Structural Time Flow Theory (TFT): A Minimal Framework for Late-Time Cosmology - v6

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 directly in the Friedmann constraint, avoiding phenomenological dark fluid re-parametrizations. Preserving ordinary matter conservation determines the corresponding Raychaudhuri equation, while the mimetic multiplier sector is retained as a pressureless inertial mode, ρ_λ=2λ. In flat normalization, the framework establishes 1=Ωb+Ω_λ+αeff(H₀). Version 6 (v6) elevates the theory to a non-perturbative regime, anchoring its macroscopic phenomenology in formal mathematical identities. The structural saturation limit is derived from first principles using Dyson-Schwinger equations and Kolmogorov-Arnold-Moser (KAM) stability, yielding the inverse Golden Ratio (φ⁻¹ ≈ 0.618) via Rogers-Ramanujan continued fractions. This limit naturally resolves the galactic Core-Cusp problem. Furthermore, the framework provides a bipartite, structurally derived resolution to the Hubble Tension: a quantum trace anomaly of the mimetic scalar mode (via Seeley-DeWitt expansion) establishing a global baseline shift, combined with a non-linear kinematic outflow driven by the local KBC Void. Finally, the vacuum energy and magnetogenesis channels are strictly regularized via Riemann Zeta analytical continuation (ζ(-1) = -1/12) and bounded by Hardy-Ramanujan structural entropy partitions. TFT stands as a minimal, theoretically rigid, and observationally falsifiable framework. Version History: Version 6 (v6): Non-Perturbative Closure, Ramanujan Identities, and Hubble Tension Resolution. This version marks the transition of the TFT framework from phenomenological scaling to first-principles mathematical derivation. Key inclusions: Exact derivation of the structural saturation limit K → φ⁻¹ ≈ 0.618 via Dyson-Schwinger auto-interaction, KAM stability, and Rogers-Ramanujan continued fractions. Bipartite resolution of the Hubble Tension: Derivation of a $+0.65%$ global baseline shift via the quantum trace anomaly of the mimetic mode, superimposed with a kinematic outflow correction (≈ +6.94%) from the Local KBC Void. Rigorous regularization of the Hubble cavity vacuum energy and magnetogenesis using Riemann Zeta analytical continuation (ζ(-1) = -1/12). Establishment of the structural entropy saturation bounds via Hardy-Ramanujan partition limits. Version 5 (v5): Formal structural closure and derivation of the magnetogenesis branch. This version marked the formal mathematical closure of the TFT structural branch. It introduced the derivation of the structural response function ZT directly from the structural flow function FTFT(z), removing previous parametric freedom in the magnetogenesis sector and establishing it as an inescapable consequence of the theory. It finalized the scaling of the structural acceleration target as aT ≡ cH₀, validated by SPARC rotation curve analysis, and explicitly demarcated 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 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.