Does QED have six figure precision for dense matter physics,.. quantities? NO.
Re QED. Perhaps you don't consider the very many experimental results accurately predicted?
THHuxleynew asserted that QM had six figure precision for the neutron-proton
Then he found 3.5 figure precision in the arxiv paper
in this post.. where he advised to "look at the predictions here" Figure 2 Post #287
I did look at the predictions here in Figure 2 using paint.. 3.5 figure precision???????..
I could only find 1 figure precision
1.5 MeV......... +/- 0,2? 0.3 ? 0.4?
versus the experiment value for n-p
1.293 332 05(48) MeV
Perhaps THHuxley should consider what 300 kev is in Mev? and read arxiv correctly.
Or enquire from Stephan Durr whether he meant to write just 3 keV .. not 300 keV?
"We performed lattice QCDand QED with four nondegenerate
Wilson fermion flavors and computed the neutron-proton mass-splitting
with an accuracy of 300 kilo-electron volts,
Durr et al 2015 https://arxiv.org/pdf/1406.4088.pdf