claims held to the range that was checked

Most of the statements this operation could make were true on the cases it had looked at. That is not a claim, it is a coincidence waiting to be reported as a result. The discipline that kept the difference visible was a convention about scope: every statement in the record carried the range it had been checked over, and nothing was asserted outside that range.

This is harder to sustain than it sounds. A pattern holds across a bounded initial stretch and the temptation is to write it down as a law. The record shows both halves of the resistance. When a claim was established over a limited range, the range went into the statement itself. When a search fanned out into a far band and confirmed only a small fraction of the cases there, the fraction came in as coverage, not as success.

The cost is that you end up with a stack of statements that are individually modest and collectively hard to present. Nobody is excited by a result with a fence around it. The fence is also what lets the stack survive a case outside it, because a fence makes the surprise a discovery rather than a contradiction.

What it proves is an operation that can hold its own inductive urge in check. It measured the edge of what it knew, wrote the edge down, and refused to let a boundary case be smuggled into a general claim. That restraint is the difference between a body of work that can be extended and one that has to be audited.