Ontological Trajectory Forecasting via Finite Semigroup Iteration and Lie Algebra Approximation in Geopolitical Knowledge Graphs

We present EL-DRUIN, an ontological reasoning system for geopolitical intelligence analysis that combines formal ontology, finite semigroup algebra, and Lie algebra approximation to forecast long-run relationship trajectories. Current LLM-based political analysis systems operate as summarisation engines, producing outputs bounded by textual pattern matching. EL-DRUIN departs from this paradigm by modelling geopolitical relationships as states in a finite set of named Dynamic Patterns, composing patterns via a semigroup operation whose structure constants are defined by an explicit composition table, and embedding each pattern as a vector in an 8-dimensional semantic Lie algebra space. Forward simulation iterates this semigroup operation, yielding reachable pattern sets at each discrete timestep; convergence to idempotent absorbing states (fixed points of the composition) constitutes the predicted long-run attractor. Bayesian posterior weights combine ontology-derived confidence priors with a Lie similarity term measuring the cosine similarity between the vector sum of composing patterns and the target pattern vector, providing interpretable, calibrated probabilities that are not self-reported by a language model. Bifurcation points -- steps at which two candidate attractors have near-equal posterior mass -- are detected and exposed to downstream analysis. We demonstrate the framework on six geopolitical scenarios including US-China technology decoupling and the Taiwan Strait military coercion trajectory. The architecture is publicly available as an open-source system with a Streamlit frontend exposing full computation traces, Bayesian posterior breakdowns, and 8D ontological state vectors.

External Reliable Information-enhanced Multimodal Contrastive Learning for Fake News Detection

With the rapid development of the Internet, the information dissemination paradigm has changed and the efficiency has been improved greatly. While this also brings the quick spread of fake news and leads to negative impacts on cyberspace. Currently, the information presentation formats have evolved gradually, with the news formats shifting from texts to multimodal contents. As a result, detecting multimodal fake news has become one of the research hotspots. However, multimodal fake news detection research field still faces two main challenges: the inability to fully and effectively utilize multimodal information for detection, and the low credibility or static nature of the introduced external information, which limits dynamic updates. To bridge the gaps, we propose ERIC-FND, an external reliable information-enhanced multimodal contrastive learning framework for fake news detection. ERIC-FND strengthens the representation of news contents by entity-enriched external information enhancement method. It also enriches the multimodal news information via multimodal semantic interaction method where the multimodal constrative learning is employed to make different modality representations learn from each other. Moreover, an adaptive fusion method is taken to integrate the news representations from different dimensions for the eventual classification. Experiments are done on two commonly used datasets in different languages, X (Twitter) and Weibo. Experiment results demonstrate that our proposed model ERIC-FND outperforms existing state-of-the-art fake news detection methods under the same settings.