A Universal Balance in Holographic Quantum Gravity The V-index and its Invariance Across Holographic Frameworks (V-index Part 2)

We propose a dimensionless invariant the V-index that quantifies the balance betweenboundary entanglement, modular energy, and generalized entropy variations in holographicsystems. At quantum extremality, the index takes a universal value of 2/ ln 2, while bulkentanglement corrections stabilize it around 2.45. We verify this behavior across threeindependent approaches: AdS3/CFT2 analytics, BTZ thermodynamics, and lifted MERAtensor networks. The V-index thus emerges as a robust diagnostic of quantum geometricconsistency The relationship between quantum information and gravitational dynamics has achieved quanti-tative precision through RT/FLM/QES/JLMS. These developments elevate entanglement froma conceptual guide to a predictive tool. In such a landscape, genuine invariants quantitiesinsensitive to microscopic details yet tightly constrained by first principles are both natural andessential.We show that a simple, dimensionless scalar, the V-index, captures the equilibrium betweenboundary entanglement, modular energy, and variations of generalized entropy. Its behaviorat and near extremality displays a universal structure: an anchor fixed solely by bit scaling,and a stability band governed by bulk entanglement. The convergence of independent methodssuggests that the index reflects a deeper principle of quantum geometric consistency. --------------------------------------------------------------------------------------------------------------------- A Dimensionless Information Energy Entropy Index (V-index):Corrected Definition, Landauer Anchored Lower Bound,and a Variational Protocol Framing ( V-index Part 1 ) https://doi.org/10.5281/zenodo.18284260 A Universal Balance in Holographic Quantum Gravity The V-index and its Invariance Across Holographic Frameworks (V-index Part 2) https://doi.org/10.5281/zenodo.18288805 Functional Vulnerability Index (V-index) for Genetic Code Degeneracy and Protein Functional Integrity: Applications to TP53 and HIV-1 Protease ( V-index Part 3 ) https://doi.org/10.5281/zenodo.18156730