Hierarchical Bounce Theory: Complete Formulation and Unified Cosmological Framework

This document presents the complete and unified formulation of the Hierarchical Bounce Theory (HBT). It replaces the Big Bang singularity with an analytic high‑density bounce generated by the correction \( p_{\text{eff}} = p - \alpha p^2 \), resolves black‑hole singularities through a unitary transition, and introduces a hereditary mechanism in which black holes seed new universes. The framework reproduces the observed spectral index, predicts a tensor‑to‑scalar ratio \( r = 0.012 \pm 0.002 \), and explains CMB hemispherical asymmetry and the early appearance of supermassive black holes observed by JWST. This article integrates and synthesizes the results of Parts I–IV and serves as the final, complete reference for the HBT cosmological framework.