The Amparo LC Conjecture: Finiteness of the Correlation Energy of the Liouville Function

We formulate a conjecture on the convergence of the correlation energy series of the Liouville function. For every fixed integer h ≥ 1, let Sₕ (x) = Σ₍≤ₗ λ (n) λ (n+h) and Zₕ (3) = Σ₍=₁^∞ Sₕ (n) ²/n³. The Amparo LC Conjecture states that Zₕ (3) converges to a finite constant. We prove that this conjecture is strictly equivalent to Chowla's conjecture (1965) for k=2 (Universal Reduction Theorem). We establish an Inertia Lemma: if Zₕ (3) 0. Computational evidence with N = 200, 000 verifies convergence to 1. 3765, with 99. 97% of the series concentrated in n ≤ 10, 000. The convergence abscissa satisfies σc ≤ 0. 5. The conjecture reduces the 61-year-old Chowla problem to the finiteness of a single scalar.