Frequency-Dependent Mathematical Information Signatures in WMAP- Cross-Validation Evidence for Information-Theoretic Cosmology

We report systematic frequency-dependent signatures in WMAP 9-year cosmic microwave background data through cross-validation analysis using our previously validated methodology (Baines 2024, 0.15% false positive rate). Analysis of three frequency bands (Q: 41 GHz, V: 61 GHz, W: 94 GHz) reveals consistent patterns in enhancements at multipoles corresponding to mathematical constants φ, e, √3, and √5.

Key Finding: Mathematical constant signatures exhibit systematic frequency evolution: φ (golden ratio) shows non-monotonic behavior with peak enhancement at 61 GHz (2.28σ), while √5 demonstrates strong correlation with frequency (r = 0.991, 0.77σ → 2.88σ). Statistical analysis indicates 91% probability that observed patterns are non-random, with different constants showing distinct frequency behaviors.

Statistical Validation: Perfect false positive control maintained (0 significant detections) across all frequencies, confirming methodological robustness. Cross-dataset comparison with Planck reveals systematic differences, suggesting dataset-specific effects rather than universal signatures.

Implications: The observed frequency dependence of mathematical constant signatures warrants further investigation across additional datasets and frequencies. The systematic nature of the patterns suggests underlying physical mechanisms that merit theoretical exploration.