## The Regular kernel has two generators

The first generator is the **located sequence of row changes**. In the matched Cainan-OFF comparison, the complete MT/LXX Regular difference from Adam through Abraham is

\[
1250,\ 1150,\ 1050,\ 950,\ 850,\ 750,\ 750,\ 650,\ 650,\ 650,\ 650,\ 650,\ 550,\ 450,\ 350,\ 250,\ 150,\ 50,\ 0,\ 0.
\]

The steps record source changes at particular names. Six pre-Flood century changes account for the 600 difference between the Creation level 1250 and Noah level 650. Native Cainan adds 130 from Arphaxad upstream, retaining the native 1380/780 levels separately.

The second generator is the **finite field of source variants**. Let the Terah difference be \(T=60\), Cainan’s Regular interval \(C=130\), and the separately sourced Sojourn choice \(S=215\). Their eight combinations give:

| Choice | Offset |
|---|---:|
| Base | 0 |
| T | 60 |
| C | 130 |
| T+C | 190 |
| S | 215 |
| T+S | 275 |
| C+S | 345 |
| T+C+S | 405 |

The consecutive gaps are \(60|70|60|25|60|70|60\). The 70 and 25 are differences between combinations; they are not additional switches.

These structures meet in the Strategy’s fivefold formulas:

\[
1250=5(C+2T),\qquad650=5C.
\]

The row mechanism gives \(12.5u\) and \(6.5u\), where the observed century is \(u=100\). Requiring the fivefold form yields \(C=1.3u\) and \(T=.6u\). Thus the coefficient five expresses a calibration between two source mechanisms. It does not itself generate the patriarchal ages.

SP supplies a further located comparison. Its post-Flood birth additions total 650; its pre-Flood shortening is \(100+120+130=350\) in the completed-year comparison, leaving 300. The Lamech contribution retains its nominal 129 plus the one-year boundary completion, counted once. These locations explain more than the identity \(950\pm300=1250,650\): the latter is a useful description of the resulting pair, while the row model explains its construction.

Source basis: File07 finite states; File18 source rows; C1253–C1264.