Structural Time Flow Theory: A Minimal Framework for Late-Time Cosmology — Version 4.2

Version 4.2 (v4.2): Magnétogenese. Version 4.1 (v4.1): This update clarifies the resolved geometric interpretation of the structural coefficient, separates the inertial mimetic sector, adds preliminary information-criterion diagnostics, and sharpens the galactic, growth, ISW, and cluster falsifiability channels. Version 4 (v4): Version 4 refines the Structural Time Flow Theory (TFT) by separating the inertial mimetic sector ρ_λ=2λ from the geometric structural acceleration term αgeoFTFT(z). This update clarifies that FTFT(z)=1 is only a recovery/control limit, not the principal TFT branch. The principal theory is formulated through a structurally generated time-flow function FTFT(z), with perturbation-level tests through linear growth and ISW cross-correlations. Structural Time Flow Theory 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. The 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), so Ωb0.05 and Ω_λ0.25 imply αeff(H₀)0.70. Current Pantheon+ SN Ia and DESI BAO calibration gives an unresolved two-parameter background compression α=0.841±0.022 and H₀=68.94±0.22\ km s⁻¹Mpc⁻¹, which must be rerun with ρ_λ separated before being interpreted as the geometric coefficient. The v4 update strengthens the distinction between TFT and flat ΛCDM by treating the constant case FTFT(z)=1 only as a recovery/control limit. The resolved principal branch is governed by αgeoFTFT(z), while ρ_λ=2λ remains the inertial mimetic clustering sector. 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 using deep galaxy tracers such as NVSS, WISE, SDSS, and DESI. Changes in v4 include: clarification of the principal TFT branch; reclassification of FTFT(z)=1 as a recovery/control limit only; stronger distinction from flat ΛCDM; preservation of ρ_λ=2λ as the inertial mimetic clustering sector; updated resolved growth and ISW formulation; and clearer falsifiability criteria using Planck cross-correlations with galaxy tracers.