A threshold requirement scan holds available energy fixed at 200 joules and varies the requirement instead: a lighter-product reaction needing only 150 joules clears with margin 50, the book's usual 200-joule requirement passes exactly at the boundary, and a heavier-product reaction needing 250 joules is rejected with margin -50, exactly for the stated toy threshold rule. Chapter six always fixed the requirement and varied the available energy; this scan shows the same available energy can pass or fail depending only on what the reaction's own output particles actually cost to produce.
The same available energy passes or fails depending on what the reaction's own product particles actually cost. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A lighter-product reaction clears the same available energy
Chapter six always fixed the requirement at 200 joules and varied the available energy. Here the available energy stays fixed at 200 joules and the requirement -- what the reaction actually costs to produce its output particles -- changes instead: 150 joules gives margin 50 and accepted bit 1.
200−150=50,a=1
The book's usual reaction sits exactly at this available energy
Chapter six always fixed the requirement at 200 joules and varied the available energy. Here the available energy stays fixed at 200 joules and the requirement -- what the reaction actually costs to produce its output particles -- changes instead: 200 joules gives margin 0 and accepted bit 1.
200−200=0,a=1
A heavier-product reaction rejects the same available energy
Chapter six always fixed the requirement at 200 joules and varied the available energy. Here the available energy stays fixed at 200 joules and the requirement -- what the reaction actually costs to produce its output particles -- changes instead: 250 joules gives margin -50 and accepted bit 0.