Cobordism-Driven Scale Separation in Weak G2-Holonomy M-Theory Compactifications

This paper investigates a novel mechanism for achieving parametric scale separation in M-theory compactifications on manifolds of weak \(G₂\) holonomy. Traditional approaches often rely on "smeared" approximations of Type IIA O6-plane singularities, which can obscure the underlying local physics. We propose that by resolving these singularities into smooth, localized Atiyah-Hitchin geometries—interpreted as End-of-the-World (ETW) branes—one can satisfy the requirements of the Swampland Cobordism Conjecture while naturally decoupling the Kaluza-Klein and AdS mass scales. Utilizing Asymptotically Locally Conical (ALC) metrics, we outline a systematic approach for verifying this hierarchy through Laplacian spectrum analysis. This research suggests that the "jagged edges" of the universe's internal geometry are not mere artifacts, but are essential stabilizers for a 4D effective theory.