The φ/ψ Duality Hypothesis: Framework, Experimental Roadmap, and Implications

The golden ratio φ ≈ 1.618 appears in verified physical phenomena including E8 quantum criticality, Fibonacci anyon statistics, and quasicrystal structure. Its algebraic conjugate ψ = -1/φ ≈ -0.618—the "anti-golden ratio"—is mathematically inseparable from φ yet has received almost no systematic investigation in physics. This paper presents a testable hypothesis: φ and ψ govern complementary physical regimes, with φ characterizing stability, propagation, and growth while ψ characterizes decay, diffusion, and relaxation. We propose five concrete experiments, specify quantitative predictions and falsification criteria, and discuss implications for fundamental physics. This is a speculative framework and research roadmap, not established physics.