Rydberg Quantum Beats as Khron Signatures: Falsifiability Test on Public Berholts Data and an Atomic-Scale Probe of Multi-Sheet c-Elasticity

This work provides a rigorous falsifiability test of the Cymalogy framework by reanalyzing the "quantum watch" experimental parameters (Berholts et al., 2022). We demonstrate that the observed Quasiunique Beat Signatures (QUBS) in helium are candidates for the first empirical signature of khrons—discrete causal injections from a multi-sheet metageometry. Key Advancements in V2: Theorem 1 (Non-Representability): We prove that a specific class of periodic corrections, ϵnsin2(πn/(i+1)), is mathematically forbidden to be represented in the standard Drake–Ritz basis. This ensures the signal cannot be absorbed by standard fitting procedures. Detection Margin: Numerical analysis shows that the predicted spectral component at f=1/2 cycle/n exceeds the Berholts detection threshold by a factor of ∼1.5×106, making it a robust target for experimental confirmation. Structural Scaling: The framework identifies a structural link between atomic-scale energy shifts and the cosmological constant (β) via a β−1/4 law, providing a coherent bridge between quantum and cosmological scales. Legacy: This work formalizes the definitive realization of de Broglie’s internal clock hypothesis (1924) within a discrete causal manifold. Conclusion: This paper identifies a specific, testable signature that standard Rydberg spectroscopy is mathematically unable to explain, providing a clear protocol to invalidate current readings of atomic time.