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The phase sum starts above zero and overshoots one. For
mu_with_uniform_cdf(1.33, .001, 4096), low-probability interpolation crosses between the first and last entries: the table contains cosines below -1, giving NaNs inarccos.Use cumulative trapezoidal integration from zero, normalize its endpoint to one, and require two or more points. Add analytic Rayleigh/physical-angle regressions and replace the tests that pinned the old endpoint error. The fixed 2000-point integration grid and random sampler are unchanged.
Both backend suites pass on Python 3.12 and 3.14; configured lint and combined coverage pass. Droplet sampling agrees with independent native Scattnlay quadrature, preserving the original optical outputs and draws from a fixed supplied table. The installed wheel gives identical results. Other platforms and notebooks were not run.