### Why the cap cannot identify the ancestral ledger

A cap preserves a value when it lies below the available capacity and removes any excess above that capacity. Its output therefore carries different information in the two cases. An uncapped lifespan identifies its input exactly. A lifespan equal to the capacity only tells us that the input was at least that large. The amount removed cannot be recovered from the capped result alone.

This distinction is visible across the full SP family. Both the MT baseline, with Lamech's 777, and the main LXX baseline, with his 753, produce the same nine SP lives under the fixed SP capacities. Their total reductions differ by 24, but the output no longer records that difference. Even supplying the three changed MT lifespans as an unordered set leaves four assignments to Jared, Methuselah, and Lamech that produce the same clipped values. The source's person-by-person placement remains necessary.

The cap consequently belongs to a different class of operation from a reversible frame translation. Applying the same cap twice changes nothing after the first application, and multiple inputs can share one output. This explains a route to compatibility between traditions while also limiting the historical claim: agreement of the capped fields does not identify which ancestral ledger came first.

*Sources:* File18 §2.1.3, §3.1.3, §4.1; Research Strategy §1, §5, Stages D, E and G.

*Research record:* C905–C906, C968–C970, C982.