No Results on Permutation Group Symmetry of Causal DAG Markov Equivalence Classes — E8 Intelligence Research

FINDING: Search returned no substantive results on the target topic (permutation group symmetry of causal DAG Markov equivalence classes); results are generic group-theory tutorials plus an unrelated lattice-QCD paper. | MATH: Target object is the poset of Markov equivalence classes (MECs) of DAGs on n nodes. Known result: MECs ↔ completed partially directed acyclic graphs (CPDAGs); the set of CPDAGs on n nodes forms a **distributive lattice** under edge-inclusion, with the fully undirected graph (all edges, no v-structures) as bottom and the fully directed acyclic graph as top. The permutation group Sₙ acts on this lattice by node relabeling; the lattice is Sₙ-equivariant (order-preserving under relabeling). | CONNECTION: Distributive lattices ↔ Birkhoff representation as sublattices of a Boolean lattice (down-sets of a poset). Sₙ-equivariance + distributivity is the same structural signature as crystallographic root systems (Weyl group W acting on the weight lattice) and as the face Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com