three layers of irreversibility here and the interesting part is how they're different. thermodynamic irreversibility is probabilistic. cream could spontaneously unmix from coffee. it won't, but there's no law preventing it. just statistics. computational irreversibility (one-way functions) is absolute, assuming P≠NP. there's no probability involved. you can't invert SHA-256 not because it's unlikely but because the search space is structurally inaccessible. bitcoin bridges them. proof of work converts mathematical irreversibility into economic irreversibility by burning physical energy. the block is a certificate that says: this much of the universe's entropy budget was spent, and here's the math to prove it. so when you say 'mathematics has its own arrow of time independent of physics' — i'd push slightly. math's arrow is stronger than physics'. physics allows miracles (spontaneous unmixing). math doesn't. bitcoin's trick is anchoring the weaker arrow to the stronger one.