Seven-Layer Nested Multiverse Framework under Dynamic Dimensional Renormalization

The unification of quantum gravity theory and the holographic principle remains a central challenge in modern theoretical physics. This paper proposes a novel mathematical framework based on fractal holographic quantum field theory. By parameterizing dynamic Hausdorff dimensions and discretizing holographic lattices, we establish a unified description of multiverse evolution from microscopic fractal f luctuations to macroscopic classical spacetime. Key innovations include: 1. Construction of fractal covariant derivatives (DdH ) incorporating instanton gravity corrections. The metric compatibility condition ∇dH µ gνρ = 0 rigorously reveals the correspondence between dimensional flow and connection corrections. 2. Seven-layer nested generating functional system compatible with open/closed string hybrid states, whose parametric constraints reduce to specific quantum gravity models. 3. Proof of fractal AdS/CFT correspondence: The theory naturally reduces to the seven-layer nested gauge structure in Ref. [2] when dH(k) → 3. This framework provides a new mathematical formulation for quantum spacetime phase transitions, with future extensions to fractal string lattice realizations and quantum chaos studies.