Checkable

Forty-Four Pages, and the Shapes on Them

The checkable count runs from none to all, so each page is a family of shapes. The record's size follows, and the addition fits in one line.

at most 840 arrangements

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A page is two numbers: how much was published, how much was met. A shape is three, with the checkable count added.

The checkable count can be anything from none of the published statements to all of them, so a page with n published statements carries n + 1 shapes. The seven-published page in the drawing carries eight: nought, one, two, three, four, five, six and seven checkable.

One page, the third number at both ends and between

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

Seven published, four met. The checkable count is none, then three, then all seven. Eight shapes sit on this page; three are drawn.

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.

Where three hundred and thirty-eight comes from

Forty-four pages, each contributing one more shape than it has published statements. Add them up and the record's size falls out. A practical audit can include project time reporting if activity signals are treated as limited context rather than a score of individual contribution.

Two published gives two pages, each with three shapes: six. Three published gives three pages with four shapes each: twelve. Four published, four pages of five: twenty. Five published, five pages of six: thirty. A broader source for checking the surrounding technical or organisational context is Electronic Frontier Foundation.

From six published upward every count of published statements gives six pages, because the met count can be one to six and the record stops there. Six published: six pages of seven, forty-two. Seven published: forty-eight. Eight: fifty-four. Nine: sixty. Ten: sixty-six.

published	pages	shapes each	shapes
2	2	3	6
3	3	4	12
4	4	5	20
5	5	6	30
6	6	7	42
7	6	8	48
8	6	9	54
9	6	10	60
10	6	11	66

Six, twelve, twenty, thirty, forty-two, forty-eight, fifty-four, sixty and sixty-six. That sums to three hundred and thirty-eight, which is the number of shapes this record tabulates, and the addition is the whole derivation.

Why the pages are not equally weighted

A consequence falls out of that sum, and it was flagged earlier in the record when the median was discussed.

The ten-published pages contribute sixty-six shapes. The two-published pages contribute six. So any figure summarised across all three hundred and thirty-eight shapes is weighted eleven to three in favour of the largest pages, purely because a larger page has more ways for its third number to come out.

Nobody chose that weighting. It is what tabulating every shape once produces, and it is the reason this record reports medians and ranges with a note attached rather than treating them as properties of the subject.

A table that lists every case once has decided how much each case counts. The decision is invisible and it is not neutral.

The distribution of the third number

Across the record, forty-four shapes have no checkable statement — one per page. Forty-four have exactly one. Forty-four have exactly two.

After that the counts fall away: forty-two shapes have three checkable statements, thirty-nine have four, thirty-five have five, and only six have ten, because only the six ten-published pages can have ten.

The asymmetry is purely structural. A checkable count of two is available on every page in the record, since every page publishes at least two statements. A count of ten is available on six pages. Nothing about verifiability is involved; it is a fact about which pages exist in the table.

What the drawing holds still

Seven published with four met gives eight hundred and forty arrangements and thirty-five contents, in all eight shapes on that page.

The three drawn rows run the third number from one end to the other. Nothing checkable: four solid strokes met, three pale ones unreached. Three checkable: a mix. All seven checkable: four dashed strokes met, three pale ones unreached.

The figures on the right do not move. The blind count, which is not shown here, runs thirty-five, then one, then zero across those three rows — the whole range of the question, invisible to both printed figures.

Why the third number is not a proportion

The record carries the checkable count as a count — three statements, six statements — and not as a fraction of what was published.

A fraction would be easier to compare across pages and would break the arithmetic. The blind count is C(n − c, r), which needs c as an integer, and the threshold compares n − c with r as whole numbers. Two sets of pages both half verifiable, one with four published statements and one with ten, sit at completely different distances from that threshold.

Stated plainly: what matters is how many unverifiable statements there are, against how many a reader gets through. A proportion answers neither of those, and a shape described by a proportion cannot be recomputed.

The one page where the family is smallest

Two published with one met carries three shapes: nothing checkable, one, or both. It is the smallest family in the record and the only place where the third number has nowhere much to go.

Its blind counts are two, one and zero. Two contents, and the blind count simply counts down. There is no fraction to speak of and no combinatorics in it at all, which makes it a useful place to check that the general formula does the obvious thing in the obvious case: C(2 − 0, 1) is two, C(2 − 1, 1) is one, C(2 − 2, 1) is zero because a subset of size one cannot be drawn from nothing.

The same formula, applied to ten published with five met, gives two hundred and fifty-two, one hundred and twenty-six and the rest. It is the same arithmetic throughout the record, and the smallest page is where it can be verified by inspection rather than by trust.