Convex Three-Distance Degree-Six Theorem and Exceptional-Word Closures

Source: doi:10.1007/BF02187746, url:https://www.erdosproblems.com/132 Authors: Egor Lyfar Status: verified Main declarations: LeanPool.Erdos132ConvexK3.convex_top_three_degree_six Tags: discrete-geometry, distance-graphs, erdos-problems, convexity MSC: 52C10, 05C12

Exceptional-Word Closures for the Convex Three-Distance Case of Erdős Problem 132

This project proves the convex three-distance degree-six theorem. A maximal-gap choice and the five-row enumeration route all thirteen canonical words through four shared geometric realization predicates. Full-two-rung, terminal, anti-saturation, and four-edge kernels close every route, so the source-facing reduction is unconditional. The development also records exceptional-branch rigidity, an explicit majorant counterexample, and rational regression witnesses. The general-k suggestion and Erdős problem 132 remain open.