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QRS research · Mathematical research tooling

MathResearchOS

A recoverable, audited operating system for mathematical work

Give it a mathematical objective. Get back a result with its evidence, or the exact stage where it stopped.

MathResearchOS is a command-line runtime that turns one objective into a staged run: normalise the problem, search the literature, explore proof ideas, try to refute them, integrate an argument and write it up. Models from the Codex CLI, the Claude Code CLI or an HTTP API do the work; every stage output must pass a verifier verdict before the next stage uses it. Each case keeps the exact objective, its frozen contract, every attempt and an event log, so a run can be paused, resumed or audited later.

Usage guide

Active

Lead: Yuhe Sui

Version 0.1.0 · Python 3.11+ · no third-party packages

One run of the MathResearchOS solve workflowIllustrative run, drawn left to right and then down. specify (thinker) starts three parallel branches: literature, an explore_swarm of five explorers, and falsify. They merge in triage (orchestrator), then integrate (thinker) writes a proof draft, refute (refuter) attacks it, and verify is a verdict gate. The gate can say accept, repair (loops back to integrate), replan or escalate (both go to a human gate). In this run there is one repair, then accept. report (writer) comes next, then a second gate, verify_final, and RESULT.md is published only after the verifier accepts. The figure shows the order of stages, not the correctness of any result.Illustrative runrepairacceptacceptreplan,escalatereplan, escalatehuman gatespecifythinkerliteratureexplore_swarm5 explorersfalsifytriageorchestratorintegratethinkerrefuterefuterverifyacceptreportwriterverify_finalacceptproof draftRESULT.mdVerdict gate:acceptrepair → integratereplan, escalate → human gate
One run of the v2 workflow: specify, explore in parallel, triage, integrate, refute, then verify. A repair verdict sends the draft back; an accept moves on, and RESULT.md is published only after the final verifier accepts. One run of the v2 workflow, from specify to RESULT.md. A verifier verdict (accept, repair, replan or escalate) gates each audited stage; RESULT.md is published only after the final verifier accepts. Illustrative run; stage names are the workflow’s own, verdicts vary.

MathResearchOS at a glance

Quick start

Install, create a case from a problem file, preview the run for free, then run it. The full guide covers each step.

pip install -e .
mathos create --mode solve --title "First problem" --objective-file problem.md
mathos run MATH-0001 --dry-run
mathos run MATH-0001 --route cross
mathos status MATH-0001

Live runs call real models and can cost money; --dry-run never does. A live run needs a logged-in codex or claude CLI. Install details →

Evidence so far

Pilot run tested

One public-benchmark problem (IMO-ProofBench, problem PB-Basic-008) through the v2 workflow with 8 explorers: 17 calls, about 11 minutes. All explorers delivered distinct ideas and the final proof was correct, checked by hand.

One problem, one run: a check that the pipeline works end to end, not a measure of accuracy.

Held-out comparisons In progress

Model and role comparisons on held-out problems, with every arm and failure reported, are planned but not run yet.

Jump to what you need

What an accept means, and the limitations →

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