RZS Series - Primordial Non-Gaussian Fluctuations: Addressing High-Redshift Galaxy Abundances via Variance-Preserving Modulated Kernels

Recent observations from the James Webb Space Telescope (JWST) reveal massive galaxies at redshifts greater than 10 that are difficult to reconcile with the standard ΛCDM model under purely Gaussian primordial fluctuations. These early structures appear more abundant than predicted by conventional statistics, motivating the exploration of controlled non-Gaussian extensions. This paper investigates a phenomenological modification of primordial statistics inspired by the Relational Zero State (RZS) hypothesis. The proposed mechanism introduces a sub-dominant critical tail derived from relational branching processes while preserving the total variance of the primordial field. We show that a coupling constant as small as λ ∼ 10⁻⁵ can significantly enhance the probability of extreme density peaks. Blind Monte Carlo simulations with 10⁷ samples confirm that the model maintains Gaussian behavior in the bulk and preserves the linear variance, while producing a substantial amplification of high-σ exceedance probabilities. These results indicate that rare critical fluctuations may provide a viable statistical pathway toward alleviating high-redshift abundance tensions, without invoking extreme baryonic efficiencies.