Duality Parameter

The Duality Parameter is the dimensionless ratio of an object's de Broglie wavelength to its characteristic form length, used to classify whether it behaves as a wave or a particle. The book uses it to resolve wave-particle duality through recursive form theory. When the wavelength is much larger than the form, D >> 1, the object is in the wave regime of extended field behavior; when it is much smaller, D << 1, it is in the particle regime of localized form; at D ≈ 1 it is in the Transition Regime where both coexist. In the limits, as recursion depth goes to infinity form persistence becomes infinite and L▢ approaches the Planck length, and as coupling rises past its critical value synchronization, coherence and form emergence grow toward 1. It is listed among the Chapter 7.6 predictions, measurable through fringe visibility in matter-wave interferometry. The formal statement is D = λ_dB/L▢, where D is the Duality Parameter, λ_dB the de Broglie wavelength and L▢ the characteristic form length scale. Dimensions: D [∅], λ_dB [𝕃], L▢ [𝕃]; the book's check is valid and verified. It connects to the Characteristic Form Length Scale, Transition Regime, Critical Coupling, Field-to-Form Transition and Visibility Prediction.