a second derivation that shares nothing

When one route establishes something, the obvious next question is whether to believe it. The answer here was to establish it again from a direction that shares no machinery with the first: a separate derivation, run separately, recorded as independent. The value is not the agreement. The value is the non-overlap.

Two arguments built from the same primitives fail together. They inherit the same blind spot, misread the same convention, and agree for the same wrong reason. A second derivation running on different machinery can only agree by arriving somewhere the first could not have reached the same way. That is a much stronger signal than a re-check, and it is a different kind of work: not reading someone else's steps, but solving the problem again.

This is expensive in a way that is hard to defend mid-run. You are paying full price for an answer you already have, and the second derivation is usually slower, because the first one had the advantage of taking the most natural route. Halfway through it looks like duplicated effort, and it is exactly the line item a cost-conscious operation cuts first.

What it proves is that agreement was treated as evidence to be produced rather than assumed. The operation spent capacity to make its own conclusions independently survivable, which is the difference between a result that is believed and a result that is merely held.