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tl;dr We’ve created a universal mathematical framework to model the non-linear evolution of any complex system’s time series that enables the creation of autonomous, instantly deployable AI models, eliminating the need for all training and continual maintenance. A foundational challenge in modern science is predicting the behaviour of complex systems. These interconnected domains, from climate systems to global finance, are defined by emergent properties and non-linear feedback loops that defy simple analysis, particularly when relying on their observable time series data. While deep learning has delivered predictive breakthroughs, these methods function as statistical learners, lacking an understanding of the underlying causal dynamics. Consequently, there is an urgent need for a unified mathematical framework capable of modelling emergent behaviour in system dynamics and describing how a disruption in one domain, such as a climate shock or a financial crash, cascades and propagates across entirely separate, interconnected systems.

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A New Paradigm for Causal Analysis

Our approach to modelling cause and effect in complex systems shifts focus from external factors to internal system dynamics. In contrast to traditional methods that link an outside cause to a single event, we analyse the system’s own behaviour, tracing the causal path from an initial system change (the observable cause) to the subsequent directional change (the observable effect).

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Underlying Mathematical Theory

Our framework for causal discovery directly infers cause and effect directly from a system’s internal behaviour, fundamentally overcoming the data-dependency of traditional AI. We use category theory to understand the underlying structure of a system’s time series data, shifting analysis from individual data points to underlying structure and relationships. This focus on systemic structure captures complex non-linear dynamics and feedback loops, which allows for an implementation that is parameter-free and memoryless, requiring zero training data. To map causal flow, we introduce a significant advancement to Takens’ Theorem. Our method operates on the core axiom that every system change begins at the highest observable frequency and progressively propagates to lower timeframes, thereby overcoming the original theorem’s dependency on past states. By leveraging the learned categorical abstractions, the framework autonomously models and validates the reconstructed state space. This capability is the foundation for revealing the step by step causal trajectory of any initial state shift and providing a clear, time-stamped mapping of the propagation across timeframes.

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Measuring True Causal Accuracy

We measure the framework’s performance using causal accuracy, which quantifies how perfectly it maps the true step-by-step chain of events. This is fundamentally different from a simplistic predictive “hit ratio.” We validate this against complex events where the ground truth is known. For example, by analysing time series data from the 2020 COVID-19 event, our technology doesn’t just predict the market crash; it precisely identifies the initial state shift in US stocks in early 2020 and maps its propagation progressively through lower timeframes, as it evolved into a widespread decline. This proves our platform provides deep, explainable understanding.

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The Unified World View

Our mission is to create the world’s first intelligence platform that provides a unified, causal view of all complex systems. By removing the traditional limitations of AI learning frameworks, this platform empowers governments, financial institutions, and organisations to instantly understand the behaviour of any complex system through transparent, time-stamped mapping, providing definitive active foresight rather than passive prediction.
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