The sharp height-four cutoff for P-partition uniqueness

For naturally labeled posets of Greene shape (4,2,2,1^k), the P-partition generating function distinguishes all orders up to isomorphism exactly when k is at most four. At k=4, a marked five-element core supports an exact enumeration of 4,837,304 isomorphism classes, separated by three exact specializations. Common isolated vertices transfer the exclusion to smaller k and extend the checked thirteen-element collision at k=5. This is a candidate theorem.