A Thought Experiment on Double-Slit Interference from a Localized Odd-Harmonic Source: Shape Preservation Is Conditional and Fragile, and the Single-Wavelength N=1 Is the Robust Special Case

Thought experiment (model calculation), not a measurement. Extends the position-readout push-forward (companion paper, isSupplementTo) to a localized source: localization is represented by a constant-amplitude odd-harmonic sum (isolated peak wave S_N). Although S_N is a sum of odd harmonics, it localizes in the far field WITHOUT changing shape only when the source-slit diagonal r_k=sqrt(L^2+(W/2)^2) is an integer/half-integer multiple of the fundamental wavelength: sqrt(L^2+(W/2)^2)=(m/2) lambda0. Alignment is a band of width ~1/(2N) (narrower for larger N); a ~3% change in lambda0 decides interference vs scattering. The central-alignment tolerance is W/L-independent; larger W gives greater off-axis fragility. An aligned localized source inherits the cos^2 fringe-shift readout under positional fluctuation but its peaks fall below cos^2 off-axis (extra scattering loss). The single wavelength N=1 has none of this fragility and reproduces the companion paper to machine precision. Net result is negative: localization adds an alignment constraint and off-axis fragility; shape preservation is conditional and fragile, with N=1 the robust special case. Distinguished from spatial coherence / van Cittert-Zernike visibility loss.