Implementation soundness: three independently written generators — the primesieve-12.15 iterator backend, an own segmented odd-bitmap Eratosthenes, and a pure-Python segmented sieve — produce byte-identical canonical certificate output on [2,10⁶) and on the offset window [10⁹, 10⁹+10⁷); the production numbers come from the primesieve backend whose counts were additionally spot-confirmed against the primesieve CLI.