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Research in Progress

Our ongoing research into mathematical frameworks for collective intelligence, AI governance, and complex systems coordination. Each paper represents a piece of our broader mission to understand and design better equilibria.

Mathematical Foundations

Developing unified mathematical frameworks and theoretical foundations for understanding collective intelligence systems.

5 projects

Towards a Langlands Program for Collective Intelligence

teamTEAM MEMBERS:Jonas Hallgren

Can a common mathematical language, based on graph transformations and variational information dynamics, unify the study of collective intelligence across diverse disciplines and reveal fundamental structural correspondences?

initial-story
100%
Initial Story
google-doc
100%
Internal Review
overleaf
60%
External Review
arxiv
0%
Preprint
journal
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Click for details

Graph Topology as the Language of Collective Intelligence: A Conjecture-Driven Program

teamTEAM MEMBERS:Jonas Hallgren

Can distinct Collective Intelligence (CI) functions (e.g., markets, hierarchies) be identified and characterized by the topological signatures of their underlying interaction subgraphs, thereby establishing graph topology as a unifying syntax for CI?

initial-story
50%
Initial Story
google-doc
0%
Internal Review
overleaf
0%
External Review
arxiv
0%
Preprint
journal
0%
Journal
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Convergent Collective Intelligence: Applying Geometric Deep Learning on Collective Intelligence Systems

teamTEAM MEMBERS:Jonas Hallgren

Can the emergence of common coordination structures like markets, networks, and democracies be explained as mathematically optimal solutions to specific information processing challenges, formalized through a spectral duality between signal processing and graph operator properties?

initial-story
100%
Initial Story
google-doc
40%
Internal Review
overleaf
0%
External Review
arxiv
0%
Preprint
journal
0%
Journal
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Spectral Duality in Collective Intelligence: Transforming Variational Dynamics to Signal Analysis

teamTEAM MEMBERS:Jonas Hallgren

Can the variational drive of collective intelligence systems to minimize surprise be equivalently represented and analyzed as an optimization problem in the spectral domain of their interaction graph, offering new predictive metrics?

initial-story
100%
Initial Story
google-doc
70%
Internal Review
overleaf
0%
External Review
arxiv
0%
Preprint
journal
0%
Journal
Click for details

Mathematical Foundations of Emergent Collective Intelligence: A Categorical Framework for Understanding Coordination Structures

teamTEAM MEMBERS:Jonas Hallgren

How can category theory be used to build a unified mathematical foundation for understanding why specific coordination structures (markets, networks, democracies) emerge as optimal solutions to information processing challenges in collective systems?

initial-story
80%
Initial Story
google-doc
20%
Internal Review
overleaf
0%
External Review
arxiv
0%
Preprint
journal
0%
Journal
Click for details

Computational Experiments

Empirical studies and simulations exploring how collective intelligence mechanisms perform under various conditions.

1 project

Democratic Mechanisms Under Pressure: An LLM Simulation Study of Organizational Resilience

teamTEAM MEMBERS:Jonas Hallgren

How do different democratic mechanisms (Predictive Direct, Representative, and Liquid Democracy) compare in maintaining collective utility under varying levels of adversarial pressure, and at what infiltration thresholds do they experience catastrophic failure?

initial-story
100%
Initial Story
google-doc
100%
Internal Review
overleaf
100%
External Review
arxiv
100%
Preprint
journal
0%
Journal
Click for details

Research Tools & Infrastructure

Building the computational tools and platforms needed to study and implement collective intelligence systems.

1 project

Mycorrhiza: A Process-Centric Multi-Agent Simulation Platform

teamTEAM MEMBERS:Equilibria Network, Jonas Hallgren

How can a process-centric, functional programming approach, separating mathematical process definition from computational execution, lead to more robust, verifiable, and scalable multi-agent simulations of collective intelligence?

initial-story
100%
Initial Story
google-doc
80%
Internal Review
overleaf
30%
External Review
arxiv
0%
Preprint
journal
0%
Journal
Click for details