The common Key landing is one agreement condition
The two routes to the transformed 1566 point use different Keys on different source paths. Let u be the Covenant-to-Levi-death span and w the Covenant-to-Joseph-death span. The regular source packet generates u=299 and w=276. Holding the Covenant coordinate Q, the two points are Q−(300/299)u and Q−(25/23)w.
They agree precisely when 13w=12u. For the supplied paths, both transformed spans are 300 and both points are 1566. The larger gain on Joseph’s route absorbs the original 23-year separation between the deaths. The agreement does not make the two Keys interchangeable, and 1566 remains a transformed comparison rather than a newly appointed historical death.
Introducing a common-point variable clarifies the dependency. One equation defines the point from the first route; the second tests whether the other route reaches it. Eliminating the generated point leaves one condition on the source paths.
That condition adds information beyond the preceding Covenant rails in the declared variable model. Its evidentiary contribution is therefore one source-path agreement, with the two displayed landings and their shared 300 measurement as dependent consequences.