Anomalous large-angle cosmic microwave background anisotropies motivate
    further searches for cosmic topology. We demonstrate that for generic
    topologies of spatially flat spacetimes, off-diagonal correlations between
    microwave background harmonic coefficients over a wide range of scales encode
    significant topological information, even if the topology scale substantially
    exceeds the diameter of the observable Universe. Observational searches have so
    far considered only a small subset of testable topologies, and current limits
    on the topology scale are much weaker than generally understood.

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