Super-ΛCDM: The Cascade Architecture of Cosmic Evolution

The standard cosmological model (ΛCDM) has achieved exceptional observational success over three decades, yet carries fundamental unexplained quantities: dark matter, dark energy, the fine-tuned cosmological constant, persistent Hubble tension, and the lensing amplitude anomaly. We propose Super-ΛCDM — not a replacement of ΛCDM, but its subsumption into a deeper geometric framework. Just as Newtonian gravity is the weak-field limit of general relativity, ΛCDM is the n = 0 meta-scale limit of the cascade architecture — the self-similar expansion geometry generated by the Feigenbaum universality constants α = 2.502907875 and δ = 4.669201609. Within this framework, every major ΛCDM assumption is derived rather than assumed: the cosmological constant Λ emerges as the cascade descent rate at meta-scale level n ≈ 21 [Paper 50]; the Hubble constant H₀ = 68.21 km/s/Mpc is derived from the CMB acoustic scale without circular assumptions [Paper 39]; the lensing amplitude Aᴸ = 0.971 is a cascade prediction [Paper 39]; galaxy rotation curves are cascade frontier effects requiring no particle dark matter [Paper 41]; early-universe massive black holes are consistent with a cascade-scale-dependent Eddington limit [Paper 56]. The Hubble tension resolves as two valid measurements at different cascade scales applying a single-scale model — not a fundamental conflict. Super-ΛCDM preserves all correct measurements, resolves all major tensions, and opens the cascade frontier as the next observational era. The complete epoch-dependent Hubble bias function g(z) is derived in companion Paper 58.