The Complexity Ceiling Benchmark: A Multi-Domain Evaluation of Sequential Reasoning Under Depth Scaling

We introduce the Complexity Ceiling Benchmark (CCB), a controlled evaluation of how language-model reasoning decays as the number of required sequential steps grows. CCB fixes the semantic content of a task and varies only its depth N in {5,...,50} across three structurally distinct regimes: grounded spatial state-tracking, abstract symbolic pointer manipulation, and transitive relational inference. Across 6,000 trials over five frontier and open-weight LLMs we find a consistent pattern of geometric per-step decay with widely separated domain ceilings: on the first two regimes the strongest mo