Lagrangian Intersection Floer Homology for Hyper-Kähler Wormhole Stability: A Motivic Approach to Topological Persistence

Mathematical Applications of Science Fiction We construct a rigorous framework for assessing thetopological stability of Einstein-Rosen bridges within 4n-dimensional hyper-Kähler manifolds using Lagrangian In-tersection Floer Homology. By modeling the wormholethroat as a Lagrangian cobordism between exact La-grangian submanifolds in the cotangent bundle of a Rie-mannian manifold, we define a filtered A∞-category ofbranes subject to non-perturbative quantum corrections.We prove that the non-vanishing of the Floer homologygroups HF ∗(L, τ (L)), where τ is a specific anti-symplecticinvolution, provides a sufficient condition for the metricstability of the wormhole against semi-classical fluctuations.The derivation utilizes spectral sequences associated withthe energy filtration of the Novikov ring and invokes thePSS isomorphism to relate quantum cohomology to theclassical intersection ring. We further demonstrate that themoduli space of pseudo-holomorphic strips with boundaryon the wormhole horizon admits a compactification com-patible with the Gromov-Witten invariants of the ambientspace.