The SP Flood cap supplies a direct connection between the Regular and Cumulative families. Begin with SP's ordered begetting ages and its fixed Noah–Flood relation. These determine each ancestor's birth and the inclusive capacity from that birth to the Flood. Taking the smaller of this capacity and a supplied baseline lifespan regenerates the whole nine-row SP lifespan field: six rows retain their baseline values, while Jared, Methuselah, and Lamech meet the shared Flood boundary. One event constraint thus explains three local changes within a complete family.
Those local changes pass into the Cumulative family by ordinary suffix addition. Their reductions of 115, 249, and 124 produce the entire pre-Flood displacement field, whose head difference is 488. Eber and official Terah contribute a separate 120, giving the already established total difference of 608. The advance is the connection between representations: the cumulative pattern follows from a rule acting on Regular birth distances, rather than standing as another collection of matching endpoints.
The same equations show what this explanation requires. With the Noah–Flood relation held, the three capped lives recover Lamech's 52 completed begetting units, Methuselah's 67, and the combined Jared–Enoch interval of 127. Enoch's independently supplied 65 then fixes Jared's 62. The cap does not recover the earlier begetting ages or the excess removed from the three ancestral lifespans. Both the MT and main LXX baseline lifespans reach the same SP result, so this reconstruction explains structural compatibility without establishing historical MT-to-SP dependence.
The cap also clarifies how operations fit together. A paired change of chronological frame preserves the capacities; nearest-five rounding commutes with the minimum when applied to resolved count values. Rounding date labels before forming those counts is a different operation. Unlike a reversible frame translation, clipping loses information. The shared account of the chronological families therefore needs ordered source rows, counting conventions, and the specific operation being applied—not merely a common endpoint. Here that small set of premises connects Regular, lifespan, Cumulative, and Rounded fields while preserving their distinct meanings.