Scale-Invariant Single-Cell Transcriptomics: Eradicating Batch Effects and Enabling Cross-Species Zero-Shot Oncology via Relational Calculus

This paper introduces a Relational Calculus Framework that converts absolute single‑cell RNA counts into dimensionless fractions of a cell’s housekeeping gene capacity, mathematically canceling sequencing‑depth artifacts. Trained exclusively on a mouse breast cancer model and tested zero‑shot on shallow‑sequenced human TNBC, a lightweight XGBoost model maintains 98.4% accuracy under a 70% covariate shift, while a derived Relational Imbalance Index (ρ) predicts therapeutic vulnerabilities, turning tumor architecture into a universal vulnerability map.