Holding forward work fixed while the return path changes makes net cycle work a checked difference. 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 small return path leaves thirty joules net

Forward work is fixed at 36 joules. Returning only 6 joules leaves net work 30 joules.

366=3036\mathbin{-}6=30
Cycle work differenceForward and return areas leave a checked net work.forwardreturnnet

The original audit row returns half

With the same forward work, return work 18 joules leaves net work 18 joules.

3618=1836\mathbin{-}18=18
Cycle work differenceForward and return areas leave a checked net work.forwardreturnnet

A large return path leaves only six joules

Returning 30 joules leaves just 6 joules net. Three rows show that hysteresis is the unreturned area.

3630=636\mathbin{-}30=6
Cycle work differenceForward and return areas leave a checked net work.forwardreturnnet