When Ideal Models Contradict Finite Reality: Causal World-Model Advantage over Empirical Traces

Finite empirical histories are evidence sampled from worlds, not the worlds themselves. This paper proposes Causal World-Model Advantage (CWMA), a baseline-relative log-score measure of how much a model improves over a declared empirical-trace baseline on a distribution of causal queries. Given a causal world W, a finite history H_n, a baseline B_n, a model M inferred from the same history, and a query distribution Π over observational, interventional, and counterfactual questions, CWMA is defined as D_Π(W || B_n) - D_Π(W || M). It is positive when M assigns higher expected logarithmic accuracy than B_n to answers generated by W. The formal core proves non-negativity of the underlying divergence, score-equivalence with expected log-score gain, decomposition across Pearl-style query levels, and a finite-trace underdetermination result. The proposal is deliberately external and distributional: high CWMA establishes functional adequacy for causal query answering relative to Π and a baseline class, not recovery of a unique structural causal model or proof of an internal mechanism. The paper situates the trace-world distinction within earlier philosophical work on data, phenomena, and semantic views of theories, and develops benchmark-design guidance for baseline classes, structural counterfactual queries, smoothing, query-weight sensitivity, and resource accounting.