Dual Geometry of Wavelength Space and Frequency Space: A Geometric and Topological Observational Model of Reciprocal Conditions, Logarithmic Representation, and Uncertainty-Weighted Counting

We place the reciprocal duality condition lambda_n = 1/nu_n between wavelength components and frequency components, and impose a constant sum-of-squares (norm) condition on the wavelength space and the frequency space respectively. We observe the resulting geometric structure: in one dimension the solution is fixed to essentially a point, whereas a 5-component / 1-constraint system retains four degrees of freedom. Under a logarithmic change of variables the reciprocal duality reduces to the sign-reversal symmetry p_n = -q_n (a slope -1 line). Finally, choosing a 4D lattice in the frequency or wavelength space turns the sum-of-squares condition into a unit-cell counting problem; we define the fully-inscribed count N0(R) for the delta=0 case and a weighted count N_delta(R) for delta>0. This is an observational mathematical model and does not derive or identify physical quantities; nu_n is not identified with physical time-frequency, energy, or momentum.