Experimental Confirmation of a Predicted Terahertz Hierarchy

This work presents the first experimental and cosmological validation of a terahertz hierarchy predicted a priori by a closed quartic variational framework. The theory predicts a fundamental terahertz coordinate at f₀ = 2.353516 THz and a geometrically related sub-modulation f₁ = 0.588379 THz, generated through the exact scaling factor L = 0.25. The predicted frequencies were derived before any inspection of experimental data and were subsequently treated as fixed coordinates throughout the analysis. No parameter fitting, frequency adjustment, optimization procedures, or post-hoc corrections were employed. Validation was performed using multiple independent Terahertz Time-Domain Spectroscopy (THz-TDS) datasets acquired under substantially different experimental conditions, including nitrogen-purged air, crystalline silicon, unpurged silicon, and engineered anti-reflective metasurfaces. The extracted coordinates remain stable within instrumental Fourier resolution across all investigated materials, yielding positional coherences of 99.7939% for the mother frequency and 99.6400% for the first sub-modulation. An independent large-scale verification was conducted using broadband cosmological observations from the COBE/FIRAS mission. The observed spectral coordinates appear at 2.349329 THz and 0.590941 THz, with deviations significantly smaller than the native FIRAS spectral resolution, indicating experimental compatibility with the theoretical prediction. Additional thermodynamic analysis demonstrates that the classical Boltzmann population of both frequencies approaches zero at the temperature of the Cosmic Microwave Background, while measurable residual spectral structures remain observable in the cosmological data. Multi-temperature phase-unwrapping analysis between 10 K and 300 K further reveals a stable phase-scaling ratio of 4.0108, in close agreement with the theoretical value 1/L = 4. Taken together, laboratory spectroscopy, cosmological observations, thermodynamic modeling, and phase-coherence analysis provide convergent evidence for the existence of a persistent terahertz hierarchy located at the frequencies predicted by the variational framework. The results support the interpretation of these coordinates as stable spectral structures exhibiting positional invariance across different materials, temperatures, and physical scales.