When Chain-of-Thought Helps and When It Hurts: An Empirical Investigation of the Serial-Depth Bottleneck in LLM Reasoning

Version 4 — framing correction. No inference outputs, data, or statistics changed from the corrected scoring in v2/v3. - The H_dp bandwidth bound (Chen, Peng & Wu, 2024) is reframed as conceptual motivation, not a literal predictor: it is asymptotic and does not bind at the context lengths tested (its failure guarantee is non-vacuous only for n* = H_dp^(2^4L), i.e. ~10^(10^34) to 10^(10^77) tokens, versus the ~10^2–10^3 tokens here). Title and abstract revised accordingly.- The within-benchmark serial-depth gradient is foregrounded as the central empirical finding.- Added limitations conceding that (i) the short-output caps deny an externalised scratchpad rather than enforce a literal single forward pass (generating m tokens is m forward passes); (ii) the no-CoT and CoT conditions differ in test-time compute, which is intrinsically entangled with externalisation; and (iii) the high TC^0 baselines (up to 95% on ARC) may reflect pretraining contamination, so the TC^0 null is not a clean architectural test.- Scoring corrections from v2 (MMLU/ARC regex artefact) and v3 (HumanEval stop-token artefact) are unchanged and fully documented in Appendix B. All main-text numbers reproduce via verify_paper_stats.py.