A Geometric Observability Framework for Wave–Particle Phenomena: Projection Geometry, Wavelength-Dependent Survivability, and the Geometric Origin of Wave–Particle Duality.

This paper introduces a Geometric Observability Framework that reinterprets wave–particle duality as an emergent consequence of the geometric relationship between actual propagation paths and projected observable distances. The central construct is the geometric excess ratio Γ = Lₐctual / dₒbs and the geometric observability factor G (λ) = 1/Γ, which interpolates continuously between particle-like behaviour (G → 1, single admissible path) and wave-like behaviour (G < 1, multiple paths with differing excess ratios). The helical path is identified as the geodesic of propagation in four-dimensional space. Wavelength dependence of G is derived and verified against experimental coherence length data across wavelengths from 0. 1 nm to 700 nm with no free parameters. Applications include interference fringe formation, broadband coherence degradation, geometric survivability over stellar distances, and the observed dominance of longer wavelengths in distant astrophysical sources. The framework introduces no new physical laws and is fully compatible with quantum mechanics, wave optics, and general relativity.