Coherence Selective Extraction: A Substrate Level Framework for Rare Earth Element Recovery

Coherence‑Selective Extraction applies the MID/QC framework to rare‑earth element recovery by leveraging the distinct coherence‑well geometries and tension‑signature profiles of f‑electron structures. Instead of relying on mechanical crushing, acid leaching, or multi‑stage chemical separation, the paper models extraction as a substrate‑level process driven by tension‑field resonance, phase‑gradient sorting, and coherence‑well modulation. These mechanisms enable selective detachment, controlled migration, and clean separation of target elements with dramatically reduced environmental impact. The work outlines the theoretical basis for coherence‑selective extraction, develops the operational pathways for tension‑gradient fracturing and substrate‑resonant separation, and introduces coherence‑signature prospecting as a new geophysical method. This paper establishes the first applied‑impact domain of the MID/QC program and demonstrates how substrate‑level physics can transform global materials recovery and resource independence.