Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Jihao Liu, Guoxiong Gao, Zeming Sun, Bin Wu, Shurui Liu, Jiedong Jiang, Haocheng Ju, Leheng Chen, Ronnie Cheng, Xiping Zhang, Bin Dong
• Venue: arXiv: cs.AI
• Published: 2026-07-07
• Collected: 2026-07-08
• URL: http://arxiv.org/abs/2607.06447v1
• PDF: https://arxiv.org/pdf/2607.06447v1
• DOI: UNKNOWN

Plain-Language Brief

The paper proposes a system called Danus that aims to help mathematical reasoning agents tackle complex, research-level problems by coordinating them effectively and managing their shared memory through a global fact graph. The system consists of a main agent, worker agents, and a verifier. The main agent plans and coordinates the workers, the worker agents perform proof search in parallel, and the verifier checks mathematical claims before they are added to the fact graph. The system can build long arguments incrementally while keeping the shared proof state organized. The authors evaluate Danus through six case studies in various mathematical fields.

What the Document Says

• Danus is an orchestration system for research-level mathematical reasoning centered on a shared fact graph.
• Danus consists of a main agent, multiple worker agents, and a stateless verifier.
• The main agent performs planning and coordination in Danus.
• Worker agents carry out proof search in parallel in Danus.
• The verifier checks mathematical claims before they are admitted into the fact graph in Danus.
• Each verified fact is stored with its proof and logical dependencies in Danus.
• Danus enables building long, detailed mathematical proofs incrementally while keeping the shared proof state organized.
• The main agent periodically summarizes the evolving proof state in Danus.
• Danus supports interaction with human mathematicians through progress reports.
• The authors evaluate Danus through six research-level case studies in algebraic geometry, singularity theory, and combinatorics.

Key Concepts Mentioned

• mathematical reasoning agents
• fact graph
• proof search
• planning
• coordination
• verification
• algebraic geometry
• singularity theory
• combinatorics

Claims Made by the Document

• Danus provides an effective route toward scaling mathematical reasoning agents for long-horizon research problems.

Evidence Used

• The results of the six case studies illustrate how the fact-graph memory mechanism enables Danus to construct long, detailed mathematical proofs

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, scaling and orchestrating such agents effectively remains challenging, due to the difficulty of coordinating parallel proof search while keeping intermediate claims organized and reliable. In this paper, we propose Danus, an orchestration system for research-level mathematical reasoning centered on a shared fact graph as a global memory-management mechanism. Danus consists of a main agent that performs planning and coordination, multiple worker agents that carry out proof search in parallel, and a stateless verifier that checks proposed mathematical claims before they are admitted into the fact graph. Each verified fact is stored together with its proof and logical dependencies, allowing the system to build long arguments incrementally while keeping the shared proof state organized. The main agent periodically summarizes the evolving proof state, redirects workers across promising directions, and supports interaction with human mathematicians through progress reports. We evaluate Danus through six research-level case studies in algebraic geometry, singularity theory, and combinatorics, illustrating how the fact-graph memory mechanism enables Danus to construct long, detailed mathematical proofs. Our results suggest that fact-graph-based orchestration provides an effective route toward scaling mathematical reasoning agents for long-horizon research problems. Danus is open source at https://github.com/frenzymath/Danus.