Hypergraph geometry localizes mutation-associated dependency vulnerabilities in cancer.

Mutation-specific therapeutic vulnerabilities remain difficult to identify in precision oncology because lineage effects and network topology can obscure true synthetic lethal relationships. Here, we present a computational framework that maps genomic mutational profiles and genome-wide CRISPR-Cas9 screens onto multi-scale hypergraphs constructed from macromolecular complexes (CORUM), protein interaction modules (STRING), and transcriptional regulons (TRRUST). Using strict reproducibility criteria across lineage-split cohorts, we identify cross-topology overlap families of dependencies that recur across independent biological organizational layers. We then characterize these candidates with discrete hypergraph geometry, including Hypergraph Fractional Ricci Curvature (HFRC) and Hypergraph Local Ricci Curvature (HLRC), and evaluate them against multidimensional matched-null distributions and degree-preserving shuffles to control for network density and node degree bias. We evaluate the 8 core cross-topology families for clinical prognostic value. Separately, to validate the pharmacological actionability of the hypergraph framework, we project our prioritized candidates onto PRISM dose-response profiles, confirming that the geometrically constrained BRAF:MAP2K1 family exhibits strong, selective drug sensitivity to downstream MAPK pathway inhibition. The strongest face-validity result is SMARCA2:SMARCA4, a clinically validated paralog synthetic lethal pair in chromatin remodeling that our pipeline recovered purely through unsupervised geometric constraints. While across the prioritized overlap families this specific class of reproducible dependencies localizes to highly integrated, negatively curved hypergraph regions, this topological separation is statistically fragile; it achieves nominal significance (p = 0.031) as a primary endpoint and is sensitive to the removal of single families. Nonetheless, this pattern persists across independent screening platforms, including Sanger and DepMap 25Q3, suggesting a potential, albeit statistically sensitive, geometric framework for prioritizing actionable targets in precision oncology.