4 papers
Morphisms of generalized affine buildings
Raphael Appenzeller, Xenia Flamm, Victor Jaeck
We define a notion of morphism for generalized affine buildings, also known as affine -buildings, extending existing definitions and giving rise to a category of generalized aff…
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of…
An incomplete real tree with complete segments
Raphael Appenzeller, Luca De Rosa, Xenia Flamm +1
Let be the field of real Puiseux series and the -tree defined by Brumfiel. We show that completing all the segments of $\mathcal{T…
(In)dependence of the axioms of -trees
Raphael Appenzeller
A -tree is a -metric space satisfying three axioms (1), (2) and (3). We give a characterization of those ordered abelian groups for which axioms (1) and (2) imply axiom (…