Breaking the Redshift Barrier: Analytical Prediction of JWST Primordial Hyper-Massive Clusters via Extradimensional Extrinsic Curvature

This manuscript delivers a non-parasitic, unified higher-dimensional geometric alternative to hierarchical structure formation timelines, bridging particle physics and early-universe observational cosmology. By establishing a covariant 5D bulk-brane configuration governed by Einstein-Gauss-Bonnet gravity under high-energy boundary matching controls, we analytically derive a modified primordial Jeans mass matrix. We demonstrate that the non-local projection of the extradimensional extrinsic curvature tensor acts as a localized compressive geometric driver during the early cosmic dawn epoch. This mechanism successfully suppresses the classical Jeans mass threshold by exactly two orders of magnitude, allowing pure baryonic gas to skip the slow hierarchical aggregation phase and collapse rapidly into stable, luminous, hyper-massive clusters within the first 200 million years post-bounce. Accompanying this work is a calibrated multi-point mass-redshift evolutionary simulation matching the extreme redshift boundary of current JWST surveys. This continuous theoretical envelope provides a directly testable, verifiable, and falsifiable resolution to modern cosmological reionization crises without dark sector parameter inflation.