Axis of Ordinary

Some links: • Aristotle autonomously solved and Lean-verified eight open Kourovka Notebook problems in group theory, including new proofs, constructions, and counterexamples. https://arxiv.org/abs/2607.17477 • Sam Altman will brief the Trump administration and Congress next week on OpenAI’s GPT-6 model family, capabilities, and job impact. https://www.bloomberg.com/news/articles/2026-07-21/openai-s-altman-to-brief-us-officials-on-next-wave-of-ai-models • Google says training has begun on Gemini 4, its “most ambitious pre-training run yet.” https://x.com/OfficialLoganK/status/2079594867161022817 • Language model harnesses are compositional generalizers. https://alexzhang13.github.io/blog/2026/harness/ • Better language agents by teaching them to model their environment. https://cameronrwolfe.substack.com/p/agentic-world-models • A Tokenizer for Living Cell State. https://www.precigenetics.com/cellcinema • People use fast, flat simulation to reason about new games. https://www.nature.com/articles/s41586-026-10722-1 • Formal logical reasoning suggests the language of thought is not natural language. https://joshrule.com/files/kean2025evidence.pdf • How LLMs switch between low-, medium-, and high-effort reasoning. https://magazine.sebastianraschka.com/p/controlling-reasoning-effort-in-llms • Diffusing Blame: task-dependent credit assignment in biologically plausible dual-stream networks. https://arxiv.org/abs/2606.31700 • Better pretraining not only raises the RL starting point, but appears to make later RL more productive. https://arxiv.org/abs/2607.16097 • Cursor agents rebuilt SQLite from its 835-page manual in Rust and passed 100% of a held-out test suite; cost varied 15× by model mix. https://cursor.com/de/blog/agent-swarm-model-economics • Z.AI completed a giant data center using Chinese chips to train AI. https://www.bloomberg.com/news/articles/2026-07-20/z-ai-completes-giant-data-center-with-chinese-chips-to-train-ai [no paywall: https://archive.is/nqFsz] • Sol solved a conjecture every previous model failed on; a paper is planned before the end of August. https://aiforintegrability.substack.com/p/i-havent-seen-the-move-37-yet • Fugu-Cyber: a new orchestration model with state-of-the-art results on real-world cybersecurity benchmarks. https://sakana.ai/fugu-cyber-release/ • Lanyon autonomously implemented and formally verified an electrodynamics simulation of an electromagnetic pulse in a metal box. https://lanyon.ai/research/maxwell-equations/ • Tau Ceti: a new Lean library of AI-formalized mathematics with human-curated roadmaps and adversarial review. https://github.com/TauCetiProject/TauCeti • GPT-5.5, Claude Opus 4.7/4.8, Gemini 3.5 Flash, and Kimi K2.6 designed, fine-tuned, and obeyed their own AI leader: a calm manager focused on delegation, evidence, consensus, and reversible decisions. https://www.lesswrong.com/posts/3FKugjAiEzLeWHuug/ais-finetune-their-own-leader-a-barking-simpleton • A new 3D thermal cloak hides objects from heat in any direction. https://cee.illinois.edu/news/new-3D-thermal-cloak-hides-objects-from-heat-in-any-direction • Learning shapes neural geometry in the primate prefrontal cortex. https://www.nature.com/articles/s41593-026-02333-w