Fractional–Temporal Lorentz Graph Networks: Integrating Physical Memory into Dynamic Knowledge Reasoning

Dynamic knowledge representation in curved manifolds conventionally relies on integer-order Markovian sequence encoders, intrinsically yielding exponential memory decay. This paradigm fails to model the anomalous diffusion and heavy-tailed historical dependencies inherent in complex evolutionary networks and dense physical environments. This manuscript proposes the Fractional–Temporal Lorentz Graph Convolutional Network (FTL-GCN), formalizing temporal evolution as a continuous fractional geometric flow explicitly defined on the tangent bundle of the Lorentz manifold. Analytical derivations demonstrate that the discrete Grünwald–Letnikov memory kernel establishes a non-exponential, power-law lower bound for historical state retention, preventing topological manifold collapse over extended temporal horizons. Empirical evaluations demonstrate that FTL-GCN achieves competitive forecasting accuracy against the latest 2025–2026 state-of-the-art discrete models within specific temporal windows, while uniquely mitigating predictive degradation by up to 52% in long-horizon dependency stress tests and maintaining sub-millisecond latency for physical control. The architecture is subsequently deployed within an in silico biophysical simulation for autonomous micro–nano robotic navigation in the Tumor Microenvironment (TME). By establishing a physical-mathematical structural analogy—mapping the empirical fractional viscoelasticity of the extracellular matrix to the cognitive network’s fractional derivative order—FTL-GCN sustains continuous-space navigation policies in dense anomalous environments where standard integer-order models experience mechanical slip.