Holographic Reconstruction of Universal DS and AdS Spacetimes and Experimental Predictions

This paper proposes a holographic duality theory independent of the AdS/CFT framework, reconstructing the dynamics of non-AdS spacetimes based on the entropygeometry duality principle and topological quantum error correction. By introducing fractional diffeomorphism mappings and dynamic renormalization group flows, a bidirectional feedback mechanism is established between the boundary quantum entanglement entropy and bulk spacetime curvature. Key innovations include: 1. Topological Origin of Dark Energy: The dark energy density is generated by coupling the second Chern class of gauge fields to the Planck scale: ΛDE ∝βℓ2 P Ch2(F), matching Planck data (ΛDE ∼ 10−123ℓ−2 P ). 2. QuantumCorrections to Black Hole Entropy: ExtendingtheBekensteinHawking entropy formula to: SBH = A 4G +β Ch2(F), where the perturbative parameter β ≪ 1 is negligible in the classical limit but dominates during quantum evaporation. 3. Observational Predictions: • Discrete gravitational wave spectra (fn ∝ n · 0.35 Hz, detectable by DECIGO), • Quantized fermion masses (m(n) ψ =n·m0, verifiable at FCC-hh), • Fractal spacetime dimension (dH = 3.02 ± 0.03, constrained by CMB power spectra). The theory is validated through causal stability, low-energy effective limit compatibility, and self-consistency in black hole thermodynamics, providing a new paradigm for unifying quantum gravity and cosmology.