What Exactly is Antimatter (Gravitationally Speaking)?

There has been renewed interest in the idea of antigravity -- that matter and antimatter repel gravitationally - in lieu of the recent beautiful ALPHA-g result for the free-fall acceleration of antihydrogen of $a_{\bar{H}}=(0.75\pm 0.13~({\rm stat.+syst.})\pm 0.16~({\rm simulation}))g$. Precision tests of the Weak Equivalence Principle (WEP) have shown that binding energy (atomic, nuclear, and nucleonic) acts like matter under gravity. Whereas the contribution of atomic binding energy to the mass of antihydrogen is negligible, the majority of the mass of the antiproton comes from the gluonic binding energy. Hence, in terms of antigravity, the antiproton is mostly composed of matter and so even if the antimatter content of the antiproton is repelled by the Earth, there would still be a net attraction of the antihydrogen to the Earth because of its dominant matter content. Using recent Lattice QCD results showing that around two-thirds of the mass of the proton (and, hence, from the $CPT$ Invariance of QCD, of the antiproton) is due to gluons, I find that in the antigravity scenario the free-fall acceleration of antihydrogen would be $a_{\bar{H}}=(0.33^{+0.10}_{-0.06})g$. The fact that antinucleons are more matter than antimatter (in the gravitational sense) leads to quite different cosmological consequences than the naive antigravity scenario (where antistars are wholly antimatter). For example, it follows naturally that there is a matter-antimatter asymmetry in the universe right from the instant of the Big Bang -- but not a baryon-antibaryon asymmetry. Again, this stems simply from the fact that antibaryons are more matter than antimatter.