Pixton Completeness Conjecture

The Pixton completeness conjecture in rational Chow asserts that all tautological relations on the moduli space of stable curves arise from Pixton's original graph-formula relation span. Let be the realization map from the strata algebra to the rational Chow ring and let be this span. The assertion is

for every stable pair . The span already includes relations placed at vertices of outer stable graphs, multiplied by arbitrary strata classes at other vertices, and glued. It is an ideal stable under the stated gluing and forgetting operations.