An RH-Conditional Prime-Gap Bound with Constant 1669/2000

This preprint presents an asymptotic prime-gap bound, assuming the Riemann hypothesis, with constant \(1669/2000=0.8345\). The argument combines an explicit Gaussian–Laguerre test function with the Fourier optimization framework of Carneiro, Milinovich, and Soundararajan. Exact rational coefficients and rigorous interval arithmetic certify the required numerical inequality. Assuming RH, there exists \(x_0\) such that, for every real \(x≥ x_0\), the interval\[{(x,\;x+1669/2000√xlog x]}\]contains a prime. The constant improves upon the reported \(0.8358\) asymptotic benchmark of Chirre, Pereira Júnior, and de Laat. The accompanying source package includes reproducible verification code. No explicit value of \(x_0\) is supplied. Independent mathematical review and confirmation of priority remain outstanding.