The geometric theory of computational spacetime models algorithmic efficiency as geodesics in a five-dimensional manifold (S,T,H,E,C) spanning space, time, memory hierarchy, energy, and quantum coherence. Classical ``wormholes'' - localized reparameterizations that bypass regions of high action - capture many known shortcuts (e.g., spectral sparsifiers, spanners, FFT/NTT, JL embeddings). This paper proposes seven new wormhole classes that leverage quantum--classical hybrids, topological structure, distributed consensus geometry, neuromorphic dynamics, differential privacy, and federated optimization. For each class we provide a formal setup, entry tolls, shortcut statements, structural preconditions, and resource trade-offs in the (S,T,H,E,C) framework. All complexity improvements are stated under explicit assumptions (e.g., QRAM-style access, partial synchrony, low-distortion embeddings, well-conditioned quantum Fisher information, sparsity, and idealized sketching/compression bounds). The analysis yields convergence conditions, approximation/stability bounds, and a comparative matrix to guide algorithm design in heterogeneous compute environments.
Michael Rey (Wed,) studied this question.