Numbers read one place at a time

An integer can be read at its places: its residue modulo each prime, or its digits along the real line, a few at a time. At a prime, arithmetic on residues is exact. These notes work out what each place can compute on its own, what it hides from the others, what it costs to read a number or to grow a modulus one place at a time, and where the one thing no finite place holds, a number's size along the real line, has to come back in. The founding example is the ring of integers modulo the product of the first k primes: each of those prime places kept once, the real one left unread.

Every page states each claim with its tier, a label for how the claim is known, and what backs it: the program that checks it, the proof it carries, or the source it is taken from. Every program is served on a page of its own, linked from each claim it checks.