C-D21-PADDING

Padding decomposition: every 13-multiset cover = minimal core + padding; padding changes multiplicity, symmetric coefficients, projective orbit and CRT compatibility, so a minimal-core-only oracle is incomplete and the full 13-multiset must be queried (brute-verified p=23: 66=66)

In plain language

A full 13-speed cover is a small core plus filler, and the filler matters: it shifts the fingerprint the compatibility test relies on.

Exact statement

Padding decomposition: every 13-multiset cover = minimal core + padding; padding changes multiplicity, symmetric coefficients, projective orbit and CRT compatibility, so a minimal-core-only oracle is incomplete and the full 13-multiset must be queried (brute-verified p=23: 66=66)