perqed.com

What It Is

Perqed is an open-source Autonomous Proof Engine whose core goal is to automatically search for mathematical witnesses, generate proofs, and machine-verify them in Lean 4. It is not a general-purpose chatbot, but a tool for automated theorem proving and formalized mathematics research. It currently focuses on open Ramsey number problems and Torus Decompositions, and already has machine-checked proof papers and source code for m=4 and m=6 Directed Hamiltonian Torus Decompositions.

Core Capabilities

Its architecture is a typical hybrid proof loop: Gemini 2.5 Flash reads conjectures, formulates strategies, explains failure modes, and proposes new search directions; 8 parallel Simulated Annealing workers perform large-scale heuristic search; Z3 handles fast SMT checking over structured subspaces, as well as LNS repair for near-witnesses. Once a witness is found, it is compiled into a Lean 4 proof and checked by the Lean kernel via decide or tactic mode. For non-constructive goals, DeepSeek Prover V2:7B Q8 generates Lean tactics locally through Ollama.

Pricing and Deployment

The source text does not provide pricing for a commercial subscription or hosted service. The project emphasizes that the core search and tactic generation run on local hardware; Gemini is used only for strategic planning, with an indicated cost of about US$0.02 per run. Running DeepSeek Prover locally requires about 7GB of VRAM, with each completion taking around 1–2 seconds on Apple Silicon. Overall, the cost profile is closer to “open-source tool + local compute + a small amount of external model API usage.”

Pros and Cons

Its main strength is a complete technical pipeline: search, SMT repair, LLM-based strategy planning, and Lean 4 kernel verification are combined, so proof reliability does not depend solely on model-generated text. GitHub, papers, and a live proof feed also improve transparency. The limitations are a very high barrier to entry: users need to understand Lean 4, Z3, Ollama, local runtime environments, and mathematical problem modeling. Its current scope is relatively narrow, and a failed search cannot guarantee a proof. The source text does not specify full installation documentation, enterprise support, a privacy policy, or stable release information.

Who It’s For and Access from China

Perqed is better suited to formal verification researchers, combinatorics research teams, Lean 4 users, and automated theorem proving developers. It is not appropriate for general office work or content generation scenarios. For access from China, the source text provides no network availability information; GitHub, the Gemini API, and obtaining Ollama models may be uncertain from within mainland China, and payment methods are not disclosed. If access is restricted, users may consider alternative toolchain combinations such as Lean 4, Z3, Coq, Isabelle/HOL, and DeepSeek Prover.