6 Discussion

The strong correlation — surviving after explicit roughness control — demonstrates that spectral complexity minimization reproduces the dominant contributions of the Euclidean path integral in minisuperspace. This supports the hypothesis that the wavefunction is the universe’s compression codec: the paths we observe as “classical” are simply the ones that are cheapest to describe spectrally.

Working in the natural Fourier basis is essential. A DFT-based computation would misattribute the correlation to spectral leakage; the natural-basis calculation isolates a genuine relationship between frequency content and Euclidean cost. The log-uniform amplitude ensemble and the roughness-controlled partial correlation together rule out the most obvious confounding explanations.

The linearity observed between and in the high-cost regime, combined with exponential suppression in probability weight, provides a natural informational reinterpretation of why smooth geometries dominate.