Iterative Causal Discovery: Per-Edge Impossibility Certificates, Tier-Aware Oracle Queries, and the $1+K$ Lower Bound

ArXi:2605.27477v1 Announce Type: cross Causal-discovery algorithms return a directed graph, yet provide no principled means of distinguishing edge directions identified by the data from those assigned without an identifying assumption. Under the standard Marko and faithfulness conditions, the observational distribution identifies only a Marko equivalence class; orientations within that class are not determined by the joint distribution and cannot be recovered from additional samples alone, but require either a functional restriction or an intervention. We.