The Lagrange Signature: Harmonic Compression in Gravitational Equilibrium Points

This document presents a harmonic compression analysis of Lagrange points in the Sun–Earth, Earth–Moon, and Jupiter–Sun systems using the Qₕ model—a novel mathematical framework that identifies order in physical structures through prime factorization, binary symmetry, and Fibonacci decomposition. Each Lagrange point’s position is rounded and analyzed for: Qₕ (largest prime factor) Binary representation Binary entropy Zeckendorf (Fibonacci) term count Despite differences in gravitational dynamics, a striking pattern emerges: Lagrange Point L3 consistently exhibits the lowest Qₕ values, binary palindromes, and minimal Fibonacci structure. This leads to the formulation of the L3 Purity Hypothesis—the idea that L3 acts not as a gravitational anchor, but as a harmonic reference point of minimal informational complexity.