Hierarchy Is Not Free: A Fair-Baseline Negative Result for Single-Mind Multi-Body Control

Abstract. The SMMB program has claimed that a slow global core over fast local controllers breaks a single-timescale bandwidth–delay constraint and yields energy or robustness advantages. This paper makes the premises explicit and tests them under a fair baseline. It contributes: (i) an assumption catalogue A1–A12; (ii) a counterexample set C1–C11, five numerically reproduced (non-convex local convergence, delay-induced instability, saturation-induced divergence, divergence under stale updates, duplicate effects under at-least-once execution); and (iii) an equal-resource matrix E1–E5 (1,700 runs) with a per-tick single-layer baseline receiving the same solver budget. Under that fair baseline the hierarchical controller shows no advantage — about twice the control effort, no faster convergence, an identical region of attraction, and no delay/staleness/oracle-failure benefit. The earlier apparent advantage was a baseline artifact; the methodological lesson is that baseline design is a first-order determinant of architecture comparisons. Contents. Markdown source, DOCX and PDF; figure; supplementary archive with the reference harness, 1,700-run JSONL dataset, analysis scripts, full assumption/counterexample documents and the executable experiment matrix. Companion artifacts. This record is part of the SMMB long-term program together with P1 (two-node systems prototype) and P3 (energy bounding-perspective). Cross-paper claims are limited to each paper's scope; see the claim-boundary table in the manuscript. Status. Working draft; not peer reviewed. Published as a preprint for citation and reproducibility. No venue deadline is implied.