Theorome Overview: Foundations and Architecture

Abstract

We present Theorome, an AI-native research institute focused on discovering fundamental structures and translating theory into systems. This paper outlines our research foundations, describes the Foundry pipeline for theory-to-system translation, and discusses our approach to building research infrastructure that integrates formal methods with practical implementation.

1. Introduction

The gap between rigorous theory and working systems remains a persistent challenge in computational science. Academic research optimizes for publication; industry optimizes for market capture. The space between—where theory meets implementation constraints and implementation reveals theoretical gaps—remains underexplored.

Theorome exists in this gap. We investigate fundamental structures at the intersection of mathematics, computation, and reality, with a commitment to both theoretical rigor and system realization.

1.1 Core Thesis

Our core thesis: The most important structures are those that generate both understanding and capability.

A theory that cannot be implemented may be incomplete. An implementation without theoretical grounding may be brittle. Progress requires institutions that can do both.

2. Research Foundations

Our research spans five interconnected directions:

2.1 AI-native Science

We develop computational methods for automated scientific discovery. This includes:

Automated hypothesis generation based on existing theory
Symbolic reasoning combined with neural approximation
Meta-learning for methodology development
Formal verification integrated into discovery pipelines

The goal is not to replace human researchers but to expand the space of hypotheses we can systematically explore.

2.2 Fundamental Reality & Causality

We investigate the mathematical structures underlying causality, observation, and physical law. Key questions include:

What are the minimal formal requirements for causal reasoning?
How do information-theoretic constraints relate to physical law?
What is the relationship between computational and physical theories of reality?

This work combines techniques from category theory, information theory, and foundations of physics.

2.3 Large-scale Multi-Agent Systems

We build frameworks for coordinating populations of autonomous agents. Research focuses on:

Coordination Protocol Schema:
  Agent := (State, Policy, Communication)
  System := Network(Agents, Channels, Resources)
  Emergence := f(LocalRules) → GlobalBehavior

Key challenges include scalable communication, resource allocation, and emergent governance structures.

2.4 Simulation & Synthetic Worlds

We create controlled environments for theory validation and experimentation. These environments must balance:

High fidelity (matching real-world complexity)
Reproducibility (exact experimental control)
Efficiency (computational tractability)

2.5 Applied Abstractions

We translate formal structures into practical systems. This includes:

Programming languages embedding formal guarantees
Type systems for distributed computation
Category-theoretic design patterns
Efficient implementation of abstract specifications

3. The Foundry Pipeline

The Foundry is our systematic process for theory-to-system translation:

Insight → Formal Model → Validation → Prototype → Spin-off

3.1 Insight

Research generates candidate insights—observations, connections, or theoretical breakthroughs that suggest practical application.

3.2 Formal Model

We translate insights into rigorous formalism:

Model M := (Structures, Operations, Axioms, Invariants)
where:
  Structures define the entities
  Operations define transformations
  Axioms define constraints
  Invariants define preserved properties

Formalization forces precision and reveals hidden assumptions.

3.3 Validation

We test models through:

Theoretical analysis (proof of properties)
Simulation (numerical experiments)
Comparative studies (behavior under varied conditions)

Failure at this stage is common and valuable. It clarifies boundary conditions and guides model refinement.

3.4 Prototype

We implement working systems. The prototype serves three purposes:

Validates that the model can be realized
Reveals practical constraints missed in theory
Provides feedback for model improvement

3.5 Spin-off

Mature systems become independent ventures. This separation:

Allows systems to scale without distorting research incentives
Maintains focus on fundamentals
Ensures successful systems reach users

4. Methodology

4.1 Integration of Formal Methods

We use proof assistants, type theory, and formal verification not as academic exercises but as practical tools for building reliable systems.

Example type signature for causal intervention:

intervene : (model: CausalModel) →
            (variable: Var) →
            (value: Value) →
            Effect (UpdatedModel, Prediction)

4.2 Failure Documentation

We document failures as rigorously as successes. A well-characterized negative result contains information: boundary conditions, failure modes, and insights for future attempts.

Our Lab Notes series publishes detailed accounts of failed approaches.

4.3 Computational Experiments

We treat simulation as a first-class research method. Synthetic experiments allow:

Exact control of variables
Reproducible results
Exploration of counterfactuals
Testing at scales impossible in physical systems

5. Infrastructure

We build and maintain research infrastructure including:

Hesva: Simulation environments for reproducible experiments
Formal systems toolchain: Compilers and verifiers for theory translation
Agent coordination framework: Infrastructure for multi-agent research

This infrastructure is both research output and research enabler.

6. Relation to Existing Work

Theorome draws from multiple traditions:

Industrial research labs (Bell Labs, Xerox PARC): Long-term fundamental research with system realization
Formal methods community: Rigor and verification as practical tools
Systems research: Implementation as validation and discovery
AI safety research: Importance of formal guarantees in intelligent systems

We differ in our emphasis on the complete cycle: theory → system → theory.

7. Open Questions

Key questions guiding our work:

What formal frameworks best capture emergent multi-agent behavior?
How can automated reasoning systems contribute to theory discovery?
What are the limits of simulation as scientific method?
How do we preserve formal guarantees through system implementation?
What structures are universal across different domains of computation and reality?

8. Conclusion

Theorome represents an experiment in research organization: Can we build an institution that values both theoretical depth and practical impact? Can formal methods integrate with rapid prototyping? Can fundamental research maintain direct connection to deployed systems?

Early results suggest the answer is yes, but the work continues.

References

For more on specific research directions, see:

Research Directions (theorome.org/research/directions)
Active Projects (theorome.org/research/active-projects)
Lab Notes for detailed technical documentation

Acknowledgments

This work builds on conversations with researchers across multiple disciplines. We thank our collaborators and early partners.

Contact: For questions or collaboration inquiries, reach out at contact@theorome.org

Version: 1.0 (January 2026)