A town pins a tournament bracket of a thousand names along a hall wall, with a short mark worked out from each pair above them all the way up to one mark at the top, copies that single mark onto a card on the public noticeboard, and a week later settles an argument about player 438 by handing over the name and ten other marks, because the man checking can work upward and see whether his result matches the card, which is a hash tree (a way of sealing many pieces of data behind one fixed-length scramble called a hash, from the French hacher, to chop) and the reason a blockchain (a shared record that every machine in a network keeps in full and nobody may edit), which charges for every byte, can hold a promise about eighty thousand steps of AI training without holding the steps. Each step is hashed on its own, the results are hashed in pairs until one is left, and proving one step means handing over its siblings (the partner hash at every round on the way up), ten for a thousand steps and twenty for a million, which is why the arrangement, first described by Ralph Merkle in 1979 to let one public key vouch for a batch of one-time signatures, grows by only one hash each time the work doubles. It has to be built carefully, because a hash cannot tell a step from two hashes glued together, so a cheat can hand over a mark from the middle of the wall as if it were a player and prove a smaller, different field to the same card, which is why the standard for certificate logs (public records of the security certificates issued to websites) puts a zero byte in front of every step and a one byte in front of every pair, and why Bitcoin, which copied the last hash of an odd row to pair it with itself, let two different lists of transactions share one top mark in 2012. What the card proves stops at in: it will not say the step was right, that nothing was left out, what order things happened in, that anything is secret or that it is current, so a worker who drops the one catastrophic step builds a perfectly valid tree over the rest, and every step that remains still passes. The honest limit is where the cost lands, because the tree is cheap for the ledger only by making somebody else keep every step, so a root with nobody holding the steps is a number nobody can argue with, and an auditor who says it could not replay a step on its own machine has said something no root has a slot for, and a flat list, which is what Gensyn publishes for open-1b (a small language model trained across machines nobody owns together, with a hash published for each of its eighty thousand nine hundred and fifty-seven steps), stays the better choice for exactly as long as nothing has to be settled on a chain. The voices in this show are AI-generated; the research and writing are human. Decentralized AI, layer by layer.