Is there a generic quantum theory for non-Hermitian Hamiltonians?

Unlike in the Hermitian case, the quantum mechanical formalism for the non-Hermitian operators is not unique, and additionally, suffers from singularities and instabilities. Here we propose a framework which is generic, unique and resolves these singularities. We find a Hilbert space of a dynamically generated Hermitian operator, namely the computational space, in which exceptional points are pushed to the vacua, leading to an analytic span of the energy eigenstates. In addition, we also discover a unique dynamical `space-time’ transformation as the dual space map, incorporating physical properties such as decoherence and spectral flow. The real energy condition manifests in the limit when the dynamical transformation becomes a static symmetry. Our framework also provides insights into other features such as gauge obstructions, symmetry-based classifications, dynamical metric manifolds, spectral flattening, among others.