Adaptive Perturbation Design for Causal Edge Recovery: Block-Graph Guarantees and Unbounded Marginal Inflation

Abstract

We study adaptive intervention design for orienting causal directed acyclic graphs within an observational Markov equivalence class under a uniform prior and atomic perfect interventions. We prove that the compelled-edge reward is adaptively monotone and adaptively submodular whenever every undirected chain component is a block graph, yielding the standard (1-1/e) adaptive-greedy approximation for every budget on this class. Beyond that positive result, we prove unconditional unbounded marginal inflation on the explicit non-block family W(s,2,1), where the conditional-to-unconditional marginal ratio grows as s/16. The paper also includes the vertex-minimal six-vertex obstruction, a signed-clamp single-cell extension with explicit finite-cell losses, exact finite-policy comparisons, and a bounded K562/RPE1 negative transfer test. General host transfer and a global greedy guarantee outside block graphs remain open. This deposit contains the 23-page preprint and its complete LaTeX source archive. Beyond, the research system operated by Nth Research Collective, materially assisted with literature retrieval, hypothesis generation, theorem development, executable verification, and adversarial review. Beyond is not an author. Ian D'Ambrosio made the final scientific judgments and accepts responsibility for the work.