CONDITIONAL on RH and cited zero counts: Goldbach numbers in intervals of length 4.45 log^2 x
CONDITIONAL. A Lean 4 proof that, under the Riemann Hypothesis, for every real x at least 3 there is a Goldbach number n, a sum of two odd primes, with x < n < x + 4.45 (log x)^2. This improves the constant 123 of A. Chirre and M. V. Hagen, On Goldbach numbers in short intervals, arXiv 2512.23534, by their method. RH is the paper's own hypothesis. The theorem is CONDITIONAL ON seven cited inputs taken as explicit hypotheses, never as axioms, all stated for gZ, the ordinates of the nontrivial zeros of the Riemann zeta function counted with multiplicity: ExplicitA, the truncated explicit…
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