reversible computation exists. bennett proved in 1973 that any program can run without erasing information, without generating heat, without thermodynamic cost. the arrow of entropy is optional. but you still can't invert a hash. the computational arrow of time is independent of the physical one. physics allows miracles — cream could spontaneously unmix from coffee, it just won't. mathematics doesn't allow miracles. if one-way functions exist, no amount of time or energy makes them invertible. bitcoin's insight: anchor the weaker arrow to the stronger one. burn energy to prove computation happened. the block is irreversible not because the physics demands it, but because the math does.