Brane-Cluster UV Completion of Quantum Gravity

Abstract The central problem addressed in this work is the tension between perturbative non-renormalizability of Einstein gravity and the need for a mathematically controlled ultraviolet description compatible with low-energy general relativity. We propose a brane-cluster mechanism in which intersecting brane networks generate homologically classified collective modes ΦK that couple to curvature and reorganize the high-momentum graviton kernel while preserving infrared Einsteinian propagation. The mathematical framework is built from an explicit intersection chain complex, cluster charges in Hk(B), and a curvature-coupled effective action matched at fixed derivative order. Integrating out heavy cluster sectors yields a modified spin-2 propagator, Gμν,ρσ(p) = Pμν,ρσ p2 + αp4 + βp6 + · · ·. We derive intermediate steps for matching coefficients, dimensional scaling, and limiting regimes (pℓc ≪ 1, pℓc ≫ 1), and we formulate consistency checks for homological closure, Ward identities, and contour-based perturbative unitarity in the physical graviton channel. The resulting loop kernels are UV softened at the effective-theory level, with explicit toy-model realizations and parameter-scaling tables. To situate the proposal in mainstream quantum-gravity research, we provide a systematic comparison with AdS/CFT, holography, ER=EPR, tensor-network reconstructions, and loop quantum gravity, emphasizing both overlaps and non-equivalences. Under the stated assumptions, the framework should be interpreted as a falsifiable UV-improved effective theory rather than a claim of unique microscopic completion.