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 introduces Danus, a system designed to effectively coordinate and scale mathematical reasoning agents by using a shared fact graph as a global memory-management mechanism. The system consists of a main agent, worker agents, and a verifier, each with specific roles in proof search and verification. The system is evaluated through six case studies in algebraic geometry, singularity theory, and combinatorics.

What the Document Says

• Danus is an orchestration system for mathematical reasoning.
• It's centered around a shared fact graph as global memory-management mechanism.
• The system includes a main agent, multiple worker agents, and a stateless verifier.
• The main agent performs planning, coordination, and interaction with human mathematicians.
• Worker agents carry out proof search in parallel.
• The verifier checks mathematical claims before they are admitted into the fact graph.
• Each verified fact is stored with its proof and logical dependencies.
• Danus constructs long, detailed mathematical proofs incrementally while keeping the shared proof state organized.
• The system is evaluated through six research-level case studies in algebraic geometry, singularity theory, and combinatorics.
• Danus is open source at https://github.com/frenzymath/Danus.

Key Concepts Mentioned

• mathematical reasoning agents
• fact graph
• orchestration system
• proof search
• verification
• shared proof state

Claims Made by the Document

• Danus is effective for scaling mathematical reasoning agents for long-horizon research problems.

Evidence Used

• Results from six case studies in algebraic geometry, singularity theory, and combinatorics

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.