C-D22-CRT-NO-PRUNING

Cross-prime CRT compatibility ALONE prunes NOTHING (measured): distinct primes give independent moduli, so every pair of local signatures is CRT-consistent and the compatible set is the full product prod|Sigma_p|. If the only global check is deferred to the reconstruction threshold 2H, the implicit master grows as prod|Sigma_p| (>= 2^519) before any cut fires, the same wall as D21-S

In plain language

Just matching fingerprints prime by prime removes nothing; a real global check has to come in earlier than the reconstruction step, or the count explodes again.

Exact statement

Cross-prime CRT compatibility ALONE prunes NOTHING (measured): distinct primes give independent moduli, so every pair of local signatures is CRT-consistent and the compatible set is the full product prod|Sigma_p|. If the only global check is deferred to the reconstruction threshold 2H, the implicit master grows as prod|Sigma_p| (>= 2^519) before any cut fires, the same wall as D21-S