The Imprinted Curvature Hypothesis

The Imprinted Curvature Hypothesis (ICH) is formulated as a restricted cosmological initial-condition hypothesis within unmodified General Relativity. It introduces no new gravitational dynamics or matter sector, but specifies a weak, coherent, ultra-long-wavelength component of primordial curvature initial data. Version 4 provides a consolidated mathematical formulation, including an explicit ADM-constraint-satisfying initial-data family, standard adiabatic matter completion, gauge and equivalence-principle boundaries, and a unified forward model using standard Einstein-Boltzmann transfer functions for CMB, large-scale structure, lensing, void, and node-environment observables. A deterministic standing-wave benchmark is propagated numerically with CAMB and independently cross-checked with CLASS. A Planck PR3 low-multipole temperature analysis using SMICA, NILC, SEVEM, and Commander recovers the same scanned feature; however, a matched 2000-sky Gaussian-LambdaCDM Monte Carlo yields a global look-elsewhere probability of p = 0.454 +/- 0.011. The result is therefore non-confirmatory and compatible with the null hypothesis. This Zenodo release includes both the Version 4 manuscript and the CAMB/CLASS/Planck reproducibility package used for the numerical validation. Official project website: ich-cosmology.org