## Local changes become complete chronological fields

Write an ordinary row as begetting age \(b\), remaining years \(r\), and lifespan \(L=b+r\). A compatible change has the form

\[
(b,r,L)\longmapsto(b+d,\ r+e-d,\ L+e).
\]

Here \(d\) changes the birth interval and \(e\) changes lifespan. If \(e=0\), years move between the two parts of a life while its total stays fixed. If \(e=d\), remaining years stay fixed while both the begetting age and lifespan rise. These are different local mechanisms even when the same century appears.

| Row and comparison | Begetting age | Remaining years | Lifespan | What the change preserves |
|---|---:|---:|---:|---|
| Adam, MT → LXX | 130 → 230 | 800 → 700 | 930 → 930 | Lifespan |
| Peleg, MT → LXX | 30 → 130 | 209 → 209 | 239 → 339 | Remaining years |
| Eber, MT → SP | 34 → 134 | 430 → 270 | 464 → 404 | Neither part nor lifespan; \(d=100,e=-60\) |
| Cainan, native LXX insertion | 130 | 330 | 460 | Adds a named row with two distinct measures |

Thus Regular and Cumulative differences are not rival readings of a single change total. They select different components of the source rows. Adam’s change is visible to a Regular birth chain and invisible to a lifespan sum. Peleg’s change is visible to both. Cainan contributes 130 or 460 according to the declared measurement.

Source basis: File18 selected rows; Strategy §3.2; C1162–C1189.