Metastasis as Attractor Relaxation: Universal Stability Landscapes Govern Cancer Evolution Across Genetic and Systemic Scales

Somatic copy-number alterations (CNAs) are a defining feature of cancer genomes and are traditionally interpreted using gene-centric, frequency-based models of oncogenic selection. However, recurrence alone often fails to predict clinical impact, therapeutic resistance, or lethality. This work introduces a state-centric, population-level framework for cancer evolution in which continuous CNA amplitudes are treated as emergent variables constrained by stability landscapes. Using large public cohorts (including TCGA, METABRIC, and DepMap), we infer effective stability landscapes directly from empirical CNA distributions via a coarse-grained potential formulation. We show that many amplified genomic states form robust, bistable attractors characterized by high stability, yet clinical impact varies substantially across loci. In particular, we demonstrate a clear decoupling between genomic stability and lethality: ZNF217 amplification forms a deep but clinically neutral attractor, whereas MYC amplification occupies a similarly stable state that is strongly associated with immune exclusion and excess mortality. Extending beyond individual genes, we find that normalized CNA stability landscapes collapse onto a conserved dimensionless form across diverse oncogenes, tissues, and randomly selected transcriptionally active loci. This universality is supported by permutation controls and model-independent analyses. Additionally, we identify a conserved scaling relationship between landscape stiffness and CNA variance, indicating that genomic fluctuations are constrained by attractor geometry rather than arising from unconstrained noise. Finally, we introduce a low-dimensional systemic biomarker (Φ) that captures tumor–immune balance and exhibits nonlinear risk stratification consistent with a phase-transition-like loss of immune control. While the analysis is retrospective and population-based, the framework yields falsifiable predictions and provides a quantitative alternative to gene-centric models of oncogenic classification. This preprint presents a descriptive, non-equilibrium stability-based view of cancer evolution, emphasizing persistent genomic states as the primary units of selection. All analyses are based on publicly available data, and limitations regarding causal inference and longitudinal dynamics are explicitly discussed.