Signed Liouville energies and the limits of maximal correlation bounds

Version 2 research revision of the Liouville-correlation preprint. The manuscript proves deterministic obstructions for maximal correlation energies, develops signed Fejer energy criteria for RH and Dirichlet GRH, and derives reciprocal-dilate approximation results, including a fixed bounded-variation taper obstruction and quantitative coefficient-cost bounds. The Riemann Hypothesis and Dirichlet GRH remain unproved. The 7/8 specialization is explicitly attributed to the external OpenAI quasi-Riemann manuscript. Novelty and journal suitability remain subject to specialist review.