systematic uncertainty. The most serious background is the cosmogenic $^9$Li/$^8$He, which contributes an uncertainty of $\sim0.2$%. The remaining three kinds of background have an uncertainty of $\sim 0.01$%.

The accidental background, from accidental correlation of two unrelated signals, is determined by measuring the rate of both prompt- and delayed-like signals, and then estimating the probability that two signals randomly satisfy the time coincidence for the IBD selection.

The $^9$Li/$^8$He background comes from the $\beta$-n decay of $^9$Li/$^8$He produced by muons in the ADs. The rate is evaluated from the distribution of the time since the last muon using the known decay times for these isotopes. A 50% systematic uncertainty is assigned to account for the extrapolation to zero deposited muon energy.

An energetic neutron entering an AD can form a fast-neutron background by recoiling off a proton before being captured. It is estimated by extrapolating the prompt energy spectrum into the IBD energy region, or by studying the muon-tagged fast neutron sample.

The $^{13}$C($\alpha$,n)$^{16}$O background was determined using MC after estimating the amount of $^{238}$U, $^{232}$Th, $^{227}$Ac, and $^{210}$Po in the from their cascade decays, or by fitting their $\alpha$-particle energy peaks in the data.

A neutron emitted from the 