Goldbach numbers in intervals of length $4.45 \log^2 x$ under the Riemann Hypothesis
Source: hexagonmath.org/abs/2610.00542v1
Assuming the Riemann Hypothesis, we prove that for every real $x \ge 3$ the interval $(x, x + 4.45 \log^2 x)$ contains an even integer that is a sum of two odd primes. The proof combines a weighted mean square bound for the Chebyshev prime counting error in short intervals with a piecewise linear weight in a bilinear identity for short interval prime counts. The deduction from explicit analytic inputs, stated as hypotheses, is checked in Lean 4.
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