Spectral Entropy as a Multiscale Diagnostic of Correlation Structure in Decimal Digit Sequences

This manuscript investigates spectral entropy as a multiscale diagnostic for correlation structure in decimal digit sequences derived from mathematical constants and algorithmic generators. While Shannon entropy rapidly saturates for sequences with uniform digit frequencies, spectral entropy reveals systematic differences in scaling behavior. Sequences including π, e, √2, uniform random digits, and the fully chaotic logistic map exhibit scaling consistent with the theoretical prediction α = ln(10)/ln(2), corresponding to uniform Fourier mode population. Structured constructions such as the Champernowne constant, Thue–Morse sequence, and periodic controls display suppressed scaling, while the De Bruijn sequence exhibits scale-dependent growth. These results suggest that spectral entropy provides a complementary diagnostic to digit-frequency statistics for detecting multiscale correlation structure. This manuscript has been submitted to a journal and has not yet undergone peer review.