Geometric Attractor Steering in Non-Equilibrium Tumor Microenvironments: A Dissipative Systems Framework for Cancer Differentiation Therapy and Pre-Metastatic Early Warning

Malignant neoplasms have conventionally been characterized through reductionist genomic paradigms as autonomous mutation accumulations, motivating cytotoxic therapies designed to maximize cell killing. However, cytotoxic chemotherapy universally induces catastrophic evolutionary selection pressures, selectively sparing drug-resistant cancer stem cells (CSCs) and precipitating lethal recurrence within fibrotic, immunosuppressive microenvironments. Transcending this cytocidal paradigm, this work formalizes oncology as a non-equilibrium dissipative dynamical system across a seven-dimensional tumor microenvironment (TME) spanning cancer stem cells (C_stem), differentiated neoplastic cells (C_diff), healthy parenchymal cells (C_norm), cytotoxic effector lymphocytes (I_cyt), immunosuppressive stroma (I_supp), metabolic acidosis/hypoxia (sigma_metab), and extracellular matrix stiffness (M_mat). Key Theoretical & Numerical Contributions: Differentiation Attractor Steering vs. Cytotoxic Relapse (Scenario 1): Under Willems' dissipative systems framework and Lyapunov energy barrier crossing, we formulate an optimal finite-duration pulsed epigenetic differentiation therapy that bypasses Darwinian cytotoxic resistance by steering C_stem across the saddle-node separatrix into the healthy parenchymal basin of attraction. Numerical simulations demonstrate that while conventional maximum-tolerated-dose chemotherapy results in 100% lethal relapse (C_tumor = 922.17, C_norm ≈ 0.0 at Day 180), eight weeks of pulsed differentiation and microenvironmental normalization achieve complete, drug-free, recurrence-free remission (C_tumor = 8.04 × 10^-9, C_norm = 999.21). Pre-Metastatic Early Warning via Spectral Gap Softening (Scenario 2): Utilizing the Koopman-Sturm-Liouville spectral gap softening criterion (Omega_1,cancer -> 0+), the framework identifies pre-metastatic niche remodeling and epithelial-mesenchymal transition (EMT) at Day 29.1, providing a 40.0-day early-warning lead time prior to clinical circulating tumor cell (CTC) dissemination (Day 69.1). Ultra-Early Immunotherapy Triage via Raychaudhuri Contraction (Scenario 3): Applying the discrete Raychaudhuri bundle expansion scalar (theta_k = Tr(L_k)) to the immunological sub-manifold, we demonstrate that immune checkpoint blockade (ICI) responders and non-responders diverge geometrically within 24 hours of treatment onset (Day 15.0), providing a 1.9-day lead time over formal RECIST 1.1 progression and a 41.0-day diagnostic lead time over standard 6-week radiographic CT scans. Open Science & Reproducibility: This work unifies high-dimensional dissipative control with clinical oncology, completing the scale-invariant universality isomorphism spanning cosmic vacuum stability, cardiac turbulence suppression, metabolic remission, and cancer normalization. The complete open-source Python implementation, simulation protocols, numerical datasets, and phase-space visualization suites are publicly accessible under the MIT License at: https://github.com/sukuyoshi/Geometric_Cancer_Attractors (This work extends the dissipative operator framework established in Yoshikai, 2026; DOI: 10.5281/zenodo.24156018, DOI: 10.5281/zenodo.24156142, and DOI: 10.5281/zenodo.24156293).