A threshold gate checks energy budget before full acceptance. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Enough energy passes the threshold gate
Two opposite photons can supply 100 J plus 100 J, matching the pair-at-rest rest-energy cost 200 J.
100+100=200≥200
Too little energy fails the threshold gate
If the two-photon setup supplies only 150 J, the energy budget is below required energy 200 J, before momentum closure is even tested.