A three-point energy gate scan shows that pair thresholds are inclusive. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
One hundred fifty joules fails the gate
Available energy 150 J is below required energy 200 J, so the threshold row is rejected.
150<200
Two hundred joules just passes the gate
Available energy 200 J equals the required 200 J, so the inclusive threshold passes.
200=200
Two hundred sixty joules also passes
Available energy 260 J exceeds required energy 200 J. Threshold acceptance is necessary, but a full reaction still needs the other ledgers.