Latent Surface Induction for Ransomware Detection via Homological Persistence Mapping in File System Topologies

High-dimensional geometric representations of filesystem states offer a structurally grounded mechanism for identifying anomalous transformations associated with encryption-based extortion attacks. Persistent homology was applied to model the evolution of file system topology through successive snapshots, enabling the characterization of ransomware impact as a deformation of latent simplicial structures. Traditional detection methods relying on entropy, byte patterns, or behavioral heuristics frequently encounter limitations when confronted with obfuscated or delayed payloads, whereas homology-based representations remain stable across such perturbations. Filtration functions derived from metadata features such as access frequency, file size, and directory depth were used to construct simplicial complexes capturing both local and global structural changes. Detection performance was benchmarked across multiple ransomware families, including LockBit, Hive, and REvil, revealing consistent topological divergence from benign system activity. A probabilistic classifier trained on persistence landscapes and images demonstrated sensitivity to subtle structural distortions without reliance on prior family-specific indicators. Variants operating in compressed or resource-constrained environments revealed increased variability in persistence image distributions, yet classification remained viable through geometric regularization techniques. Structural generalization was observed across operating platforms, albeit with reduced precision when metadata granularity was inconsistent. Results suggest that ransomware behavior may be effectively inferred through abstract structural patterns, enabling detection architectures that rely less on specific event signatures and more on systemic disruption of topological coherence.