Ontological Trajectory Forecasting via Finite Semigroup Iteration and Lie Algebra Approximation in Geopolitical Knowledge Graphs
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2026
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| _version_ | 1866913024016646144 |
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| author | Wu, Qihang |
| author_facet | Wu, Qihang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_10087 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ontological Trajectory Forecasting via Finite Semigroup Iteration and Lie Algebra Approximation in Geopolitical Knowledge Graphs Wu, Qihang Artificial Intelligence 20M99, 17B99, 62F15 I.2.4; I.2.1; H.3.3 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. |
| title | Ontological Trajectory Forecasting via Finite Semigroup Iteration and Lie Algebra Approximation in Geopolitical Knowledge Graphs |
| topic | Artificial Intelligence 20M99, 17B99, 62F15 I.2.4; I.2.1; H.3.3 |
| url | https://arxiv.org/abs/2604.10087 |