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The mass came from ln_gamma differences (relative error 1.1e-13 at n = 100, 1.5e-11 at n = 10,000) and the cumulative forms summed up to 10,000 of them. The mass now comes from Loader's saddle-point formula, the cumulative sum walks away from the mode by the ratio of neighbouring terms and stops when terms stop mattering, and the incomplete beta / gamma branches take the same mass as their prefactor. Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>