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Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
arXiv:2606.02588v1 Announce Type: new Abstract: We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pipeline consisting of PDF-to-LaTeX preprocessing, autoformalization into Lean 4, and verification of informal-formal correspondence.
Muscle growth drug ‘could reduce loss of lean tissue’ when using slimming jabs
Trial suggests monoclonal antibody can help retain lean body mass when losing weight with GLP-1 medicinesA drug that promotes muscle growth could significantly reduce the loss of lean body mass when using slimming jabs, research suggests. While GLP-1 based jabs such as Wegovy and Mounjaro have proved highly effective at helping people who are overweight or obese, experts have warned it is not only fat that is lost. Studies suggest 25-40% of total weight loss is down to a reduction in lean...
Muscle growth drug ‘could reduce loss of lean tissue’ when using slimming jabs
Trial suggests monoclonal antibody can help retain lean body mass when losing weight with GLP-1 medicinesA drug that promotes muscle growth could significantly reduce the loss of lean body mass when using slimming jabs, research suggests. While GLP-1 based jabs such as Wegovy and Mounjaro have proved highly effective at helping people who are overweight or obese, experts have warned it is not only fat that is lost. Studies suggest 25-40% of total weight loss is down to a reduction in lean...
The continuous functional calculus in Lean
Announce Type: replace-cross Abstract: The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially $C^{*}$-algebras. Here we document our formalization of the continuous functional calculus in Lean, which constitutes the first such formalization in any proof assistant. Our implementation is already merged into Lean's mathematical library, Mathlib.
LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization
Announce Type: new Abstract: Long-horizon autoformalization of research mathematics fails not only at hard lemmas, but at scale: statements drift, dependencies tangle, context decays, and local repairs corrupt distant work. We present LeanMarathon, a multi-agent harness for reliable research-level Lean autoformalization. Its core abstraction is an evolving blueprint: a Lean file that serves simultaneously as formal proof skeleton, natural-language proof graph, and shared system of record.
AMA: I'm Eric Ries (The Lean Startup) & Author of New Bestseller Incorruptible
Hey gang, you may remember me from such books as _The Lean Startup_ and _The Startup Way_.It's been fifteen years since I wrote The Lean Startup, and in that time I've seen some things. In both big companies and tiny startups, NGOs and governments, in almost every industry you can name. I've helped a lot of people create a lot of amazing companies, but I've also seen so many ways this can go wrong.
Muscle-boosting drug could help retain lean tissue when using weight-loss jabs
The Independent's journalism is supported by our readers. When you purchase through links on our site, we may earn commission. Muscle-boosting drug could help retain lean tissue when using weight-loss jabs
Lean, Not Backpressure
Lean, not backpressure Lucas Costa has written a good article on how to build systems that can handle code-generating robots. Unfortunately, when calling it backpressure, he used the wrong metaphor.1 Which, to his credit, he seems aware of. It’s just that he’s spent too much time using the wrong metaphor that it’d be silly to switch now.
Optimizing the Cost-Quality Tradeoff of Agentic Theorem Provers in Lean
arXiv:2606.04883v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly used in workflows for generating formal proofs in Lean. These workflows often decompose problems into smaller lemmas, sample many proof attempts, and use compiler feedback to guide search. However, they can be prohibitively expensive, often spending substantial compute on attempts that ultimately fail.
A Kernel-Clean Lean Mechanization of Classical Lottery in Action and the Wakker--Debreu--Koopmans Representation Layer
Announce Type: new Abstract: We present a Lean 4/Mathlib formalization of the additive representation theory behind Classical Lottery in Action and the Wakker-Debreu-Koopmans (WDK) layer it relies on. Our central result is a machine-checked proof that the cross-pair Thomsen / double-cancellation (hexagon) condition is irreducible from the ordinal axioms of additive conjoint measurement (weak order, restricted solvability, Archimedean condition, and tradeoff consistency). We exhibit an...