Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

2026-07-08 · Source: cs.CL updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

Danus, an open-source orchestration system, addresses the challenge of scaling and coordinating LLM-based mathematical reasoning agents for research-level problems. It features a main agent for planning, multiple worker agents for parallel proof search, and a stateless verifier that checks claims before they are added to a shared fact graph. This fact graph serves as a global memory, storing verified facts with their proofs and logical dependencies, enabling the incremental construction of long arguments. The system also supports human interaction through progress reports and can generate paper-style expositions from completed proofs. Evaluated through six research-level case studies in algebraic geometry, singularity theory, and combinatorics, Danus demonstrates its ability to construct detailed mathematical proofs, suggesting fact-graph-based orchestration is effective for long-horizon research.

Key takeaway

For Research Scientists developing LLM-based reasoning systems, Danus demonstrates that a shared fact-graph memory and orchestrated multi-agent architecture are critical for tackling long-horizon mathematical problems. You should explore implementing similar fact-graph mechanisms to manage intermediate claims and coordinate parallel proof searches, ensuring reliability and scalability in your own agentic systems. This approach can significantly enhance the ability to construct complex, detailed proofs.

Key insights

Danus orchestrates mathematical reasoning agents using a shared fact graph for scalable, organized proof generation.

Principles

• Fact graph acts as a single source of truth.
• Strict separation of agent roles prevents unverified math.
• Parallel exploration broadens problem-solving search.

Method

A main agent plans and coordinates, worker agents perform parallel proof search, and a stateless verifier checks claims before adding them to a directed acyclic fact graph, which enables incremental, organized argument building.

In practice

• Implement fact graphs for multi-agent memory management.
• Utilize generate-verify-revise loops for reliability.
• Decompose complex problems by rank or case for targeted attacks.

Topics

• Mathematical Reasoning
• LLM Agents
• Fact Graphs
• Multi-Agent Orchestration
• Proof Generation
• Algebraic Geometry

Code references

• frenzymath/Danus

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CL updates on arXiv.org.