The object: every finite place at once

The ring of integers modulo the product of the first k primes, the tower those rings form as k grows, and what the tower keeps of the integers and what it drops: element orders, the code the residues form, and one real number read off a residue's channels, with what it keeps of the residue. Beside them, a global constraint read with one place left out, and the primes outside a ring's own that divide the Euler characteristic of the clique complex of its Hamming graph.

• TOWER — the primorial rungs
• FINGERPRINT — one real number reads a residue tuple up to sign
• BUDGET — what omitting a place frees at a global constraint
• NAMING — which primes divide a set's Euler characteristic