A conceptual synthesis of causal assumptions for causal discovery and inference

Abstract: This work presents a conceptual synthesis of causal discovery and inference frameworks, with a focus on how foundational assumptions -- causal sufficiency, causal faithfulness, and the causal Markov condition -- are formalized and operationalized across methodological traditions. Through structured tables and comparative summaries, I map core assumptions, tasks, and analytical choices from multiple causal frameworks, highlighting their connections and differences. The synthesis provides practical guidance for researchers designing causal studies, especially in settings where observational or experimental constraints challenge standard approaches. This guide spans all phases of causal analysis, including question formulation, formalization of background knowledge, selection of appropriate frameworks, choice of study design or algorithm, and interpretation. It is intended as a tool to support rigorous causal reasoning across diverse empirical domains.