A dark ion scatters few photons, so the readout count stays below threshold and the state is classified as bit 0. The count 4 against threshold 10 gives result bit 0 exactly for the stated dark-state and threshold ledger; real readout has photon-count shot noise, state-preparation error, threshold drift, detector dark counts, background counts, and calibration uncertainty.
Dark-state fluorescence remains below the threshold. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The cited internal state is dark
The source bit is 0, so the readout count must stay below threshold.
bstate=0
Dark state stays below the count threshold
The count is 4 against threshold 10, giving result bit 0.