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

Can AI reason about a war before its trajectory becomes historically obvious? Analyzing this capability is difficult because retrospective geopolitical prediction is heavily confounded by training-data leakage. We address this challenge through a temporally grounded case study of the early stages of the 2026 Middle East conflict, which unfolded after the training cutoff of current frontier models. We construct 11 critical temporal nodes, 42 node-specific verifiable questions, and 5 general exploratory questions, requiring models to reason only from information that would have been publicly available at each moment. This design substantially mitigates training-data leakage concerns, creating a setting well-suited for studying how models analyze an unfolding crisis under the fog of war, and provides, to our knowledge, the first temporally grounded analysis of LLM reasoning in an ongoing geopolitical conflict. Our analysis reveals three main findings. First, current state-of-the-art large language models often display a striking degree of strategic realism, reasoning beyond surface rhetoric toward deeper structural incentives. Second, this capability is uneven across domains: models are more reliable in economically and logistically structured settings than in politically ambiguous multi-actor environments. Finally, model narratives evolve over time, shifting from early expectations of rapid containment toward more systemic accounts of regional entrenchment and attritional de-escalation. Since the conflict remains ongoing at the time of writing, this work can serve as an archival snapshot of model reasoning during an unfolding geopolitical crisis, enabling future studies without the hindsight bias of retrospective analysis.

Predictive political question answering (QA), such as predicting how a political actor will vote, goes beyond factual lookup. External political resources offer rich historical evidence, but rarely contain the answer itself. Existing LLM augmentation methods, including actor-profile-based simulation and knowledge graph evidence injection, improve political reasoning but largely treat external resources as knowledge-based evidence, leaving prediction-relevant signals under-modeled. We identify two complementary signals for predictive political QA: actor stances that capture issue-specific preferences, and high-order structure signals that capture indirect dependencies among political actors. We propose PSL, a dual-view framework that converts semi-structured political records into inference-oriented evidence for LLMs. PSL extracts stance signals from question-relevant actor records in a semantic view, and learns structure-aware actor representations from an actor interaction graph in a vector view. Across three real-world datasets and multiple LLMs, PSL consistently outperforms baselines, with ablations confirming the complementary gains of stance and structure signals.

Geopolitical event forecasting is a challenging task, as it requires understanding complex regional contexts, dynamic event signals, and uncertain future outcomes. Recent advances in large language model agents provide new opportunities for building forecasting systems that can reason with diverse sources and expert perspectives. In this paper, we present ForecastAgentSearch, a preliminary framework that formulates geopolitical event forecasting as a multi-expert agent search problem. Given a forecasting query, the system first analyzes the task context, then searches and ranks relevant expert agents based on their regional knowledge, domain expertise, reliability, and complementarity. The selected agents provide specialized analyses, which are further coordinated to generate a final forecast with explanations and uncertainty awareness. We discuss the key design challenges of agent profiling, expert retrieval, ranking, and multi-agent coordination, and outline possible evaluation protocols for future development. This work aims to provide an initial step toward searchable and reliable agent-based forecasting systems.