The Unified Spectral Bottleneck Theorem

We prove that a single abstract theorem governs information loss in quantum systems under Lindbladdynamics, in neural networks under domain shift, in gravitational decoherence, and in non-Markovian open systems. The theorem requires three objects: a metrized configuration space (X,d),a positive semidefinite operator ρ on X decomposed into shells by d, and a distance-monotone contraction—any completely positive map that suppresses off-diagonal elements monotonically in d.From these alone, we derive the spectral bottleneck D∗, the peeling order, the entropy–shell connectionvia the Kubo-Mori kernel, and the parameter-free collapse time ratio. Lindblad dephasing,gravitational self-energy channels, spectral projection in transfer learning, and time-dependentnon-Markovian dynamics are all shown to be instantiations of the same abstract structure, with D∗emerging from the same theorem in every case.