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Vladmir Sicca

Publications and source records attributed to Vladmir Sicca.

5 recordsLinked to original sources
arXiv2025

Aristotle: IMO-level Automated Theorem Proving

We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main components: a Lean proof search system, an informal reasoning system that generates and formalizes lemmas, and a dedicated geometry solver. Our system demonstrates state-of-the-art performance with favorable scaling properties for automated theorem proving.

cs.AI↗
arXiv2024

Newclid: A User-Friendly Replacement for AlphaGeometry

We introduce a new symbolic solver for geometry, called Newclid, which is based on AlphaGeometry. Newclid contains a symbolic solver called DDARN (derived from DDAR-Newclid), which is a significant refactoring and upgrade of AlphaGeometry's DDAR symbolic solver by being more user-friendly - both for the end user as well as for a programmer wishing to extend the codebase. For the programmer, improvements include a modularized codebase and new debugging and visualization tools. For the user, Newclid contains a new command line interface (CLI) that provides interfaces for agents to guide DDARN. DDARN is flexible with respect to its internal reasoning, which can be steered by agents. Further, we support input from GeoGebra to make Newclid accessible for educational contexts. Further, the scope of problems that Newclid can solve has been expanded to include the ability to have an improved understanding of metric geometry concepts (length, angle) and to use theorems such as the Pythagorean theorem in proofs. Bugs have been fixed, and reproducibility has been improved. Lastly, we re-evaluated the five remaining problems from the original AG-30 dataset that AlphaGeometry was not able to solve and contrasted them with the abilities of DDARN, running in breadth-first-search agentic mode (which corresponds to how DDARN runs by default), finding that DDARN solves an additional problem. We have open-sourced our code under: https://github.com/LMCRC/Newclid

cs.GR↗
arXiv2022

A prescribed scalar and boundary mean curvature problem and the Yamabe classification on asymptotically Euclidean manifolds with inner boundary

We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean curvature on an asymptotically Euclidean manifold with inner boundary. We obtain a necessary and sufficient condition in terms of a conformal invariant of the zero sets of the target curvatures for the existence of solutions to the problem and use this result to establish the Yamabe classification of metrics in those manifolds with respect to the solvability of the prescribed curvature problem.

math.AP↗
arXiv2016

Non-Euclidean ideal spectrometer

We describe the mathematical scheme for an anomaly-free ideal spectrometer, based on a 2-dimensional plane medium with conical regions of bounded slope. Moreover, the construction may be realised in many different configurations.

physics.ins-det↗