Externalized CPDAG Summaries Improve LLM Causal Deduction

Corr2Cause asks whether a causal claim holds in every DAG compatible with observed correlations and conditional independencies. We frame this as latent-object reasoning: the label is defined by a CPDAG query, but free-form chain-of-thought often collapses the Markov-equivalence-class problem into local pattern matching. We propose Structured Thinking, a two-turn pipeline that first externalizes a typed, schema-constrained CPDAG summary and then answers against that graph state. On the Corr2Cause full test, Structured Thinking raises Qwen3.5-27B from $73.0$ to $86.4$ $F_1$(Yes) over a strong PC-instruction baseline in the primary paired run ($+13.4$ pp; McNemar $p=2.4\times 10^{-6}$; bootstrap $95\%$ CI [$+8.4$, $+18.6$]); across three full-ID seeds, the mean gain is $+8.1 \pm 5.3$ pp. A PC-scaffolded two-turn prose control reaches only $67.6$ $F_1$, indicating that a detailed PC scaffold plus a schema-free prose intermediate is not sufficient. The same pattern holds on Qwen3.6-27B, Paraphrase-OOD, and GPT-5.4-mini. Scrambling the emitted CPDAG costs $12.0$ pp $F_1$, and a full-split audit shows close agreement with the reference CPDAG (ID skeleton $F_1$ $0.960$; exact match $75.9\%$). These results support a bounded design principle: externalize the latent object that defines the label, constrain its form, and test whether downstream answers use it.