Spatiotemporal Topological Order E: Unified Theory and Experimental Roadmap of Spatiotemporal Topological Order

This paper proposes “spatiotemporal topological order” as a new testable paradigmfor quantum gravity research. By establishing five core axioms of spatiotemporaltopological duality, this work constructs a self-consistent theoretical frameworkthat relates anyon braiding in space with barcode structures in temporal evolutionthrough categorical equivalence. The theory automatically reduces to general relativity and the Standard Model in the low-energy limit, ensuring consistency withknown physics. To achieve multi-scale testing, this paper outlines a ten-year experimental roadmap, covering four stages: proof-of-principle on quantum processors(2025–2027), finite-temperature phase transition studies in medium-scale systems(2028–2030), large-scale quantum simulation of early universe evolution (20312033), and joint search for characteristic cosmological signals with next-generationastronomical observations (CMB-S4, SKA) (2034–2035). The theory provides precise observable predictions, including periodic modulation of the cosmic microwavebackground angular power spectrum (amplitude 0.02 ≤ A ≤ 0.08), a nanohertzstochastic gravitational wave background (peak frequency fc ≈ 3.2×10−9 Hz), andspecific primordial non-Gaussianity. These predictions are coupled through microscopic barcode statistical parameters, forming a unique “multi-messenger correlation” that provides strong falsifiability tests for the theory. This paper aims toprovide a clear path integrating mathematical physics, quantum information, andobservational cosmology for exploring the quantum nature of spacetime.