Spectral Framework and Non-Standard Magnetic Responses in Quantum Heterostructures: Symmetry Breaking, Exceptional Points, and Formal Verication

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Contemporary quantum spintronic engineering demands predictive mathematical-physics frameworks that expose the symmetry assumptions behind measured transport coecients. Motivated by recent reports of an in-plane anomalous Hall eect (AHE) in low-symmetry TaIrTe4/Cr2Ge2Te6 heterostructures, we formulate a spectral framework for perturbed Dirac Bloch operators with interfacial spinorbit coupling and exchange elds. The construction separates Hermitian band-structure eects from non-Hermitian open-system eects, and uses generalized paritytime symmetry to identify exceptional-point (EP) singularities. We derive explicit perturbative expressions, a square-root Puiseux law near second-order EPs, and a symmetry-resolved scaling form for the transverse conductivity. The intrinsic response is connected to Berry curvature through a Kubo formulation. Finally, we give an ACSL/Frama-C contract for a computational post-processing routine and state precisely which numerical properties the contract can and cannot establish. The result is a falsiable analytical and verication-oriented blueprint for compact vector-magnetometry architectures; it is a theoretical framework rather than a report of new experimental data.