GENESIS Computational Model for ME/CFS and Long COVID: Dominance Shift Analysis, Monostability Proof, and a Structural Theorem on the Topological Impossibility of Bistability in Physiological Damage-Recovery Systems (R8–R9 Series

DOCUMENT SUMMARY This document presents the combined technical documentation of the GENESIS Computational Model's R8 and R9 development series — two sequential phases of a rigorous, analytically-driven investigation into the mathematical conditions required for chronification in the context of ME/CFS (Myalgic Encephalomyelitis/Chronic Fatigue Syndrome) and Long COVID. The GENESIS model is a dynamical systems framework that describes mitochondrial dysfunction (M) and structural capacity degradation (S) using coupled differential equations. Its goal is to capture the progression from resilient health to chronic illness in biologically plausible, mathematically verifiable terms. R8 Series — Dominance Shift Analysis (Iterations R8.1–R8.5b) The R8 series systematically investigated whether a one-dimensional regeneration model, extended with damage amplification (k), recovery saturation (Michaelis-Menten, γ), and structural drift (S), could emergently produce chronification. The central finding is conclusive: 1D systems with smooth nonlinearity are inherently monostable and globally reversible. Chronification — as an irreversible qualitative shift — cannot arise in this architecture. The series produced the analytically derived dominance formula Δ = rS − D·γ·(1+k·(1−S)) and a complete Delta-metric classification of system states from resilient to decompensated. The methodological discipline was rated 9.2–9.8/10 throughout, with zero governance violations across eight iterations. R9 Series — Feedback Architecture & Bistability Analysis (R9.1, R9.1b, R9.2) The R9 series introduced a second dynamic state variable — I(t), representing maladaptive inflammation — to create a 2D feedback system. This was the first attempt in GENESIS history to engineer true bistability. The result is a structural theorem of high scientific value: the positive baseline damage term D_base > 0 constitutes a topological barrier that prevents the Stable-Unstable-Stable (S-U-S) fixed-point topology required for genuine bistability. All tested extensions (linear I-feedback, cubic I·M-feedback, modified recovery) produced only a Stable + Saddle configuration. GENESIS is therefore formally characterized as a robust resilience model, not a tipping-point model. This finding is consistent with the clinical reality of ME/CFS as a condition of graded severity rather than binary state transitions. Strategic Outlook Following the R9 analysis, two architectural paths are identified for future development: Path A formalizes GENESIS as a resilience and drift model (reactivating S-drift), while Path B introduces a 3D memory model with an accumulating damage variable D(t) that may enable genuine irreversibility. The structural theorem established in R9.2 is proposed as a standalone scientific contribution suitable for academic publication.