Recent formal reasoning systems achieve IMO-level performance, but create a fragmented landscape: algebra and number theory use Lean, while geometry relies on domain-specific languages with limited formal guarantees. This fragmentation increases the trusted computing base and hinders unified model development. Existing geometry-in-Lean efforts (LeanEuclid, LeanGeo) introduce custom axiom systems incompatible with standard \\mathlib{}, and their small scale (1K problems) prevents large-scale training. However, native \\mathlib{} autoformalization of geometry poses unique challenges: explicating implicit diagrammatic assumptions (e.g., topological configuration and non-degeneracy)—unlike existing custom systems that defer validity checks to external solvers—and adapting to \\mathlib{}’s small, rapidly-evolving geometric constructs. We present \\method{}, a framework that addresses these challenges through a four-stage pipeline—constraint explication, configuration anchoring, formalization mapping, and iterative repair—to automatically formalize geometry in native \\mathlib{}. We construct OMNI-Geometry (768 competition problems) and Numina-Geometry (177,597 problems), the largest geometry formalization dataset in Lean. Human evaluation shows 48.89\\% TOP1 and 73.33\\% TOP5 accuracy. Training Goedel v2 on our formalizations improves proof success from 13.6\\% to 15.1\\%, validating dataset quality for unified neural theorem proving.<\/p>\n","protected":false},"excerpt":{"rendered":"
Recent formal reasoning systems achieve IMO-level performance, but create a fragmented landscape: algebra and number theory use Lean, while geometry relies on domain-specific languages with limited formal guarantees. This fragmentation increases the trusted computing base and hinders unified model development. 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