Ratio Theory: Axioms for Cross-Domain Resonance

This paper develops Ratio Theory, a six-axiom framework that treats proportions—not magnitudes—as the primary descriptors of structure, stability, and transition across domains. We formalize structural universality, contextual embedding, cross-domain invariance, critical thresholds, embodied detection, and provisional directionality, and show how persistent ratios index coherence in physics (orbital resonances, scaling laws), biology (DNA helical pitch, gene-expression balances), cognition (oscillatory coupling, perceptual consonance), culture (meter, symmetry, harmonic intervals), and socioeconomics (debt-to-GDP, reserves-to-liabilities). The theory provides operational tools for early-warning detection via ratio thresholds, a translation layer for cross-domain pattern recognition, and a probabilistic lens that biases outcomes without determinism. We also outline a minimal bridge to CAT-12, where ratio invariants serve as inputs to resonance lattices (e.g., CMB peak spacing). The result is a compact, testable grammar for identifying, interpreting, and forecasting ratio-governed regime changes across scales. Keywords: Ratio Theory; proportional invariants; critical thresholds; cross-domain invariance; embodied detection; predictive indicators; CAT-12 (contextual link); CMB ratios; orbital resonances; gene regulation; perceptual consonance; symmetry; early-warning signals Funding/Notes (optional): Corresponding author: William Arthur, DPM ([email protected]).