Tri-Phasic Cosmology from a Discrete Microstructure: Non-Singular Bounce, Phase Transitions, and Verification Protocols

We propose a non-singular cyclic cosmology in which continuous spacetime emerges from a discrete weighted-graph microstructure governed by tri-phasic order parameters (Out, In, Dual). We construct an emergent spatial metric from the weighted Laplacian and argue that Einstein–Hilbert gravity is recovered as the infrared effective theory under coarse-graining and RG flow. Employing a polymerization scheme analogous to Loop Quantum Cosmology, we obtain a modified Friedmann equation H 2 = 8πG 3 ρ (1 − ρ/ρ c ) with a quantum bounce at ρ = ρ c . A density-driven I→O transition can generate Dual-phase excitations and a stochastic gravitational-wave background. To support falsifiability and independent replication, we specify two quantitative diagnostics: (i) spectraldimension flow d s (σ) computed via stochastic trace estimation, and (ii) a Planck 2018 likelihood fitting workflow (CLASS + MontePython/Cobaya). This paper establishes the algorithmic templates, code modification protocols, and reporting standards required for rigorous confrontation with data.