Emergent macroscopiccorrelationsfrom alate-time nonlocalinformationalsector

The standard ΛCDM paradigm accurately describes the homogeneous expansion history and the quasi-linear statistics of large-scale structure on scales up to O(102)Mpc, yet it does not naturally generate new macroscopic comoving correlation lengths at late times once the primordial spectrum and the early-time transfer functions are fixed. Motivated by reports of extreme structures andlarge-scalecoherencefeatures,andbythebroaderprogramconnectinggravityandinformationviaentanglementandmodular considerations, we develop a conservative effective framework in which a continuous informational sector 𝜓becomes active only at latetimesandexhibitscontrollednon-localdynamics. Weshowthatafinitecomovingcorrelationlength 𝐿𝜓 emergesgenerically when the activated non-local kernel induces a non-analytic structure in the effective dispersion relation, selecting an imaginary pole thatyields𝐶𝜓(𝑟)∝𝑒−𝑟/𝐿𝜓 /𝑟. Crucially,thecouplingtomatterisimplementedstatisticallyratherthandynamically: 𝜓modulates large-scalecorrelationsthroughanon-localresponsekernelwithoutintroducingfifthforcesormodifyinglocalgrowthequations. The resulting phenomenology leaves early-universe observables intact while enhancing the tail of large-scale structure statistics. We further close the theoretical framework by deriving the Einstein field equations as a condition of local modular equilibrium, with the spacetime metricemergingunambiguouslyfromquantum–informational structure.