The Quantum Gravity V-Index: A Universal Holographic Stability Invariant

This is a preliminary study and not the final version. An updated revision will be available shortly. We thank you for your feedback. We propose a dimensionless scalar quantity, the V-index, designed to organize the interplay between boundary entanglement entropy, modular energy, and variations of generalized entropy in holographic systems. Rather than introducing new microscopic dynamics, the V-index provides a compact diagnostic of how information and energy balance under small deformations of holographic states. Across several fundamentally different realizations including continuum AdS33/CFT22 calculations with Faulkner Lewkowycz Maldacena (FLM) quantum corrections, numerical analyses in BTZ geometries, and discrete tensor network constructions based on MERA we observe convergence toward a common critical value V≃2.45, corresponding to an effective holographic efficiency η≃0.85. We interpret this value not as an exact invariant, but as an emergent critical point separating regimes of under and over focusing of quantum information, consistent with Quantum Null Energy Condition (QNEC) constraints and with the stationarity of the generalized entropy. Our results suggest that the V-index functions as a robust organizing parameter for holographic stability across disparate microscopic implementations. A falsifiable, testable tool that brings us closer to a unified theory of quantum gravity and a deeper understanding of black hole dynamics. The V-index (2.45) emerges not only within the framework of Quantum Gravity but also manifests across various other stability thresholds of nature, such as the Roche limit and dielectric resonance. Mathematical formulas and the formal definition of the V-index. https://doi.org/10.5281/zenodo.18147084