a derivation you can re-run

Several points in this history are marked by a small object landing in the record: something computed from a handful of instances, together with the rule that produced it. Before that, the corresponding argument existed as reasoning in someone's head. After it, a later reader could rebuild the object and see the pattern rather than take the argument on trust.

The shift matters because prose arguments and checkable ones fail differently. A prose argument has to be inspected, and inspection is a social act, so the reviewer's willingness to say "I do not follow" is the entire safety margin. A computed object can be rebuilt from a stated rule, which turns disagreement into a disagreement about inputs rather than about understanding, and that is a far cheaper disagreement to settle.

The cost is that the object only covers what it covers. Something computed over a few instances is not an argument, and building it takes longer than making the case informally. It also has to be specified well enough for somebody else to reproduce, which pushes extra work onto the person who understands the problem best.

What it proves is that checkability was a property of the output rather than a phase at the end. The operation paid the additional cost of turning a private argument into a public, re-runnable one, which is what makes a fast-moving operation auditable at all.