Structural Time Flow Theory: A Minimal Framework for Late-Time Cosmology — Version 5

ersion 5 (v5): Formal structural closure and derivation of the magnetogenesis branch. This version marks the formal mathematical closure of the TFT structural branch. It introduces the derivation of the structural response function ZT directly from the structural flow function FTFT(z), effectively removing the previous parametric freedom in the magnetogenesis sector and establishing it as an inescusable consequence of the theory. It finalizes the scaling of the structural acceleration target as aT ≡ cH₀, validated by the SPARC rotation curve analysis, and explicitly demarcates the theory into a "Core Minimal Framework" (Expansion, Growth, ISW) and "Conditional Extensions" (Magnetogenesis), ensuring internal consistency and falsifiability. Version 4.2 (v4.2): Introduced the structural magnetogenesis channel and preliminary galactic scaling. This version established the viability of the structural pumping mechanism for electromagnetic modes without violating atomic stability (Δ αEM/αEM < 10⁻⁵). Version 4.1 (v4.1): Clarified the resolved geometric interpretation of the structural coefficient, separated the inertial mimetic sector, added preliminary information-criterion diagnostics, and sharpened the galactic, growth, ISW, and cluster falsifiability channels. Version 4 (v4): Refined the Structural Time Flow Theory (TFT) by separating the inertial mimetic sector ρ_λ=2λ from the geometric structural acceleration term αgeoFTFT(z). Established FTFT(z)=1 as a recovery/control limit. Abstract: Structural Time Flow Theory (TFT) is formulated as a conditional and testable proposal in which time is treated as a structural component of spacetime rather than as a passive external parameter. This manuscript refines the minimal low-curvature background sector by placing the structural correction in the Friedmann constraint, not in a separately conserved phenomenological sector or renamed ΛCDM component. Preserving ordinary matter conservation then determines the corresponding Raychaudhuri equation. The mimetic multiplier sector is retained as a pressureless structural component, ρ_λ=2λ, and is interpreted as the structural pressureless/inertial mimetic mode of the homogeneous branch. In flat normalization, 1=Ωb+Ω_λ+αeff(H₀). Calibration using Pantheon+ SN Ia and DESI BAO data confirms the validity of the structural acceleration branch. The galactic-scale analysis of SPARC rotation curves independently recovers the structural acceleration scale aT ≡ cH₀ ≈ 7.8 × 10⁻¹⁰ m/s². The growth and ISW sector is reformulated through the resolved kernel d/dz[μ(z,k)D(z)(1+z)], allowing comparison with Planck cross-correlations. v5 completes the theory by deriving magnetogenesis directly from the structural response function ZT, demonstrating that the TFT structural dynamics naturally amplify primordial electromagnetic fluctuations while preserving the constancy of the fine-structure constant.