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Chronic metabolic and autoimmune disorders have conventionally been treated as irreversible, progressive pathologies managed through lifelong pharmacotherapy or perpetual hormonal replacement. Challenging this palliative paradigm, this paper establishes a unified dissipative systems framework that formulates Type 1 and Type 2 diabetes as topological phase transitions within a coupled, multi-scale 8-dimensional metabolic-immune manifold. Key Theoretical & Numerical Contributions: Type 2 Diabetes Remission via Least Action Pulse Steering: We model the bistable potential landscape governing plasma glucose, insulin, and functional versus dedifferentiated beta-cell pools under ectopic lipid accumulation. Applying Willems dissipative inequalities and Pontryagin optimal control, we derive a finite-duration least action pulse steering protocol capable of driving the physiological state across the separatrix saddle barrier into the healthy homeostatic basin of attraction. Numerical simulation demonstrates that an 8-week targeted intervention achieves complete, drug-free remission: following total cessation of external therapy, the system autonomously converges to and stabilizes at normal fasting glucose (97.26 mg/dL at Day 180), whereas insufficient interventions relapse to severe hyperglycemia (589.01 mg/dL). Type 1 Diabetes Pre-Symptomatic Screening: By tracking the Sturm-Liouville spectral turbulence gap (Omega_1,immune) of the local Koopman generator governing autoimmune repertoire fluctuations (effector T-cells, regulatory T-cells, and pro-inflammatory cytokines), the diagnostic framework identifies the loss of self-tolerance restoring forces 149.4 days (~5 months) prior to macroscopic clinical hyperglycemia. Raychaudhuri-Informed Autonomous Insulin Delivery (AID): For patients with established endocrine failure, we formulate a geometry-informed closed-loop artificial pancreas algorithm based on discrete Raychaudhuri bundle expansion (theta_k = Tr(L_meta,k)). In an acute 75 g carbohydrate challenge, the controller detects postprandial divergence early, blunting hyperglycemic peaks (168.93 mg/dL) and eliminating reactive hypoglycemic undershoots (safe nadir of 105.23 mg/dL vs. 95.32 mg/dL under standard PID control). Analytical Fold Bifurcation Triage: We prove a codimension-1 saddle-node (fold) bifurcation theorem establishing a critical irreversible beta-cell loss threshold (rho_crit), providing an exact clinical triage rule separating reversible dedifferentiation eligible for curative steering from irreversible apoptotic loss requiring autonomous closed-loop substitution. Open Science & Reproducibility: The complete open-source Python simulation models, differential equation solvers, and numerical trajectory datasets are publicly accessible under the MIT License at: https://github.com/sukuyoshi/metabolic_immune_dynamics. (This work extends the universal dissipative operator framework established in Yoshikai, 2026; DOI: 10.5281/zenodo.24156018 and DOI: 10.5281/zenodo.24156142).
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Reiji Yoshikai (2026) studied this question.
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