Cancer as Domain Sovereignty Failure: A Scale-Recursive Framework for Oncogenesis, Tumor Progression, and Bioelectric Therapy

We present a scale-recursive framework for cancer based on Scale-Recursive Non-Uniform Domain Tiling (SRNUDT), in which cancer is reframed as a domain sovereignty failure — a remainder accumulation pathology at the cell-tissue boundary. In SRNUDT, remainder is the organized excess that a domain generates but cannot internally contain — the output that must propagate outward through boundary channels to drive higher-scale organization. In healthy tissue, each cell is a sovereign domain that generates remainder (metabolic products, growth signals, structural outputs) and propagates it correctly to the containing tissue domain. Cancer initiation corresponds to a failure of this boundary propagation: the cell's internal tiling becomes decoupled from the tissue domain's boundary conditions, causing remainder to accumulate internally rather than flow outward. Tumor growth corresponds to the propagation of a competing tiling — the cancer cell's deviant boundary conditions converting adjacent nodes. Metastasis corresponds to remainder cascade: accumulated remainder exceeding local containment and re-establishing the competing tiling at distant sites through the organism's macro-scale remainder channels (vasculature, lymphatics). This framework generates five testable hypotheses (H1--H5) concerning the relationship between remainder accumulation markers, boundary condition deafness, bioelectric gradient disruption, and cancer progression. It directly interprets the experimental results of Levin et al. (Tufts University) on bioelectric cancer normalization — in which restoring correct tissue-level bioelectric gradients causes cancer cells to reintegrate or undergo apoptosis without cytotoxic intervention. The SRNUDT framework explains why this works: bioelectric gradients are tissue-level boundary conditions, and restoring them restores the cell's external remainder channel. The therapeutic target is not the cancer cell — it is the boundary.