Relation Consistency Theory: A Unified Geometric Framework for Cosmogenesis and Epochal Evolution

Standard cosmological models, while empirically robust, rely on disconnected theoretical frameworks to explain the distinct epochs of the universe. Primordial inflation, matter-dominated deceleration, and late-stage dark energy acceleration are traditionally modeled using separate, compartmentalized mechanisms (e.g., Inflaton fields, ). This paper introduces Relation Consistency Theory (RCT), a purely geometric model of cosmogenesis that derives all macroscopic universal epochs from a single, continuous complex differential generator: dΨ/dτ = (γ(τ) + i)Ψ. By modeling the universe as a unified complex state Ψ that bifurcates into orthogonal standard and anti-phase relations, we mathematically eliminate the need for hardcoded initial mass or energy. The observable cosmic scale emerges natively as the dimensionless invariant C = u^2 + v^2. Calibrating the fundamental expansion field γ(τ) to modern astronomical data (γ_0=0.5616, κ=0.3143, γ_Λ=0.0643) perfectly recovers the three observed cosmological eras. The model accurately predicts the epochal transition to dark energy at 9.8 Gyr, cleanly resolves to a present-day Hubble Constant of H_0 = 70.0 km/s/Mpc with a deceleration parameter of q_0 = -0.55, and mathematically proves an asymptotic deep-future limit equivalent to a de Sitter universe (q → -1). Furthermore, RCT resolves the early structure anomaly observed by JWST, proving that an exponential decay in early expansion geometrically forces rapid phase-locking, allowing massive galaxies to form within the first 500 million years.