On 20 research theorems in theoretical computer science, OpenAI’s GPT-6 Astra produced a complete, machine-checked Lean proof in 70.0% of attempts, according to TCSExam, a benchmark paper posted to arXiv on November 5 by researchers from Tsinghua University, Moonshot AI and the Shanghai Qizhi Institute. The same model resolved none of the 30 open conjectures in the benchmark.
Moonshot’s Kimi K3.1 Pro came second on theorem proving at 38.3%, and the other six agents tested on the full suite reached at most 11.7%, the paper says. On the paper’s combined TCSExam Index, Astra scores 71.9 points and Kimi K3.1 Pro 57.4: a 14.5-point gap, by our arithmetic. Moonshot AI co-authored the paper and makes the Kimi models.
Business Pill · AI Agents Explained
An evergreen Business Engineer explainer on AI agents. It teaches the general idea only and does not discuss TCSExam or theorem proving.
The key insight: The TCSExam paper reports that GPT-6 Astra produced complete, machine-checked Lean proofs of research theorems in 70.0% of attempts and leads the 100-task full suite with 71.9 points, ahead of Moonshot’s Kimi K3.1 Pro at 57.4. No agent settled any of the 30 open conjectures beyond adapting counterexamples and proofs OpenAI had already published, the paper says.
TCSExam-Full contains 100 expert-reviewed tasks in four tracks: 20 theorems that must be proved in Lean, 30 solver-engineering problems judged on hidden instances, 20 constructions, and 30 open conjectures, according to the paper and its public repository. Submissions are checked by the Lean kernel or an executable task checker.
The Index weights theorem proving, solver engineering and constructions at 30 points each and open conjectures at 10; because construction scores above 100% are not capped, the Index can exceed 100, the repository says. A 20-task Lite suite, five tasks per track, adds Anthropic’s Opus 5.5, which was not run on the full suite.
TCSExam Index on the 100-task full suite, from the paper’s Table 2: GPT-6 Astra 71.9 points, Kimi K3.1 Pro 57.4, Kimi K3 46.8, DeepSeek V4.1 Flash 1017 46.0, GLM-5.3 45.5, Qwen3.8 Max 44.8, Grok 4.6 40.5 and DeepSeek V4.1 Flash 0910 40.4. Moonshot AI, which makes the Kimi models, co-authored the paper. The 14.5-point gap is our arithmetic. Opus 5.5 was run on the 20-task Lite suite only, where it leads with 72.3.
What Was Posted on X
New Tsinghua and Moonshot AI paper finds that GPT-6 Astra proves 70.0% of research-level computer science theorems in Lean, yet the same model resolves 0 of 30 open conjectures in theoretical computer science (TCS).
Theoretical computer science is a natural test for AI research, because proofs can be machine-checked and records can be beaten. Existing benchmarks cover only slices, like proofs or code.
TCSExam has 100 expert-reviewed tasks in 4 tracks: Lean theorem proving, solver engineering, record-setting constructions, and 30 open conjectures. The Lean kernel or a task checker verifies every submission.
Without supplied lemmas, GPT-6 Astra fully proved theorems in 70.0% of attempts, Kimi K3.1 Pro in 38.3%, and the other 6 agents in at most 11.7%. The few accepted conjecture submissions adapted counterexamples and proofs OpenAI had already published.
Rohan Paul posted this on 8 November, summarising the TCSExam paper (arXiv 2611.07962) from Tsinghua University, Moonshot AI and the Shanghai Qizhi Institute. The figures in the post (GPT-6 Astra at 70.0% on theorem proving, Kimi K3.1 Pro at 38.3%, the other six agents at most 11.7%, and no resolved open conjectures for Astra) match the paper’s Table 2; the paper adds that the only accepted conjecture submissions adapted results OpenAI had already published.
The Results
On the full suite, GPT-6 Astra leads every track except open conjectures: 70.0% on theorem proving, 64.7% on the solver score and 104.9% on constructions, for an Index of 71.9. Kimi K3.1 Pro follows at 57.4, then Kimi K3 at 46.8, DeepSeek V4.1 Flash 1017 at 46.0 and GLM-5.3 at 45.5.
Qwen3.8 Max scores 44.8, Grok 4.6 40.5 and DeepSeek V4.1 Flash 0910 40.4, the paper’s Table 2 shows. On the Lite suite, Opus 5.5 leads with 72.3 points, completing four of five theorem tasks against three for Astra, which scores 67.0.
The paper reports that Full and Lite rankings are strongly aligned across the eight shared agents, with a Spearman correlation of 0.93.
Theorem-proving success and open conjectures resolved on the TCSExam full suite, from the paper’s Table 2: GPT-6 Astra 70.0% and 0.0%, Kimi K3.1 Pro 38.3% and 1.1%, DeepSeek V4.1 Flash 1017 6.7% and 5.6%. The only accepted conjecture submissions adapted counterexamples and Lean proofs OpenAI had already published; the other 28 conjecture tasks have no accepted complete solution, the paper says.
The Open Conjectures
No agent settled an open conjecture on its own. During network-enabled runs, Kimi K3.1 Pro and DeepSeek V4.1 Flash 1017 retrieved counterexamples and Lean proofs that OpenAI had already published for two conjectures, Ryser and MIRUP, and adapted them, the paper says. Those are the only accepted conjecture submissions; “The other 28 conjecture tasks have no accepted complete solution”.
While attempting one conjecture, GPT-6 Astra proved the Alon–Jaeger–Tarsi conjecture over the field with five elements for every dimension up to nine, extending earlier results to n = 9, with independent Lean verification, according to the paper. The authors list four further verified special cases and bounds.
As we read the paper, its four tracks separate checking known results from producing new ones: Astra completes most theorem tasks, yet the conjecture track stays at zero for every agent working without OpenAI’s published results.
As we read Table 9, the comparison is between agent systems, not bare models: GPT-6 Astra ran in Codex with one attempt per task and the Kimi models in Kimi Code with three, as the paper lists.
As we read it alongside our earlier coverage, formal verification gives the AI-for-science race a scoreboard every lab can be checked against: the Lean kernel accepts or rejects a proof regardless of who submitted it.
TCSExam paper, Luo et al., arXiv 2611.07962
“OpenAI’s results highlight the potential for AI-assisted conjecture resolution”
Three Implications
FOR LABS The paper says GPT-6 Astra leads the full suite on theorem proving, solver engineering and constructions, while Opus 5.5 leads the 20-task Lite suite with 72.3 points.
FOR OPEN-WEIGHTS CHALLENGERS Moonshot’s Kimi K3.1 Pro is second on the full suite at 57.4 points, and the paper discloses Moonshot AI as a co-author.
FOR WHAT TO WATCH The authors suggest future work could evaluate agents without Internet access on conjectures still open at the time of testing.
The essay says “With fewer than one in a hundred individual users on the agentic surface, the conversational interface still overwhelmingly owns the consumer base.”
As we read it, TCSExam measures the other side of that split: every agent in the paper runs inside an agentic harness such as Codex, Kimi Code, Claude Code or Grok Build. The essay does not discuss TCSExam or theorem proving.
What Is Not Established
TCSExam is a new benchmark from a team that includes Moonshot AI, whose Kimi models rank second and third on the full suite; the paper has not been independently replicated in the documents we read. Opus 5.5 was evaluated only on the 20-task Lite suite, so its full-suite score is not known. The paper ran each agent in its own harness: GPT-6 Astra in Codex with one attempt per task, and the Kimi models in Kimi Code with three attempts per task, according to its Table 9. The 14.5-point gap is our arithmetic from the paper’s Table 2.
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The TCSExam paper reports that GPT-6 Astra completed machine-checked proofs of research theorems in 70.0% of attempts and leads the full suite with 71.9 points, 14.5 ahead of Moonshot’s Kimi K3.1 Pro by our arithmetic. No agent settled any of the 30 open conjectures beyond adapting proofs OpenAI had already published, the paper says.
A note on sourcing. This piece is based on the TCSExam paper by Yifan Luo, Zhengying Liu, Yang Yuan, Zhilin Yang and Andrew Chi-Chih Yao (arXiv 2611.07962, November 5, 2026), which we read in full in its HTML version, and on the project’s public GitHub repository. Moonshot AI, a co-author, makes the Kimi models in the results. All scores are as reported in the paper; the 14.5-point gap is our arithmetic.
The lead came from a Rohan Paul post on X. We did not contact the authors or the labs whose models were tested.
Gennaro Cuofano is a CRO and tech executive who has worked in AI since late 2015, starting with bringing NLP, natural-language generation, voice and chatbot products to the marketing industry. His background is in law and finance: he holds a Master's degree in Law and an International MBA with an emphasis on corporate finance (LUISS Business School and the University of San Diego, 2012), and worked as a financial analyst at a real-estate investment firm in San Diego and as an assistant controller. His work focuses on business model strategy, business engineering and, more broadly, structural analysis: how companies make money, read from their own filings. He created FourWeekMBA and leads research there and at The Business Engineer, his newsletter on AI and business strategy, with over 95,000 subscribers and more than 1,000 published analyses. His writing has also appeared on Entrepreneur (for example, How to Digitize a Family Business in Europe) and HackerNoon. Find him on LinkedIn and Substack. See how we source.
