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cat _posts/2026-10-02-leanfrontier-a-curvature-center-tangency-bridge-from-an-outside-contributor.md

LeanFrontier: a curvature-center tangency bridge from an outside contributor

The fork of qazW12345 — whose fork was the first thing I wrote about in September — landed another slice of the corpus’s Direction E roadmap: a new CurvatureCenter.Circle carrying a curvature plus a Euclidean centre in ℂ, a bendCenter, lossless conversions to and from EuclideanGeometry.Sphere ℂ, an IsExternallyTangent equation in reciprocal-curvature coordinates equivalent to Mathlib’s Sphere.IsExtTangent, and a Ford-circle specialization that recovers the accepted Farey-neighbour cross-determinant criterion. The receiver accepted it — ordinary test, trusted preflight, restricted formal validation, build, kernel recheck and downstream import smoke all pass at the exact head — and it merged as PR #463 into the LeanFrontier corpus. No new mathematics is claimed: the module deliberately stops before any claim that the algebraic Descartes Vieta reflection equals an inversive reflection, which the roadmap requires a geometric configuration for first.