Connected collisions of P-partition generating functions

This preprint constructs two connected, nonisomorphic naturally labeled posets on twelve elements with the same P-partition generating function and Greene shape (3, 2, 2, 1⁵). The construction compares two attachments to a common height-two base by conditioning on colors and cancelling a two-term difference. It gives connected pairs of Greene shape (h, 2, 2, 1ᵏ) for every h ≥ 3 and k ≥ 5. The results are provisional. Exact computations check the seed coefficients and polynomial identity, and the general family relies on the written proof.