Danus orchestration: fact-graph memory for math agents

Danus, an orchestration system for mathematical reasoning agents, appeared on arXiv on 7 Jul 2026 (arXiv:2607.06447). The paper presents a coordinator-based design that centers a shared fact graph as global memory, and evaluates the system across six research‑level case studies in algebraic geometry, singularity theory, and combinatorics.

How does Danus work?

Danus coordinates a main agent, multiple worker agents, and a stateless verifier around a shared fact graph: the main agent plans and redirects, worker agents run parallel proof search, and the verifier checks proposed claims before they enter the graph. Each verified fact is stored with its proof and logical dependencies so the system builds long arguments incrementally while keeping the shared proof state organized.

The paper describes three named roles. The main agent performs planning and coordination and periodically summarizes the evolving proof state. Worker agents carry out proof search in parallel and are redirected across promising directions by the main agent. A stateless verifier checks proposed mathematical claims before admission into the fact graph. The system also supports interaction with human mathematicians through progress reports.

How was Danus evaluated?

The authors evaluated Danus through six research‑level case studies spanning algebraic geometry, singularity theory, and combinatorics, illustrating the system constructing long, detailed mathematical proofs. Those six case studies serve as the primary empirical evidence presented in the paper.

The evaluation focuses on how the fact‑graph memory mechanism enables coordinated, long‑horizon proof construction: verified facts are kept with their proofs and logical dependencies, allowing incremental composition of arguments while multiple workers search in parallel. The paper frames these case studies as demonstrations that fact‑graph‑based orchestration can scale mathematical reasoning agents for long research problems.

Why it matters

Danus tackles two persistent bottlenecks in automated mathematical reasoning: coordination of parallel proof search and reliable management of intermediate claims. The shared fact graph enforces a single, verifiable state that workers and the coordinator read and update, which reduces duplication and preserves logical dependencies. For researchers trying to apply language models to open mathematical problems, that combination of parallel search plus structured memory addresses practical scaling constraints.

What to watch

The paper is publicly available on arXiv (arXiv:2607.06447, submitted 7 Jul 2026) and the authors note Danus is open source at a URL provided in the manuscript. Watch for community uptake of the repository and for independent reproductions or extensions of the six case studies in algebraic geometry, singularity theory, and combinatorics as the next concrete signals of impact.

References and specifics cited here are taken from the arXiv submission "Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory" (Jihao Liu et al.), submitted 7 Jul 2026.