Classical-mean power sums: the exact real-exponent ranges

For the arithmetic, geometric, harmonic and quadratic means A,G,H,Q of two positive inputs, the inequality A^n+G^n<=Q^n+H^n holds universally exactly when n<=0 or n>=1. The reverse holds universally exactly at n=0. This gives one complete real-exponent classification resolving the published Mestrovic–Andjic conjecture, including strict failures in its asserted interval. Both classifications and the actual positive-input witnesses are certified in Lean. AI-assisted preprint by Myeongjin Kang, with no affiliation. Internal AI review is not external journal peer review. The accompanying Lean certificate covers the precise scoped main statement; inspect the formal endpoint, assumptions and provenance in the supporting package. Prior-art investigations are documented bounded searches, not worldwide-priority certification. Original prose is offered under CC BY 4.0 and original code/Lean under MIT; third-party rights and existing notices are preserved. The public supporting ZIP contains original proof sources and verification evidence, with bibliographic links and hashes instead of redistributed third-party source manuscripts. Recorded prior-art/source-access limits: Actual published source and nearest primary comparisons inspected; no known earlier full classification found. MathSciNet/zbMATH unavailable, Sándor survey only partially extractable; bounded literature search does not certify absolute worldwide priority. Parent corrected original review prose errors; unchanged complete reports retained.