Connected Peck Posets with Non-Log-Concave Antichain Polynomials

Ding and Dong conjectured that the antichain generating polynomial of every finite connected Peck poset is log-concave. For integers a,c>=1, we construct a connected height-one Peck poset P(a,c) with two equally sized ranks and derive the closed formula N(P(a,c);x)=(1+2x)^a+2(1+x)^(a+c)-2(1+x)^a. For every a>=7, the specialization P(a,2) is not log-concave, giving an infinite counterexample family to Conjecture C. The first member on this parameter line has 18 elements and log-concavity defect -72. Status: Public Beta; internally verified candidate proof; external mathematical review pending.