What the capped lives determine about the ages
The Flood-cap relation can also be read backward, but only with its retained premises in view. Fix the Noah–Flood relation at 600 completed units, so that the inclusive contribution is 601. Lamech's capped life of 653 then leaves 52 completed units from his birth to Noah's. Methuselah's 720 exceeds Lamech's capacity by 67, recovering his begetting interval. Jared's 847 exceeds Methuselah's capacity by 127, recovering the combined Jared–Enoch interval.
These three equations determine three quantities. They do not separate Jared from Enoch. When Enoch's independently supplied 65 is held, Jared's interval is fixed at 62. Without that input, adding one unit to Jared's begetting age and subtracting one from Enoch's changes Enoch's birth while preserving all nine capped lifespan outputs. The earlier five begetting ages are likewise not determined by these three active capacities.
The distinction matters for the wider unification. A complete ordered boundary field can recover its local intervals by adjacent differences; selected capped outputs retain less information. The source's exact lifespan values fix the inclusive contribution at 601, whereas merely naming the same three clipped rows permits a wider range. Forward and backward readings therefore express one conditional relation, rather than two separate reasons to accept its premises.
Sources: File18 §3.1, §3.1.3; Research Strategy §5, Stages D and F, §6.