THE AARAVIN ASYMMETRON: A PRINCIPLE OF ASYMMETRY AND A CLASS OF CYCLIC RADICAL INEQUALITIES

Note: This Manuscript created by Aarav Ahaani(original name: Aarav Gupta), is accepted in "International Journal Of Mathematics And Computer Research (IJMCR)" and the acceptance letter, "IJMCRV13I07Y2025-13 (2).pdf" is uploaded. Consider that this manuscript was created by Aarav at the age of 7, then it was enhanced for publication. This paper establishes a new class of strict inequalities for positive real numbers whose structure, though cyclically symmetric in form, reveals a fundamental functional asymmetry. The central result, the Asymmetron is termed Aaravin Asymmetron to distinguish it from others; it demonstrates that for any distinct positive real numbers a, b, c, the inequality √(a(b+c)) + √(b(c+a)) + √(c(a+b)) > √(ab) + √(bc) + √(ca) holds. We provide a rigorous proof based on a geo-metric substitution and an application of the Root-Mean-Square vs. Arithmetic-Mean inequality. This work introduces the concept of ad-ditive amplification under radicals as a source of asymmetry. We first establish the underlying two-variable Radical-Asymmetry Principle via a detailed variational analysis and subsequently explore the theoretical consequences of the main theorem, including a refinement of the AM-GM inequality and a formal conjecture for its generalization to n variables.