything about which statements matter is outside it, permanently, and no figure here should be read as covering it.