How the figures were made

This record counts one thing: how many different impressions a fixed set of published statements can produce, given that nobody reads such a set whole and nobody reads it from the beginning.

Three hundred and thirty-eight shapes are tabulated, spread across forty-four pages. Each shape is three numbers and the arithmetic that follows from them. Nothing here is surveyed, sampled, estimated or forecast, and no figure on the site depends on the date it is read.

Three assumptions, declared rather than buried

Everything counted here rests on three conventions. They are choices, not findings, and they are stated at the front because a convention discovered later reads as a defect. Before turning this model into a live management process, a team can Monitask and decide which records are actually necessary.

A shape is described by three numbers: how many statements are published, between two and ten; how many a reader meets, between one and six; and how many of those published are checkable from outside, between none and all. What the statements say is outside the record entirely. A broader source for checking the surrounding technical or organisational context is W3C.

An encounter is an ordered selection without repetition. A reader meets some of the statements, in some sequence, and each at most once. Re-reading, skimming and half-attention all exist and none of them is modelled.

Checkability is a property of the statement, not of the reader. The line between what somebody can confirm without taking it on trust and what they cannot is drawn once, by hand. The record does not derive it and makes no claim to.

Four counts and one ratio

Arrangements, written P(n, r), is how many distinct encounters are possible. Contents, written C(n, r), is how many distinct subsets are possible. Orders per content is the first divided by the second, which comes to r factorial exactly. Blind contents, C(n − c, r), is how many subsets contain no checkable statement at all. The ratio is blind contents over contents.

Arrangements run from 2 to 151 200 across the record, median 210. Contents run from 1 to 252, median 21. Orders per content takes only six values anywhere in the table — 1, 2, 6, 24, 120 and 720 — because it depends on nothing but how many statements a reader met.

The figure that is usually missing

Dividing arrangements by contents leaves r factorial, and that is the load-bearing fact of the whole record.

Six statements that a reader got through are one content and seven hundred and twenty different impressions. The author chose none of the seven hundred and twenty. Entry point, scroll depth, which fragment a search engine lifted out, which heading caught the eye first — these settle the order, and the page has no say in any of them. A page can be rewritten word by word and every one of those seven hundred and twenty remains available.

This is why a count of what has been published answers almost nothing. Contents and arrangements are different sizes of ignorance about the same page, and only the second is the one a reader actually lands in.

Where the third number earns its place

The pair (arrangements, contents) pins down a page exactly. All forty-four pairs in the record are distinct, and from a pair both original numbers can be recovered: the quotient gives r factorial and hence how many statements were met, after which contents gives how many were published. This is checked by recomputation rather than taken on the strength of the argument.

What the pair says nothing about is whether any of it can be checked. In 199 of the 338 shapes a reader can leave having met no checkable statement; in 139 that cannot happen; and in 44 it happens whatever order they read in, those being the shapes with no checkable statement published at all. The median blind share across the record is one in fourteen.

Even three numbers do not separate every shape. Only 243 of the 338 have a distinct trio of drawn figures. The 95 duplicates are all shapes where nothing can be blind: once fewer than r statements are unchecked, the blind count is zero and stays zero however much higher the checkable count goes. The drawing says so by leaving the panel empty, not by printing a zero.

How to check any of it

Every figure on the site is recomputable with a pencil from the three numbers printed beside it. There is no dataset to request, no procedure to take on faith and no source to chase, because there is no source: the arithmetic is the subject.

The worked example that recurs throughout is eight statements published, four met, three checkable. That gives 1680 arrangements, 70 contents, 24 orders per content and 5 blind contents — one in fourteen, which is where the record's median sits, and why that example was chosen over a tidier one.

What is absent on purpose

No product, service, platform, company, tool or person is named anywhere on this site, in any sentence, including sentences that would deny something. Nothing is ranked, compared, scored, recommended or reviewed. No figure is quoted from anybody else's report. There is no form, no field, no mailbox and no account, and no page carries a byline, because a record that can be recomputed does not need one and a name invites the reader to weigh the author instead of the arithmetic.