A Deterministic Hydrogen Validation of the Scretching Quantum Chain and the Maxwell–Scretching Electromagnetic Chain II: The Lyman Series (n = 2…6)

This work presents a first-principles validation of the Scretching Quantum Chain (SQC) and its macroscopic electromagnetic counterpart, the Maxwell–Scretching Chain (MSC), using the hydrogen Lyman series as a reference system. Hydrogen provides a uniquely rigorous testbed because its transition properties are analytically derivable and independently benchmarked by NIST standards, allowing a clean separation between deterministic physical law and empirical curve-fitting.

By examining five Lyman transitions (n = 2…6), the study demonstrates that the SQC enforces a strict linear relationship among core quantum observables—oscillator strength, transition frequency, statistical weight, and Einstein A coefficients—governed solely by fundamental constants. Agreement at the ~10⁻⁵ relative level is achieved using a single electromagnetic prefactor, establishing deterministic closure across the chain. The analysis further shows how the MSC provides the unique Maxwellian projection linking microscopic oscillator strength to macroscopic absorption and attenuation, completing the bridge from quantum structure to observable electromagnetic behavior.