On Higher-Dimensional Soul Perturbations via Higgs–Photon Couplings

 We propose an extension of the photon soul theorem to higher-dimensional geometries
 where the electromagnetic field acquires novel topological couplings to the Higgs sector. In
 four-dimensional spacetime, electroweak symmetry breaking leaves the photon massless and
 its cohomological soul invariant. We demonstrate that in a D > 4 bulk or derived-stack con
text, nontrivial morphisms in the derived category of sheaves can induce Higgs–photon soul
 deformations that vanish under naive dimensional reduction but leave calculable imprints
 on low-energy interference phenomena. We provide precise cohomological constructions,
 compute obstruction classes, and derive phenomenological bounds on measurable visibility
 shifts.