A Ginzburg-Landau Field Formalism for the Enteric Nervous System: Asymmetric Coupling and Autonomous Field Dynamics in the Gut-Brain Axis

This paper extends the Cortical Informational Field Theory (CIFT) framework to the enteric nervous system (ENS), deriving a one-dimensional enteric field Φ_E(x,t) propagating along the oral-anal axis and governed by a Ginzburg-Landau equation of the Stjepovic form. The gut microbiota is formalized as a structured external control parameter M(x,t) acting through an epithelial transmission operator T — not stochastic noise — grounded in the tubular topology of the gastrointestinal tract. The celiac plexus complex is introduced as a state-dependent inter-field coupling operator Γ, formalized as a sigmoidal transfer function with variable gain, mediating asymmetric coupling between the enteric field Φ_E and the cortical field Φ_C. A Jacobian stability analysis of the coupled system demonstrates an infrastructure dependence structure: the enteric field is robust to high-frequency cortical perturbations under the assumptions of the model, while the cortical field's equilibrium state is anchored to enteric coherence. The hierarchy of the gut-brain axis is thus not one of command, but of infrastructure dependence — the brain processes information on a stability base generated and maintained by the enteric field. The paper includes three figures, two tables, a formal mathematical appendix, 42 references with DOIs, and four explicit testable predictions. This is Paper XI of the CIFT series (DOI compendium: 10.5281/zenodo.19135398).