AI agents are taking on mathematical formalization, software reconstruction and model training, while Mirendil says a researcher still directed its model-building work and assessed the results.
Resolution, an alignment research organization, says its Lean project encoded mathematician Heisuke Hironaka's 1964 result on resolving singularities, along with later treatments involving schemes and analytic spaces. Resolution connects the work to singular learning theory, which it uses to study how the geometry of training loss relates to a model's ability to generalize. The organization presents the formalization as groundwork for future alignment research; it did not report a safety test showing that a model became safer.
The autoformalization stage ran from Sept. 4 to Sept. 10, with a final audit on Sept. 11. Resolution says substantial refactoring followed. It reported about 100 billion input tokens, 300 million output tokens and an estimated $135,000 in token costs for the formalization, which produced roughly 600,000 lines of Lean code. A researcher intervened at about 30 points during that stage, according to Resolution.
ProgramBench asks agents to reproduce software behavior using a compiled program and its documentation. Its May paper covered 200 tasks and reported that none of nine language models solved a task fully; the strongest passed at least 95% of tests on 3% of tasks.
The official ProgramBench board, updated Thursday, Oct. 22, lists Anthropic's Claude Opus 5.5 (xhigh), running mini-SWE-agent, as resolving 18.5% of tasks. Separately, it marks 70.5% as “almost resolved,” meaning at least 95% of behavioral tests passed. The May paper and October board cover different model versions, so the results do not show what caused the difference.
Mirendil says one researcher built Mirendil-Base in 3.5 months, with compute costs below $10 million across research, small-scale experiments and the final training run. The company credits agents with producing more than 99% of the code and assisting with experiments and troubleshooting. The researcher chose which approaches to pursue and assessed the results.
On seven external code repositories published after training, Mirendil reported an average cross-entropy score of 0.222 bits per byte for Mirendil-Base. Its comparisons were 0.193 for Kimi-K3, 0.247 for Nemotron-550B-Base, 0.242 for GLM-5.3 and 0.243 for DeepSeek-V4-Pro-Base; lower scores are better. Mirendil noted that Kimi-K3 and GLM-5.3 are post-trained models. These company-reported scores measure next-token prediction, not performance on an independent coding-task benchmark.
Mirendil said post-training of Mirendil-Base had begun. At the time of its announcement, Mirendil-Base-Large was about 80% through training and Mirendil-Base-XL about 19% through. The company said it had not reached fully autonomous recursive self-improvement and gave no dates for further model updates. Resolution expects to report additional work linking its formalization to singular learning theory in the coming months.
