R-layer Mode Theory (RLMT) XLI‑M: Early Composite Condensation Mode — Microscopic Modes, Layer Hierarchy, and Observational Correspondence

This volume develops the mathematical formulation of the Early Composite Condensation Mode (ECCM) within R-layer Mode Theory (RLMT). Using the unified AUP/MUP/CUP mode specification, we construct an effective potential for composite condensation, derive instability conditions, growth rates, and the characteristic ECCM mass scale as a function of redshift. We then show how ECCM provides a natural explanation for several observational classes that challenge the standard ΛCDM + nucleosynthesis framework: Little Red Dots and X-ray Dots at high redshift, early heavy-element enrichment in z ≈ 13–14 galaxies, failed supernovae leading to direct black-hole formation, and the presence of Fe‑60 in the local interstellar cloud. The unified mode hierarchy and ECCM together yield a coherent cross-scale picture of early structure formation.