The Saturation Theorem: Axiomatic Constraints on Quantum Gravity from Cosmological Relaxation

The Saturation Theorem: Axiomatic Constraints on Quantum Gravity from Cosmological Relaxation This paper establishes the Saturation Theorem within the Cosmological Relaxation Model (CRM) framework. Starting from five axioms — monotone relaxation, spectral boundedness, holographic consistency, Lorentz recovery, and graviton coherence — we derive that any quantum-gravity completion compatible with cosmological relaxation must reproduce the tanh-saturation profile of the CRM effective metric. The theorem constrains the UV completion uniquely: the Pöschl–Teller potential emerges as the sole consistent spectral generator, and the saturation scale coincides with the holographic bound. This is Paper V (CRM V) of the Cosmological Relaxation Model series. Related works: CRM Papers I–IV: doi:10.5281/zenodo.18728936 FST-RH (Free-Energy Spectral Theory and the Riemann Hypothesis): doi:10.5281/zenodo.19035845 FST-RH Code Repository: github.com/research-line/fst-rh Both English and German versions are included.