Spectro-Polarimetric Corridors and Resonant Structure in Photon–Dark Matter Scattering: A CAT-12 Ratio-Lattice and Cross-Domain Analysis

This paper introduces a harmonic ratio–lattice classification framework for photon–dark matter (DM) scattering, using the Cosmic Algorithm Theory-12 (CAT-12) resonance structure as a model-independent structural filter. Traditional approaches to DM phenomenology rely on specific cross-section calculations and model fits, which can produce degenerate predictions across different scenarios. In contrast, the CAT-12 lattice provides a universal harmonic scaffold that can rapidly classify observed spectral and polarimetric features before invoking detailed particle models. We focus on three observational ratios—color, polarization, and notch depth—which are derived from gamma-ray spectra and polarization data. These ratios are mapped onto the CAT-12 resonance lattice to identify whether scattering signatures occupy stable harmonic corridors. Using simulated Fermi–LAT and CTA datasets alongside observational templates, we find that photon–DM scattering scenarios populate well-defined lattice families, with Ratio Precision Index (RPI) values of 0.68–0.91. These values are comparable to known astrophysical resonance benchmarks such as GRO J1655–40 HFQPOs, TRAPPIST-1e orbital ratios, and B1938+666 micro-perturber signatures. This cross-domain harmonic placement suggests that scattering phenomena are not randomly distributed but may reflect deeper resonant symmetries in spacetime and field interactions. CAT-12 does not replace particle physics or general relativity; rather, it complements them by functioning as a structural pre-classification layer, analogous to Fourier or wavelet transforms. This approach can streamline future analyses by identifying signals with strong harmonic coherence prior to model-specific fitting. Potential applications include optimizing gamma-ray observational strategies for instruments like Fermi–LAT, CTA, AMEGO-X, and POLAR-2, and mining archival datasets for previously overlooked resonant features. The paper includes eight figures, a detailed reference section, and an appendix with ratio equations and worked examples.