A counterexample to Greedy Sparsest Poset consistency under restricted faithfulness

The oracle consistency conjecture for Greedy Sparsest Poset asks whether every starting graph can reach a globally sparsest graph by legitimate mark changes and reconstruction, without increasing the edge count. We give a counterexample under its stated Markov and restricted-faithfulness assumptions. For a nondegenerate Gaussian distribution on six variables, an explicit starting poset maps to an eight-edge graph whose entire reachable component consists of three eight-edge graphs, whereas the global minimum is six. Both applications of the poset-to-graph construction and the maximal ancestral closure fix each of these three graphs. The Gaussian input is a previously published example; the obstruction is established by analyzing all possible mark changes. Exact conditional-independence and reconstruction tables are included. The example does not address consistency under full faithfulness.