How the figures were made
This record measures one object: the schema of a board of listings. Not the listings, not the people reading them, not anybody posting. Only the structure of the filters themselves.
A schema here is a count and a set of counts: how many facets the board carries, and how many values each facet offers. Four hundred and sixty-one of them fit inside the bounds set below, and every figure on this site is a product of whole numbers derived from one of them.
The two things that were decided rather than counted
A schema is only its facet sizes. What a facet is called, what its values mean, whether one of them is more common than another — none of that enters. A facet carries between two and six values, because one value is not a choice, and a schema carries between one and six facets. Both bounds are a decision, and nothing here pretends otherwise.
A query sets each facet to one value or leaves it alone. That is the second decision, and it is the larger one. Boards that let a person tick several values at once are doing different arithmetic, and the section on limits says how much different rather than smuggling it in.
Everything else was counted.
The three figures
| figure | how it is got | what it bounds |
|---|---|---|
| cells | the facet sizes multiplied | what can be told apart |
| queries | each size plus one, multiplied | what can be asked |
| sizes | how many of the subset products differ | how many grains of answer exist |
The first two are the spine. Cells is a ceiling on distinction: two listings that agree on every facet occupy one cell, and no question the board permits will ever separate them. Queries is a ceiling on expression: it counts the different things anybody can ask, whether or not any listing answers them.
They are not the same ceiling, and they do not move together.
What follows from the two of them
Four schemas in every five share their cell count with at least one other schema. One hundred and fifteen separate groups of them do. The largest group holds seven schemas, running from three facets up to six, all telling exactly the same number of listings apart.
So a single figure describing a board — however carefully chosen — does not identify how that board is built.
Both figures together do, and exactly: across all four hundred and sixty-one schemas, no two produce the same pair. That is not a coincidence noticed afterwards; it is checked by the program that builds the record, and it is the reason this site quotes two numbers wherever one would read more smoothly.
How to check any of it
Multiply. There is nothing else.
For cells, multiply the facet sizes. For queries, add one to each size and multiply those. For the grain count, take every subset of the facets, multiply each subset out, and count how many distinct answers you get. A pencil does all three, and every page here prints the inputs so that the pencil has something to work on.
What is deliberately absent
The calculations remain the core of this record. Practical guides are kept in a separate editorial section, use stated scenarios and point readers to current official product information for verification.
The reason is uniform. Claims of that sort go out of date without changing their tone: the page still reads as confidently as the day it was written, nothing on it marks the moment it stopped being true, and somebody acts on it anyway. Arithmetic on whole numbers does not have that failure mode, so arithmetic on whole numbers is what this record holds.