The preceding papers in this series treated the fluidic supervisor as a central astrocytic gel regulated by two unfiltered peripheral channels: olfaction and vagal afference.The present paper corrects this simplification.The fluidic supervisor is not central.It is distributed across at least four anatomically distinct levels, each constituting an autonomous rheological gel with its own state vector, its own monoaminergic regulation, and its own phase-transition dynamics. The enteric nervous system -- 500 million neurons, 95\% of the body's serotonin, complete autonomy from the central nervous system -- constitutes the first supervisory level, maintaining a continuous $\sigma_\mathrm{body}$ for the visceral gel independently of any central instruction.The pre-vertebral ganglia (coeliac, superior, and inferior mesenteric) constitute an intermediate integration level, synthesising enteric and sympathetic signals before vagal transmission.The spinal cord -- through its central pattern generators, its dorsal horn interneurons, and its autonomous nociceptive integration -- constitutes a third level of rheological processing that pre-filters all ascending information before it reaches the astrocytic syncytium.The central astrocytic gel receives not raw peripheral signals but a triple-synthesised rheological declaration produced by three autonomous gels operating in series. This architecture resolves a structural anomaly in the preceding account: the observed inertia of somatic states against cognitive override.A somatic state maintained by three autonomous gels cannot be modified by a single central gel transition, however large.Therapeutic implications are direct: rheological intervention at each level requires modality-specific approaches, and ordering interventions (enteric before spinal before central) is a physical constraint, not a clinical preference. Eight falsifiable predictions are presented (P40--P47), each targeting a specific level of the distributed supervisor.The model is falsified if enteric serotonin depletion leaves central $\beta$ unchanged, or if central spinal pattern generators are found to lack autonomous rheological memory.