Wilton’s conjecture on uniform negative immersions

Prove that every finite 2‑complex with uniform negative immersions has a locally quasi‑convex hyperbolic fundamental group.

Background

Uniform negative immersions yield strong subgroup control and coherence results. Wilton’s conjecture proposes that such complexes always produce hyperbolic, locally quasi‑convex groups, aligning with the virtual compact special framework.

This would unify combinatorial immersion negativity with large‑scale hyperbolicity for a broad class of complexes.