Alignment as Geometry, Not Correction A Research Hypothesis Connecting the φ-Necessity Proof to Structural Stability in AI Systems

Recent work has established that alignment in large language models concentrates inlow-dimensional parameter subspaces with sharp curvature, making ne-tuned alignmentintrinsically fragile under gradient descent (Springer et al., 2026). Independently, we have proved that on a homogeneous toroidal eld with isotropic suppression and dynamic itera-tion, the golden ratio φ = (1 + √5)/2 is the unique stable winding rationot selected byoptimization but forced by the geometry of the system itself (Barteau, 2026). This paperdoes not claim to resolve AI alignment. It identies a structural parallel between these two results and poses a precise research question: under what conditions, if any, can a computational system be constructed such that alignment is a geometric invariant of the system's architecture rather than a property imposed through post-hoc optimization? We state theemergence theorem, identify the gap between its mathematical domain and neural networkparameter spaces, and propose three testable conditions that would need to be satised forthe analogy to hold. The paper is oered as an invitation to collaboration, not a declarationof results. 10.5281/zenodo.19589224