Does a CPF generated here pass a Receita Federal lookup?
No. The generator only closes the modulo-11 calculation over a random base, without querying any registry; the number is synthetic, useful for testing input masks and form validation, and proves nothing about a real registration.
Why do some CPFs end in digit 0?
Because the remainder of the weighted sum divided by 11 landed on 0 or 1; the modulo-11 rule converts both cases to digit 0 instead of leaving a negative or two-digit remainder.
Is a CPF with all matching digits mathematically valid?
Modulo 11 closes normally for repeated sequences, as the 111.111.111-11 example above shows; but the Receita Federal never issues a CPF like that, so generators and validators treat it as a case separate from the arithmetic.
Can I use a CPF generated here in a real registration?
No. The number is meant only for software testing and mask validation in a development environment; using it to impersonate someone else or fill out a real registration is misuse of the document.