What the numbers on this site mean

Why explanation pages at all

A number without a meaning is decoration. The record pages report that an address is 56 characters and passes an alphabet check, and neither statement helps anybody unless they know why 56 is the right answer and why four digits are missing from the alphabet.

More importantly, the numbers have a shape that is not obvious. Some parts of an onion address are expensive to control and some are free. Some are checked constantly and some are never checked. Those two divisions do not line up, and the gap between them is where every practical problem with these addresses lives.

These pages set out the gap. The short version is that the beginning of a string is cheap to imitate and heavily trusted, the end is partly fixed by the format and lightly trusted, and the middle is impossible to control and completely ignored. Once that is clear, the advice everybody gives about checking the first few characters stops sounding like caution and starts sounding like the opposite.

The order to read them in

If you want the mechanism, start with what 56 characters are, then the alphabet, then the checksum and version byte. Those three between them account for every field on every record page, including the ones that look arbitrary, such as why four digits never appear and why all 12 addresses here end identically.

If you want the practical part, start instead with the cost of a vanity prefix, then where a forgery differs, then copying. That sequence builds one argument across three pages: control over the string is cheap at the front and impossible everywhere else, attention runs the opposite way, and the only procedure that survives the mismatch is to stop reading these strings by eye altogether.

The two remaining pages mark the boundary. What a published set is covers what a list can establish, which is less than people assume. What this site cannot tell you states the refusals in one place so that no page here has to be read suspiciously.

What is argued and what is counted

Everything in a metric card or a data row on this site is arithmetic over the twelve strings. It can be recomputed and it can be shown to be wrong.

The pages on this shelf contain arguments as well as arithmetic. Which parts of a string are worth checking is a judgement. That the middle is the best place to look for a substitution is a judgement, supported by reasoning about cost rather than by a measurement. Those are written as arguments so that a reader can disagree with them, which is the difference between an argument and a claim.