R-layer Mode Theory XXXIX: R-layer Mode Theory and the Hierarchical Emergence of the Early Universe

This is Version 2 of Volume XXXIX in the R‑layer Mode Theory (RLMT) series. This update adds a formal declaration regarding the use of Microsoft Copilot for proofreading, text refinement, and LaTeX‑related structural assistance. Minor corrections were made to the reference list, while all theoretical content, layer definitions, and cosmological interpretations remain unchanged. Volume XXXIX develops a unified description of the early universe based on the eight‑layer hierarchy 220–227. These layers describe the emergence of the cosmos from a single origin: AUP/MUP mode ignition (220), spacetime formation (221), gravitational activation (222), dark‑skeleton formation (223), visible‑structure emergence (224), stabilization (225), complexity (226), and self‑organization (227). A key result of this volume is the identification of the Early Composite Condensation Mode, a mechanism arising from non‑annihilating AUP/MUP interactions. This mechanism naturally explains the unexpectedly early appearance of Population III stars, rapid chemical enrichment, and the presence of mature galaxies at high redshift observed by JWST. The volume provides a coherent single‑origin cosmology in which dark matter is interpreted as a residual AUP/MUP structure, eliminating the need for a separate “dark Big Bang.” This version preserves all scientific results and improves documentation clarity and transparency regarding AI‑assisted writing.