OAI.Release075.main

The theorem states, without a verified proof (it is admitted), that there exists a group G, in the lowest universe Type, that is torsion-free, word-hyperbolic, and not residually finite. Torsion-free means that for every g in G and every positive integer n, g^n = 1 implies g = 1, so no nonidentity element has finite order (this does not assert unique roots). Word-hyperbolic means that there is a finite subset S of G whose unit-edge Cayley graph (the simple graph with the multiplicative Cayley adjacency determined by S) is connected, which says that S generates G, and a natural number δ such that geodesic triangles are uniformly δ-thin. Precisely, for all vertices x, y, z and walks p from x to y, q from y to z and r from z to x, each of which is a geodesic (its length equals the graph distance between its endpoints), every vertex of each side lies within graph distance δ of some vertex on one of the other two sides. The statement also requires that G fail the Mathlib property Group.ResiduallyFinite.