Cancer as a Topological Phase Transition: Geometric Parsimony and Logical Collapse in Biological Information Processing

Conventional oncology treats cancer as a stochastic accumulation of genetic mutations. This paper proposes a radical shift toward an information-theoretic framework, drawing on the principle of Geometric Parsimony observed in tiny language models. We hypothesize that cancer is a topological phase transition occurring when a cellular system, under extreme environmental stress (hypoxia, inflammation), can no longer sustain the metabolic cost of high-dimensional regulatory logic. To avoid total systemic dissolution, the cellular manifold collapses into a low-dimensional "logical skeleton"—a highly stable, crystalline geometric configuration (Cosine Similarity ≈ 1.0). In its early stages, this crystallization acts as a compensatory survival mechanism, preserving core existence at the expense of global functional alignment.