Shortening long chains in P-partition equivalence

For two nonisomorphic naturally labeled finite posets of Greene shape (h,2,2,1^4) with equal P-partition generating functions and h ≥ 666, the paper gives a simultaneous one-vertex deletion preserving equality and nonisomorphism. The deletion lowers the first Greene part by one. Together with ordinal-sum padding, this reduces uniqueness throughout the fixed-tail family to height 665, on 673 vertices. Both results are provisional. Uniqueness at height 665 remains open.